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ISA HANDBOOK OF
Measurement Equations and Tables, 2nd Edition Edited by ...
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front of book.qxd
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ISA HANDBOOK OF
Measurement Equations and Tables, 2nd Edition Edited by Jim Strothman
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Notice The information presented in this publication is for the general education of the reader. Because neither the author nor the publisher have any control over the use of the information by the reader, both the author and the publisher disclaim any and all liability of any kind arising out of such use. The reader is expected to exercise sound professional judgment in using any of the information presented in a particular application. Additionally, neither the author nor the publisher have investigated or considered the affect of any patents on the ability of the reader to use any of the information in a particular application. The reader is responsible for reviewing any possible patents that may affect any particular use of the information presented. Any references to commercial products in the work are cited as examples only. Neither the author nor the publisher endorses any referenced commercial product. Any trademarks or trade names referenced belong to the respective owner of the mark or name. Neither the author nor the publisher makes any representation regarding the availability of any referenced commercial product at any time. The manufacturer’s instructions on use of any commercial product must be followed at all times, even if in conflict with the information in this publication. Copyright © 2006 ISA – The Instrumentation, Systems, and Automation Society All rights reserved. Printed in the United States of America. 10 9 8 7 6 5 4 3 2 ISBN-13: 978-1-55617-946-4 ISBN-10: 1-55617-946-4 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher. ISA 67 Alexander Drive P.O. Box 12277 Research Triangle Park, NC 27709
Library of Congress Cataloging-in-Publication Data ISA handbook of measurement equations and tables / edited by Jim Strothman.-- 2nd ed. p. cm. ISBN 1-55617-946-4 (pbk.) 1. Physical measurements--Handbooks, manuals, etc. I. Strothman, Jim. QC39.C8 2006 530.8'10212--dc22 2006005270
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Purpose
Simply stated, this 2nd edition of the ISA Handbook of Measurement Equations and Tables was produced by ISA to enable engineers and technicians designing and controlling industrial processes to find answers needed to solve day-to-day problems. It is also intended to be a useful reference tool for engineering students. The hundreds of equations, conversion values and tables this handbook contains will hopefully speed technical problem-solving so you can do your job better, and faster.
vii
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• Humidity Measurement • Electrical Measurement • Viscosity Measurement In keeping with our “knowledge consists of knowing where to find it” doctrine, I would particularly like to thank Dr. Allan H. Harvey of the National Institute of Standards and Technology’s Physical and Chemical Properties Division for producing customized Steam Tables for Chapter 3, Pressure Measurement. Thanks go to David A. Glanzer and the Fieldbus Foundation for providing the foundation’s “Standard Unit Codes Table” seen in Chapter 7, Industrial Communications Buses, and to InTech magazine editors Greg Hale and Nick Sheble for the Industrial Networking Technologies comparison table in the same chapter. Thanks also to Ametek Drexelbrook for important content seen in Chapter 6, Level Measurement. For Chapter 8, Safety, FM Approvals, an FM Global Technologies LLC enterprise, contributed to the sections covering hazardous classes and zones. In the same chapter, thanks go to ISA safety standards veteran Vic Maggioli for advising us what to include regarding Safety Instrumentation Functions (SIF)/Safety Integrity Level (SIL) verification. Several of ISA’s distinguished ISA Fellows and other ISA volunteer leaders contributed advice, counsel, and some content. The editor would particularly like to thank Cullen Langford, Nicholas P. Sands, Vernon Trevathan, Dick Caro, Michael Ruel, Bruce Land, Robert Zielske, David Spitzer, David Braudaway, Fred Meier, and Warren Weidman. Several ISA and ANSI/ISA standards served as information sources, and the editor thanks Lois Ferson, ISA Manager – Standards and Technical Publications, and Linda Wolffe, ISA’s librarian, for helping identify them. Last, but not least, considerable credit is due to the late editor of this handbook’s 1994 first edition, William H. “Bill” Cubberly, whose work was used as the starting point.
—Jim Strothman, Editor
x
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Table of Contents
Purpose
............................................................................................................................
Preface & Acknowledgments Units of Measurement
1
..............................................................................................
29
......................................................................................................
55
Temperature Measurement Level Measurement
...................................................................................
119
..................................................................................................
161
Industrial Communications Buses Safety
ix
..................................................................................................
Pressure Measurement Flow Measurement
.................................................................................
vii
.....................................................................
181
...............................................................................................................................
211
Environmental Measurement
..............................................................................
239
Humidity Measurement
..........................................................................................
251
Electrical Measurement
..........................................................................................
259
...........................................................................................
299
.................................................................................................................................
311
Viscosity Measurement Index
v
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Preface & Acknowledgments While updating and expanding this 2nd edition of the ISA Handbook of Measurement Equations and Tables, I zealously followed a single, eightword doctrine that has guided me during more than 35 years writing and editing high-tech publications. That doctrine is: “Knowledge consists of knowing where to find it.” Realizing no human brain can store all knowledge – especially from multiple technical disciplines required to control a wide range of industrial manufacturing processes – that credo served me well when I was editor of ISA’s InTech magazine during the 1990s. Numerous equations and tables from the first edition – edited by William H. Cubberly and published by ISA in 1994 – were determined to still be useful today and, therefore, remain in this 2nd edition. However, chapters in the 1994 handbook have been significantly updated and three brand new chapter topics have been added: Industrial Communications Buses, Safety, and Environmental Measurement. Also, thanks to graphics and layout editor Vanessa French, this edition is much easier to read – no magnifying glass is needed to read superscripts and subscripts, for example. This ISA Handbook of Measurement Equations and Tables, 2nd Edition, has eleven primary sections: • Units of Measurement (including conversion tables frequently used for several other sections, below) • Pressure Measurement • Flow Measurement • Temperature Measurement • Level Measurement • Industrial Communications Buses • Safety • Environmental Measurement ix
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• Humidity Measurement • Electrical Measurement • Viscosity Measurement In keeping with our “knowledge consists of knowing where to find it” doctrine, I would particularly like to thank Dr. Allan H. Harvey of the National Institute of Standards and Technology’s Physical and Chemical Properties Division for producing customized Steam Tables for Chapter 3, Pressure Measurement. Thanks go to David A. Glanzer and the Fieldbus Foundation for providing the foundation’s “Standard Unit Codes Table” seen in Chapter 7, Industrial Communications Buses, and to InTech magazine editors Greg Hale and Nick Sheble for the Industrial Networking Technologies comparison table in the same chapter. Thanks also to Ametek Drexelbrook for important content seen in Chapter 6, Level Measurement. For Chapter 8, Safety, FM Approvals, an FM Global Technologies LLC enterprise, contributed to the sections covering hazardous classes and zones. In the same chapter, thanks go to ISA safety standards veteran Vic Maggioli for advising us what to include regarding Safety Instrumentation Functions (SIF)/Safety Integrity Level (SIL) verification. Several of ISA’s distinguished ISA Fellows and other ISA volunteer leaders contributed advice, counsel, and some content. The editor would particularly like to thank Cullen Langford, Nicholas P. Sands, Vernon Trevathan, Dick Caro, Michael Ruel, Bruce Land, Robert Zielske, David Spitzer, David Braudaway, Fred Meier, and Warren Weidman. Several ISA and ANSI/ISA standards served as information sources, and the editor thanks Lois Ferson, ISA Manager – Standards and Technical Publications, and Linda Wolffe, ISA’s librarian, for helping identify them. Last, but not least, considerable credit is due to the late editor of this handbook’s 1994 first edition, William H. “Bill” Cubberly, whose work was used as the starting point.
—Jim Strothman, Editor
x
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1
UNITS OF MEASUREMENT The International System of Units, established in 1960 by the 11th General Conference on Weights and Measures (CGPM), is the modern metric system of measurement used throughout the world. It is universally abbreviated SI (from the French Le Système International d’Unités). The editor of this updated version of the ISA Handbook of Measurement Equations and Tables credits the National Institute of Standards and Technology (NIST) Special Publications 811, Guide for the Use of the International System of Units (SI), and Special Publications 330, The International System of Units, for several of the useful tables presented in this chapter. Greek Alphabet in Roman and Italic Type . . . . . . . . . . . . . . . . . . . . . . 3 Three Classes of SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 • SI Base Units & Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 • SI Derived Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 • SI Derived Units with Special Names and Symbols, Including the Radian and Steradian . . . . . . . . . . . . . . . . . . . . . . . 8 • SI Prefixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Units Accepted for Use with the SI . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 English to SI Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 English to Metric Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 English Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Fraction Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Fundamental Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Area/Geometry Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
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Chapter 1/Units of Measurement
3
Greek Alphabet in Roman and Italic Type Name
Capital Roman
Lower Case Roman
Capital Italic
Lower Case Italic
alpha
Α
α
Α
α
beta
Β
β
Β
β
gamma
Γ
γ
Γ
γ
delta
∆
δ
∆
δ
epsilon
E
ε,∈
E
ε,∈
zeta
Ζ
ζ
Ζ
ζ
eta
Η
η
Η
η
theta
Θ,θ
Θ,θ
Θ,θ
Θ,θ
iota
Ι
ι
I
ι
kappa
Κ
κ
Κ
κ
lambda
Λ
λ
Λ
λ
mu
Μ
µ
Μ
µ
nu
Ν
ν
Ν
ν
xi
Ξ
ξ
Ξ
ξ
omicron
Ο
ο
Ο
ο
pi
Π
π, ϖ
Π
π, ϖ
rho
Ρ
ρ
Ρ
ρ
sigma
Σ
σ
Σ
σ
tau
Τ
τ
Τ
τ
upsilon
ϒ
υ
ϒ
υ
phi
Φ
ϕ, φ
Φ
ϕ, φ
chi
Χ
χ
Χ
χ
psi
Ψ
ψ
Ψ
ψ
omega
Ω
ω
Ω
ω
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ISA Handbook of Measurement Equations and Tables
The Three Classes of SI Units and the SI Prefixes SI units are currently divided into three classes: • Base units • Derived units • Supplementary units Together, the three classes form what is called “the coherent system of SI units.”
SI base units The following table gives the seven base quantities, assumed to be mutually independent, on which the SI is founded, and the names and symbols of their respective units, called “SI base units.” Definitions of the SI base units follow. The kelvin and its symbol K are also used to express the value of a temperature interval or a temperature difference.
SI Base Units Base Quantity
Name
Symbol
length
meter
m
mass
kilogram
kg
time
second
s
electric current
ampere
A
thermodynamic temperature
kelvin
K
amount of substance
mole
mol
luminous intensity
candela
cd
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Chapter 1/Units of Measurement
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Definitions of SI Base Units Meter (17th CGPM, 1983) The meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second. Kilogram (3d CGPM, 1901) The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. Second (13th CGPM, 1967) The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. Ampere (9th CGPM, 1948) The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 Newton per meter of length. Kelvin (13th CGPM, 1967) The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. Mole (14th CGPM, 1971) 1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. In the definition of the mole, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to. Note that this definition specifies at the same time the nature of the quantity whose unit is the mole. Candela (16th CGPM, 1979) The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of (1/683) watt per steradian.
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ISA Handbook of Measurement Equations and Tables
SI Derived Units Derived units are expressed algebraically in terms of base units or other derived units, including the radian and steradian, which are two supplementary units. The radian is defined as the plane angle between two radii of a circle that cut off on the circumference an arc equal in length to the radius. The steradian is fined as the solid angle that, having its vertex in the center of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere. SI Derived Units Quantity
SI Unit
SI Symbol
Frequency
Hertz
Hz
Force
Newton
N
Pressure, Stress
Pascal
Pa
Energy, Work, Heat
Joule
J
Power, Radiant Flux
Watt
W
Electric Charge
Coulomb
C
Electric Potential, Force
Volt
V
Electric Resistance
Ohm
Ω
Electric Conductance
Siemens
S
Electric Capacitance
Farad
F
Magnetic Flux Density
Tesla
T
Magnetic Flux
Weber
Wb
Inductance
Henry
H
Temperature
°Celsius
°C
Luminous Flux
Lumen
lm
Illuminance
Lux
lx
Radioactive Activity
Becquerel
Bq
Absorbed Dose
Gray
Gy
Dose Equivalent
Sievert
Sv
Plane Angle
Radian
rad
Solid Angle
Steradian
sr
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Chapter 1/Units of Measurement
7
The symbols for derived units are obtained by means of the mathematical operations of multiplication and division. For example, the derived unit for the derived quantity molar mass (mass divided by amount of substance) is the kilogram per mole, symbol kg/mol. Additional examples of derived units expressed in terms of SI base units are given in the following table. Examples of SI Derived Units Expressed in Terms of SI Base Units Derived Quantity
Name
Symbol
area
square meter
m2
volume
cubic meter
m3
speed, velocity
meter per second
m/s
acceleration
meter per second squared
m/s2
wave number
reciprocal meter
m-1
mass density (density)
kilogram per cubic meter
kg/m3
specific volume
cubic meter per kilogram
m3/kg
current density
ampere per square meter
A/m2
magnetic field strength
ampere per meter
A/m
amount-of-substance concentration (concentration)
mole per cubic meter
mol/m3
luminance
candela per square meter
cd/m2
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ISA Handbook of Measurement Equations and Tables
SI Derived Units with Special Names and Symbols, Including the Radian and Steradian Derived quantity
Special Name
Special Expression Symbol in Terms of Other SI Units
Expression in Terms of SI Base Units
plane angle
radian
rad
-
m · m-1 = 1
solid angle
steradian
sr
-
m2 · m-2 = 1
frequency
hertz
Hz
-
s-1
force
newton
N
-
m · kg · s-2
pressure, stress
pascal
Pa
N/m2
m-1 · kg · s-2
energy, work, quantity of heat
joule
J
N·m
m2 · kg · s-2
power, radiant flux
watt
W
J/s
m2 · kg · s-3
coulomb
C
-
s·A
volt
V
W/A
m2 · kg · s-3 · A-1
capacitance
farad
F
C/V
m-2 · kg-1 · s4 · A2
electric resistance
ohm
Ω
V/A
m2 · kg · s-3 · A-2
siemens
S
A/V
m-2 · kg-1 · s3 · A2
magnetic flux
weber
Wb
V·s
m2 · kg · s-2 · A-1
magnetic flux density
tesla
T
Wb/m2
kg · s-2 · A-1
inductance
henry
H
Wb/A
m2 · kg · s-2 · A-2
Celsius temperature
degree Celsius
°C
-
K
luminous flux
lumen
lm
cd · sr
cd · sr
lux
lx
lm/m2
m-2 · cd · sr
electric charge, quantity of electricity electric potential, potential difference, electromotive force
electric conductance
illuminance
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Chapter 1/Units of Measurement
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SI Prefixes Factor
Prefix
Symbol
Factor
Prefix
Symbol
1024 = (103)8
yotta
Y
10-1
deci
d
1021 = (103)7
zetta
Z
10-2
centi
c
1018 = (103)6
exa
E
10-3 = (103)-1
milli
m
1015 = (103)5
peta
P
10-6 = (103)-2
micro
µ
1012 = (103)4
tera
T
10-9 = (103)-3
nano
n
109 = (103)3
giga
G
10-12 = (103)-4
pico
p
106 = (103)2
mega
M
10-15 = (103)-5
femto
f
103 = (103)1
kilo
k
10-18 = (103)-6
atto
a
102
hecto
h
10-21 = (103)-7
zepto
z
101
deka
da
10-24 = (103)-8
yocto
y
Units Accepted for Use with the SI Certain units that are not part of the SI are essential and used so widely that they are accepted by the CGPM for use with the SI. These units are given in the table below. Units Accepted for use with the SI Name minute (time)
Symbol min
Value in SI units 1 min = 60 s
hour (time)
h
1 h = 60 min = 3600 s
day (time)
d
1 d = 24 h = 86,400 s
degree (plane angle)
°
1° = (π/180) rad
minute (plane angle)
'
1'= (1/60)° = (π/10,800) rad
second (plane angle)
"
1" = (1/60)' = (π/648,000) rad
liter metric ton
l, L t
1 L = 1 dm3 = 10-3 m3 1 t = 103 kg
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ISA Handbook of Measurement Equations and Tables
Conversion Tables, English to SI Units English Units Quantity
SI Equivalent
Absorbed Dose Rate
Gray per Second
Acceleration
Meter per Second Squared
Angular Acceleration
Radian per Second Squared
Angular Velocity
Radian per Second
Area
Square Meter
Concentration
Mole per Cubic Meter
Current Density
Ampere per Square Meter
Density, Mass
Kilogram per Cubic Meter
Electric Charge Density
Coulomb per Cubic Meter
Electric Field Strength
Volt per Meter
Electric Flux Density
Coulomb per Square Meter
Energy Density
Joule per Cubic Meter
Entropy
Joule per Kelvin
Exposure, Radiation
Coulomb per Kilogram
Heat Capacity
Joule per Kelvin
Heat Flux Density, Irradiance
Watt per Square Meter
Luminance
Candela per Square Meter
Magnetic Field Strength
Ampere per Meter
Magnetic Permeability
Henry per Mole
Molar Energy
Joule per Mole
Molar Entropy
Joule per Mole Kelvin
Molar Heat Capacity
Joule per Mole Kelvin
Moment of Force
Newton Meter
Permittivity
Farad per Meter
Power Density
Watt per Square Meter
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Chapter 1/Units of Measurement
Conversion Tables, English to SI Units (cont.) English Units Quantity
SI Equivalent
Radiance
Watt per Square Meter Steradian
Radiant Intensity
Watt per Steradian
Specific Heat Capacity
Joule per Kilogram Kelvin
Specific Energy
Joule per Kilogram
Specific Entropy
Joule per Kilogram Kelvin
Specific Volume
Cubic Meter per Kilogram
Surface Tension
Newton per Meter
Thermal Conductivity
Watt per Meter Kelvin
Velocity
Meter per Second
Viscosity, Dynamic
Pascal Second
Viscosity, Kinematic
Square Meter Second
Volume
Cubic Meter
Wave Number
One per Meter
11
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ISA Handbook of Measurement Equations and Tables
Conversion Table, English to Metric To Convert From
To
Multiply by:
angstrom
m
1.00 x 10-10
atm
Pa
1.0133 x 105
J
1.054 x 103
W/m2
3.1525
W/m2 K
5.6745
Btu/ft2 s, Thermochemical
W/m2
1.135 x 104
Btu in/ft2 °F, Thermochem.
W/m K
0.14413
Btu in/s ft2 °F, Thermochem.
W/m K
518.87
Btu/lb mass °F, Thermochemical
J/kg K
4184.0
J
4.0840
W/m K
418.40
J/kg
4184.0
J/kg K
4184.0
m2
5.0671 x 10-10
K
°C + 273.15
degree
rad
0.017453
dyne/cm2
Pa
0.100
°F
°C
°F - 32/1.8
°F
K
°F + 459.67/1.8
ft
m
0.30480
Btu, Thermochemical Btu/ft2h, Thermochemical Btu/ft2h °F, Thermochemical
cal, Thermochemical cal cm s °C, Thermochemical cal/g, Thermochemical cal/g °C, Thermochemical circ mil °C
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Chapter 1/Units of Measurement
Conversion Table, English to Metric (cont.) To Convert From
To
Multiply by:
ft2
m2
0.092903
ft3
m3
0.028317
ft H2O, at 32.4 °F
Pa
0.0029890
m2/s
2.58064 x 10-5
ft lb force
J
1.3558
ft lb force/s
W
1.3558
m/s
0.30480
T
0.00010
m3
0.0037854
g/cm3
kg/m3
1000.0
g/cm3
Mg/m3
1.00
hp, mechanical
W
745.70
hp, electrical
W
746.00
in
m
0.0254
in2
m2
0.00064516
in2
m3
0.000016387
in of Hg, avoirdupois
Pa
0.0033864
in of H2O at 32.2 °F
Pa
0.024908
K
°C
K - 273.15
kg force
N
9.80665
kg force/mm2
Pa
9.80665 x 106
ft2, hr
ft/s gauss gallon, U.S.
13
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ISA Handbook of Measurement Equations and Tables
Conversion Table, English to Metric (cont.) To Convert From
To
Multiply by:
ksi
MPa
6.8948
ksi
Pa
6.8948 x 106
lb
kg
0.45359
kg/m3
27,680.0
N
4.4482
lb force in
Nm
0.11298
lb force ft
Nm
1.3558
mil
m
0.0000254
N/m2
Pa
1.00
A/m
79.578
kg/m2
0.30515
psi
Pa
6894.8
°R
K
°R/1.8
ton, 2000 lb
kg
907.18
ton, 2240 lb
kg
1016.0
ton/in2
Pa
13,786.0
tonne
kg
1000.0
torr
Pa
133.32
Ohm m
1.6624 x 10-9
lb/in3 lb force
oersted oz/ft2
Ohm/circ mil ft
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Chapter 1/Units of Measurement
Conversion Table, English Units To Convert From
To
Multiply by:
gram
grain
15,432
pennyweight
grain
24
pennyweight
ounce
20
ounce
grain
480
pound
ounce
16
pint, liquid
gill
4
pint, liquid
quart
2
pint, dry
quart
2
quart, liquid
gallon
4
peck
8
barrel, liquid
gallon
31.5
barrel, dry
quart
105
hogshead
barrel
2
foot
inch
12
yard
foot
3
rod
yard
5.5
furlong
yard
40
mile
furlong
8
mile
foot
5280
league
mile
3
square foot
144
quart, dry
square inch
15
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ISA Handbook of Measurement Equations and Tables
Conversion Table, English Units (cont.) To Convert From
To
Multiply by:
square yard
square foot
9
square rod
square yard
30.25
acre
square rod
4840
acre
640
cubic foot
cubic inch
1728
cubic yard
cubic foot
27
board foot
cubic inch
144
cord
cubic foot
128
foot
6
cable length
fathom
100
cable length (Navy)
fathom
120
nautical mile
cable length
10
nautical mile
foot
6076.1033
nautical mile
mile
1.1508
nautical mile
60
minute, circular
seconds
60
degree
minutes
60
quadrant
degree
90
quadrants
4
square mile
fathom
degree, terrestrial
circle, circumference
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Chapter 1/Units of Measurement
Conversion Table, Fractions Fraction
inches
mm
1/64
0.015625
0.39687
1/32
0.03125
0.79374
3/64
0.046875
1.19061
1/16
0.0625
1.58748
5/64
0.078125
1.98435
3/32
0.09375
2.38123
7/64
0.109375
2.77809
1/8
0.125
3.17497
9/64
0.140625
3.57183
5/32
0.15625
3.96871
11/64
0.171875
4.36557
3/16
0.1875
4.76245
13/64
0.203125
5.15931
7/32
0.21875
5.55620
15/64
0.234375
5.93505
0.25
6.34994
17/64
0.265625
6.74679
9/32
0.28125
7.14368
19/64
0.296875
7.54053
5/16
0.3125
7.98743
21/64
0.328125
8.33427
11/32
0.34375
8.73117
23/64
0.359375
9.12801
0.375
9.52491
0.390625
9.92175
1/4
3/8 25/64
17
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ISA Handbook of Measurement Equations and Tables
Conversion Table, Fractions (cont.) Fraction
inches
mm
13/32
0.40625
10.31865
27/64
0.421875
10.71549
7/16
0.4375
11.11240
29/64
0.453125
11.50923
15/32
0.46875
11.90614
31/64
0.484375
12.30297
0.50
12.69988
33/64
0.515625
13.09671
17/32
0.53125
13.49362
35/64
0.546875
13.89045
9/16
0.5625
14.28737
37/64
0.578125
14.68419
19/32
0.59375
15.08111
39/64
0.609375
15.47793
0.625
15.87485
41/64
0.640625
16.27167
21/32
0.65625
16.66859
43/64
0.671875
17.06541
11/16
0.6875
17.46234
45/64
0.703125
17.85915
23/32
0.71875
18.25608
47/64
0.734375
18.65289
0.75
19.04982
1/2
5/8
3/4
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Chapter 1/Units of Measurement
Conversion Table, Fractions (cont.) Fraction
inches
mm
49/64
0.765625
19.44663
25/32
0.78125
19.84356
51/64
0.796875
20.24037
13/16
0.8125
20.63731
63/64
0.828125
21.03411
27/32
0.84375
21.43015
55/64
0.859375
21.82785
0.875
22.22479
57/64
0.890625
22.62159
29/32
0.90625
23.01853
59/64
0.921875
23.41533
15/16
0.9375
23.81228
61/64
0.953125
24.20907
31/32
0.96875
24.60602
63/64
0.984375
25.00281
7/8
1
1.0
25.40
19
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ISA Handbook of Measurement Equations and Tables
Fundamental Physical Constants Fundamental Quantity
Value
Units
Speed of Light, Vacuum
299,792,458.0
m s-1
Permeability of Vacuum
12.566370614
10-7 N A-2
Permittivity of Vacuum
8.854187817
10-12 F m-1
6.67259
10-11m3kg-1s-2
Planck Constant
6.6260755
10-34 J s
Elementary Charge
1.60217733
10-19 C
Magnetic Flux, h/2e
2.06783461
10-15 Wb
Electron Mass
9.1093897
10-31 kg
Proton Mass
1.6726231
10-27 kg
Newtonian Constant of Gravity
Proton-Electron Mass Ratio
1836.152701
Fine-Structure Constant
7.29735308
10-3
10,973,731.534
m-1
Avogadro Constant
6.0221367
1023 mol-1
Faraday Constant
96 485.309
C mol-1
Molar Gas Constant
8.31451
J mol-1 K-1
Boltzmann Constant
1.380658
10-23 J K-1
Stefan-Boltzmann Constant
5.67051
10-8 W m-2 K-4
Electron Volt
1.60217733
10-19 J
Atomic Mass Unit
1.6605402
10-27 kg
Planck Mass
2.17671
10-8 kg
Planck Length
1.61605
10-35 m
Planck Time
5.39056
10-44 s
Rydberg Constant
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Chapter 1/Units of Measurement
21
Fundamental Physical Constants (cont.) Fundamental Quantity
Value
Units
Josephson Frequency Voltage Ratio
4.8359767
1014 Hz V-1
Hall Conductance
3.87404614
10-5 S
Hall Resistance
25 812.8056
Ohm
Electron Specific Charge
-1.75881962
1011 C kg-1
Electron Molar Mass
5.48579903
10-7 kg/mol
Compton Wavelength, h/m-1c
2.42631058
10-12 m
Electron Magnetic Moment
928.47701
10-26 J T-1
Proton Specific Charge
9.5788309
107 C kg-1
Proton Molar Mass
1.00727647
10-3 kg/mol
Neutron Molar Mass
1.008664904
10-3 kg/mol
3.343586
10-27 kg
Deutron Molar Mass
2.013553214
10-3 kg/mol
Molar Planck Constant
3.99031323
10-10 J s mol-1
Deutron Mass
Absolute Entropy Constant
-1.151693
First Radiation Constant
3.7417749
10-16 W m2
Second Radiation Constant
0.01438769
mK
Wien Displacement Law Constant
2.897756
10-3 m K
Bohr Magneton
9.2740154
10-24 J T-1
Bohr Magneton, Electron Volts
5.78838263
10-5 eV T-1
Bohr Magneton, Hertz
1.39962418
1010 Hz T-1
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ISA Handbook of Measurement Equations and Tables
Geometry Measurements
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Chapter 1/Units of Measurement
23
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ISA Handbook of Measurement Equations and Tables
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Chapter 1/Units of Measurement
25
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ISA Handbook of Measurement Equations and Tables
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Chapter 1/Units of Measurement
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2 Pressure Measurement
Principles of Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Units of Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Fundamental Constants and Conversion Factors . . . . . . . . . . . . . 32 Examples of Absolute and Gauge Pressure. . . . . . . . . . . . . . . . . . 33 Some Pressure Units and Conversions . . . . . . . . . . . . . . . . . . . . . 34 Additional Pressure Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . 35 kg/mm2 to psi Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 ksi to MPa Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 MPa to ksi Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 ft-lb to Joule Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Joule to ft-lb Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Height Conversions for Liquid Manometers . . . . . . . . . . . . . . . . . 44 Mercury and Distilled Water Density at Various Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Measuring Differential Pressure with Transducers . . . . . . . . . . . . 46 Steam Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
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Chapter 2/Pressure
Principles of Pressure Pressure is the force per unit area a fluid or gas exerts on its surroundings. A container of gas contains numerous atoms and molecules constantly bouncing of its walls. The pressure they create is the average force those atoms and molecules produce on the walls. Therefore, pressure, P, is a function of force, F, and area, A. P = F/A The SI unit for pressure is the Pascal (N/m2). Other frequently used units of pressure include atmospheres (atm), pounds per square inch (psi), bars, inches of mercury (in Hg), and millimeters of mercury (mm Hg). Pressure measurements are typically described as either static or dynamic. Static pressure occurs where no motion is involved, such as air pressure inside a tire or balloon. When the motion of a fluid or gas changes the force applied to its surroundings, the pressure measurement is known as dynamic.
Head pressure (or pressure head) is the measurement of a static pressure in a tank or a pipe and is a function solely on the liquid's height and weight density.
31
Measurement Types and Sensors There are three types of pressure measurements: absolute, differential, and gauge. Absolute pressure is measured relative to a vacuum. Differential pressure measurements are taken with respect to a specific reference pressure, while gauge pressure is measured relative to ambient atmospheric pressure. Pressure sensors come in many different types of designs. When pressure is converted to an intermediate form such as displacement, three universal types of pressure transducers used are the strain gauge, variable capacitance, and piezoelectric. Each of those types of sensors convert the displacement into an electrical output such as voltage or current. Perhaps the most common of all pressure sensors are Wheatstone bridge (strain-based) sensors. They vary in accuracy, size, ruggedness, and cost. Bridge sensors are used for high and low pressure applications and can measure absolute, gauge, or differential pressure.
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ISA Handbook of Measurement Equations and Tables
Units of Pressure atm = Atmospheres
in H2O = inches of Water column in Hg = inches of Mercury column Pa = Pascals, also Newtons per square meter kPa = kiloPascals psi = pounds per square inch Torr = millimeters of Mercury column (often used to express low vacuum pressures)
Fundamental Constants Conversion Factors Metric 1 cm = 0.3937 inches 1 meter = 39.37 inches 1 meter = 3.280840 feet 1 cm2 = 0.1550003 in2 1 m2 = 10.76391 ft2 1 cm3 = 0.06102374 in3 1 m3 = 35.31467 ft3 1 kg = 2.204623 lb 1 gm = 0.03527397 oz
English / Metric Pressure Units
1 liter = 1000.028 cm3
Quantity
1 liter = 61.02545 in3
Force Pressure, Stress Energy, Work
English Units Poundal ksi, psi, psig Btu, ft-lb
Metric Units Newton Pascal Joule
1 cm3 = 0.9999720 liter 1 gm/cm3 = 62.4280 lb/ft3 1 gm/cm3 = 0.0361273 lb/in3 1 gm/ml = 0.9999730 gm/cm3 1 gm/cm3 = 1.000028 gm/ml English 1 inch = 2.54 cm 1 foot = 30.48 cm 1 in2 = 6.4516 cm2 1 ft2 = 929.0304 cm2 1 in3 = 16.387064 cm3 1 in3 = 0.01638661 liter 1 ft3 = 0.028316847 m3 1 lb = 453.59237 gm 1 oz = 28.349523 gm 1 lb/ft3 = 0.0160185 gm/cm3 1 lb/in3 = 27.6799 gm/cm3
and
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Chapter 2/Pressure
30 P1 = 28 psia P1 - P2 = 7.5 psig Differential Pressure
25
P1 - Patm = 13.4 psig Gauge Pressure 20
Absolute Pressure (psia)
15
P2 = 20.5 psia
P1 = 28 psia Absolute Pressure Atmospheric Pressure
Patm = 14.7 psia P3 - Patm = 6.1 psig Gauge Pressure
10
P3 = 8.5 psia (Barometric Pressure) 5
0
P3 = 8.5 psia Absolute Pressure Absolute Zero (Perfect Vacuum)
Examples of Absolute and Gauge Pressure
33
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ISA Handbook of Measurement Equations and Tables
Some Pressure Units and Conversions Pascal
bar
Newtons per square millimeter
kp/m2
kp/cm2 (=1 at)
1 Pa (N/m2)=
1
10-5
10-6
0.102
0.102× 10-4
1 bar (daN/cm2) =
105
1
0.1
10,200
1.02
0.987
750
1 N/ mm2 =
106
10
1
1.02× 105
10.2
9.87
7,501
1 kp/ m2 =
9.81
9.81× 10-5
9.81× 10-6
1
10-4
0.981
0.0981
10,000
1
0.968
736
1.013
0.1013
10,330
1.033
1
760
0.00133
1.33× 10-4
13.6
0.00132
0.00132
1
1 kp/ cm2 98,100 (1 atm) = 1 atm 101,325 (760 torr) = 1 torr (mmHg) =
133
atm
torr
0.987× 0.0075 10-5
0.968× 0.0736 10-4
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Chapter 2/Pressure
Additional Pressure Conversions
To Convert From Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Atmosphere Bar Bar Bar Bar Bar Bar Bar Bar Bar Bar Bar Bar cm of Mercury@0° cm of Mercury@0° cm of Mercury@0° cm of Mercury@0° cm of Mercury@0° cm of water@0° C cm of water@0° C cm of water@0° C cm of water@0° C cm of water@0° C cm3 Atmosphere ft3 Atmosphere ft3 Atmosphere Gram (Force)/cm
C C C C C
To Bar in. water ft. water in. Mercury Kilopascal mm water Millibar mm Mercury Micron Newton/cm2 Pascal Pound/Force ft2 psi Torr Atmosphere in. water ft. water in. Mercury Kilopascal mm water mm Mercury Newton/cm2 Pascal Pound/Force/ft2 psi Torr Atmosphere Millibar mm of water Pascal psi Atmosphere Millibar mm of Mercury Pascal psi Joule Foot-Pound (Force) Joule Joule
Multiply by: 1.01325 406.78@32° F 33.89854@32° F 22.92126@32° F 101.325 10.3326@4° F 1013.25 760.000@0° C 760000.000 10.1325 101325.000 2116.22 14.69595 760.000 0.9869233 401.46@32° F 33.4553@32° F 29.53@32° F 100.00 0.101972@0° C 750.062@0° C 10.00 100000.00 2088.54 14.50377 750.062 0.0131579 13.3322 135.951 1333.22 0.193368 0.000967841 0.980665 0.735559 98.0665 0.0142233 0.101325 2116.22 2869.28 0.0000980665
35
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ISA Handbook of Measurement Equations and Tables
Additional Pressure Conversions (cont.) Gray in. of Mercury@32° F in. of Mercury in. of Mercury in. of Mercury@32° F in. of Mercury in. of Mercury in. of water in. of water@32° F in. of water in. of water in. of water KG (Force)/cm2 KG (Force)/cm2 KG (Force)/cm2 KG (Force)/cm2 KG (Force)/cm2 KG (Force)/cm2 KG (Force)/cm2 KG (Force)/m2 KG (Force)/mm2 KG (Force)/mm2 Kilopascal liter-Atmosphere liter-Atmosphere liter-Bar MPa MPa Millibar mm of Mercury@0° C mm of Mercury@0° C mm of Mercury@0° C mm of Mercury@0° C mm of Mercury@0° C mm of Mercury@0° C mm of Mercury@0° C mm of water mm of water mm of water mm of water Newton/m2 Newton/mm2
Joule/Kilogram Atmosphere in. of water Millibar mm of water@32° F Pascal psi in. of Mercury Millibar mm of Mercury Pascal psi Atmosphere ft of water in. of Mercury meter of water mm of Mercury Pascal psi Pascal MPa psi psi ft3-Atmosphere Joule Joule Bar Newton/mm2 Pascal Atmosphere Dyne/cm2 Millibar mm of water Pascal psi Torr Millibar mm of Mercury Pascal psi Pascal MPa
1.000 0.0334211 13.5951 33.8639 345.316 3386.39 0.491154 0.0735559 2.49089 1.86832 249.089 0.0361273 0.96784 32.8084 28.9590 10.000 735.559 98066.5 14.22334 9.80665 9.80665 1422.334 0.1450377 0.0353147 101.325 100.000 10.000 1.000 100.000 0.001315789 1333.224 1.333224 13.5951 133.3224 0.0193368 1.000 0.0980665 0.0735559 9.80665 0.00142233 1.000 1.000
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Chapter 2/Pressure
Additional Pressure Conversions (cont.) Pound Pound Pound Pound Pound psi psi Torr Torr Torr
(Force)/in2 (Force)/in2 (Force)/in2 (Force)/in2 (Force) Second/in2
mm of water mm of Mercury Millibar Pascal Pascal-Second in H20 Pound (Force)/in2 Millibar mm of Mercury Pascal
0.00070307 51.7149 68.9476 6894.76 6894.76 27.679899 1.000 1.333224 1.000@0° C 133.3224
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ISA Handbook of Measurement Equations and Tables
Conversion Table, kg/mm2 to psi Kg/mm2 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
psi
Kg/mm2
14,223 15,646 17,068 18,490 19,913 21,335 22,757 24,180 25,602 27,024 28,447 29,869 31,291 32,714 34,136 35,558 36,981 38,403 39,826 41,248 42,670 44,093 45,515 46,937 48,360 49,782 51,204 52,627 54,049 55,471 56,894 58,316 59,738 61,161 62,538 64,005 65,424 66,580
48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85
psi 68,272 69,695 71,117 72,539 73,962 75,384 76,806 78,229 79,651 81,073 82,495 83,918 85,340 86,762 88,185 89,607 91,029 92,452 93,874 95,296 96,719 98,141 99,563 100,986 102,408 103,830 105,253 106,675 108,097 109,520 110,942 112,364 113,787 115,209 116,632 118,054 119,477 120,899
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Chapter 2/Pressure
Conversion Table, kg/mm2 to psi (cont.) Kg/mm2 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118
psi 122,321 123,744 125,166 126,588 128,011 129,433 130,855 132,278 133,700 135,122 136,545 137,967 139,389 140,812 142,234 143,656 145,079 146,501 147,923 149,346 150,767 152,190 153,613 155,035 156,457 157,880 159,302 160,724 162,147 163,569 164,991 166,414 167,836
Kg/mm2 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150
Conversion Equation, kg/mm2 to psi
Pressure/inch2 = kg/mm2 (1.42234)
psi 169,258 170,681 172,103 173,525 174,948 176,370 177,792 179,215 180,637 182,059 183,482 184,904 186,327 187,749 189,171 190,594 192,016 193,438 194,861 196,283 197,705 199,128 200,550 201,972 203,395 204,817 206,239 207,662 209,084 210,506 211,929 213,351
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ISA Handbook of Measurement Equations and Tables
Conversion Table, ksi to MPa ksi
MPa
ksi
MPa
ksi
MPa
ksi
MPa
1
6.895
26
179.264
60
413.685
310
2137.375
2
13.790
27
186.158
70
482.633
320
2206.322
3
20.684
28
193.053
80
551.581
330
2275.270
4
27.579
29
199.948
90
620.528
340
2344.217
5
34.474
30
206.843
100
689.476
350
2413.165
6
41.369
31
213.737
110
758.423
360
2482.113
7
48.263
32
220.632
120
827.371
370
2551.060
8
55.158
33
227.527
130
896.318
380
2620.008
9
62.053
34
234.422
140
965.266
390
2688.955
10
68.948
35
241.316
150
1034.214
400
2757.903
11
75.842
36
248.211
160
1103.161
410
2826.850
12
82.737
37
255.106
170
1172.109
420
2895.798
13
89.632
38
262.001
180
1241.056
430
2964.746
14
96.527
39
268.896
190
1310.004
440
3033.693
15
103.421
40
275.790
200
1378.951
450
3102.641
16
110.316
41
282.685
210
1447.899
460
3171.588
17
117.211
42
289.580
220
1516.847
470
3240.536
18
124.106
43
296.475
230
1585.794
480
3309.483
19
131.000
44
303.369
240
1654.742
490
3378.431
20
137.895
45
310.264
250
1723.689
500
3447.379
21
144.790
46
317.159
260
1792.637
510
3516.326
22
151.685
47
324.054
270
1861.584
520
3585.274
23
159.597
48
330.948
280
1930.532
530
3654.221
24
165.474
49
337.843
290
1999.480
540
3723.169
25
172.369
50
344.738
300
2068.427
550
3792.116
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Chapter 2/Pressure
41
Conversion Table, MPa to ksi MPa
ksi
MPa
ksi
MPa
ksi
1
0.145
50
7.252
1300
188.552
2
0.290
100
14.504
1350
195.804
3
0.435
150
21.756
1400
203.056
4
0.580
200
29.008
1450
210.308
5
0.725
250
36.260
1500
217.560
6
0.870
300
43.512
1550
224.812
7
1.015
350
50.764
1600
232.064
8
1.160
400
58.016
1650
239.316
9
1.305
450
65.268
1700
246.568
10
1.450
500
72.520
1750
253.820
11
1.595
550
79.772
1800
261.072
12
1.740
600
87.024
1850
268.324
13
1.886
650
94.276
1900
275.576
14
2.031
700
101.528
1950
282.828
15
2.176
750
108.780
2000
290.080
16
2.321
800
116.032
2050
297.332
17
2.466
850
123.284
2100
304.584
18
2.611
900
130.536
2150
311.836
19
2.756
950
137.788
2200
319.088
20
2.901
1000
145.040
2250
326.340
21
3.046
1050
152.292
2300
333.592
22
3.191
1100
159.544
2350
340.844
23
3.336
1150
166.796
2400
348.096
24
3.481
1200
174.048
2450
355.348
25
3.626
1250
181.300
2500
362.600
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ISA Handbook of Measurement Equations and Tables
Conversion Table, ft-lb to Joule ft-lb
Joule
ft-lb
Joule
ft-lb
Joule
ft-lb
Joule
1
1.3558
26
35.2513
55
74.5700
180
244.0472
2
2.7116
27
36.6071
60
81.3491
185
250.8263
3
4.0675
28
37.9629
65
88.1282
190
257.6054
4
5.4233
29
39.3187
70
94.9073
195
264.3845
5
6.7791
30
40.6745
75
101.6863
200
271.1636
6
8.1349
31
42.0304
80
108.4654
220
298.2799
7
9.4907
32
43.3862
85
115.2445
240
325.3963
8
10.8465
33
44.7420
90
122.0236
260
352.5126
9
12.2024
34
46.0978
95
128.8027
280
379.6290
10
13.5582
35
47.4536
100
135.5818
300
406.7454
11
14.9140
36
48.8094
105
142.3609
320
433.8617
12
16.2698
37
50.1653
110
149.1400
340
460.9781
13
17.6256
38
51.5211
115
155.9191
360
488.0944
14
18.9815
39
52.8769
120
162.6982
380
515.2108
15
20.3373
40
54.2327
125
169.4772
400
542.3272
16
21.6931
41
55.5885
130
176.2563
420
569.4435
17
23.0489
42
56.9444
135
183.0354
440
596.5599
18
24.4047
43
58.3002
140
189.8145
460
623.6762
19
25.7605
44
59.6560
145
196.5936
480
650.7926
20
27.1164
45
61.0118
150
203.3727
500
677.9090
21
28.4722
46
62.3676
155
210.1518
520
705.0254
22
29.8280
47
63.7234
160
216.9308
540
732.1417
23
31.1838
48
65.0793
165
223.7099
560
759.2581
24
32.5396
49
66.4351
170
230.4890
580
786.3744
25
33.8954
50
67.7909
175
237.2681
600
813.4908
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Chapter 2/Pressure
43
Conversion Table, Joule to ft-lb Joule
ft-lb
Joule
ft-lb
Joule
ft-lb
Joule
ft-lb
1
0.7376
26
19.1766
55
40.5659
180
132.7612
2
1.4751
27
19.9142
60
44.2537
185
136.4490
3
2.2127
28
20.6517
65
47.9415
190
140.1368
4
2.9502
29
21.3893
70
51.6293
195
143.8246
5
3.6878
30
22.1269
75
55.3172
200
147.5124
6
4.4254
31
22.8644
80
59.0050
220
162.2637
7
5.1629
32
23.6020
85
62.6928
240
177.0149
8
5.9005
33
24.3395
90
66.3806
260
191.7661
9
6.6381
34
25.0771
95
70.0684
280
206.5174
10
7.3756
35
25.8147
100
73.7562
300
221.2686
11
8.1132
36
26.5522
105
77.4440
320
236.0199
12
8.8507
37
27.2898
110
81.1318
340
250.7711
13
9.5883
38
28.0274
115
84.8196
360
265.5224
14
10.3259
39
28.7649
120
88.5075
380
280.2736
15
11.0634
40
29.5025
125
92.1953
400
295.0248
16
11.8010
41
30.2400
130
95.8831
420
309.7761
17
12.5386
42
30.9776
135
99.5709
440
324.5273
18
13.2761
43
31.7152
140
103.2587
460
339.2786
19
14.0137
44
32.4527
145
106.9465
480
354.0298
20
14.7512
45
33.1903
150
110.6343
500
368.7811
21
15.4888
46
33.9279
155
114.3221
520
383.3532
22
16.2264
47
34.6654
160
118.0099
540
398.2835
23
16.9639
48
35.4030
165
121.6977
560
413.0347
24
17.7015
49
36.1405
170
125.3856
580
427.7860
25
18.4390
50
36.8781
175
129.0734
600
442.5372
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ISA Handbook of Measurement Equations and Tables
Height Conversion Equations for Liquid Manometers
Centimeters of distilled water to kilograms per square centimeter.
Inches or millimeters of a liquid to pounds per square inch or kilograms per square centimeter.
P = 0.0009990 h where P = pressure, kg/cm2 h = height, cm 0.0009990 = the density of water at 60oF, 15.6oC
P = dh where P = pressure, lb/in2 or kg/cm2 d = density, lb/in3 or kg/cm3 h = height, in or cm Inches of Mercury to pounds per square inch.
P = 0.48977 h where P = pressure, lb/in2 h = height, in 0.48977 is the density of Mercury at 60oF, 15.6oC Inches of distilled water pounds per square inch.
to
P = 0.036092 h where P = pressure, lb/in2 h = height, in 0.036092 is the density of water at 60oF, 15.6oC Centimeters of Mercury to kilograms per square centimeter.
P = 0.013557 h where P = pressure, kg/cm2 h = height, cm 0.013557 is the density of Mercury at 60oF, 15.6oC
Standard Conditions for Measuring Pressure Based on the Height of a Column of Liquid. [Note: Some vendors, system design firms and other organizations use their own “standards,” which may vary from those below.] Mercury Column Gravity: 980.665 cm/sec2 32.1740 ft/sec2 Temperature: 0oC, 32oF Atmosphere: 760 mm of Mercury 29.9213 in of Mercury Water Column Gravity: 980.665 cm/sec2 32.1740 ft/sec2 Temperature: 20oC, 68oF Atmosphere: 1035.08 cm of water 407.513 in of water
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Chapter 2/Pressure
45
Density of Mercury and Distilled Water at Various Temperatures Deg. F
Deg. C
Mercury, lb/in3
Mercury, kg/cm3
Distilled Water, lb/in3
Distilled Water, kg/cm3
0
-17.8
0.49275
0.013639
20
-6.7
0.49175
0.013612
32
0.0
0.49116
0.013595
40
4.4
0.49076
0.013584
0.036127
0.0009997
60
15.6
0.48977
0.013557
0.036092
0.0009990
80
26.7
0.48879
0.013530
0.036005
0.0009966
100
37.8
0.48780
0.013502
0.035876
0.0009931
120
48.9
0.48683
0.013475
0.035713
0.0009885
140
60.0
0.48585
0.013448
0.035522
0.0009832
160
71.1
0.48488
0.013421
180
82.2
0.48391
0.013394
200
93.3
0.48293
0.013368
0.034792
0.0009630
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ISA Handbook of Measurement Equations and Tables
Measuring Differential Pressure with Transducers.
P =A
C0 − C p Cp
where P = pressure Cp = capacitance of transducer at operating pressure C0 = capacitance of transducer at zero pressure A = current from a constant source
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Chapter 2/Pressure
47
Steam Tables Standard representations for the thermodynamic properties of water and steam (commonly known as “steam tables”) are established by the International Association for the Properties of Water and Steam (IAPWS). The latest IAPWS standard formulation for general and scientific use was adopted in 1995. The numbers in the following tables were supplied by the Physical and Chemical Properties Division of NIST as calculated from their database (A.H. Harvey, A.P. Peskin, and S.A. Klein, NIST/ASME Steam Properties, NIST Standard Reference Database 10, Version 2.2 ([National Institute of Standards and Technology, Gaithersburg, MD, 20899]) that implements the IAPWS standard. Further information may be found at www.iapws.org and at www.nist.gov/srd/nist10.htm. Thermodynamic Properties of Saturated Water and Steam as a Function of Temperature t, °C p, MPa
Density, kg/m3 ρL ρV
0.01 0.000 612 999.79
Enthalpy, kJ/kg ∆h hL hV
Entropy, kJ/(kg·K) ∆s sL sV
0.004 855
0.00 2500.9 2500.9 0.000 00 9.1555 9.1555
5
0.000 873 999.92
0.006 802
21.02 2510.1 2489.0 0.076 25 9.0248 8.9486
10
0.001 228 999.65
0.009 407
42.02 2519.2 2477.2 0.151 09 8.8998 8.7487
15
0.001 706 999.06
0.012 841
62.98 2528.3 2465.4 0.224 46 8.7803 8.5558
20
0.002 339 998.16
0.017 314
83.91 2537.4 2453.5 0.296 48 8.6660 8.3695
25
0.003 170 997.00
0.023 075 104.83 2546.5 2441.7 0.367 22 8.5566 8.1894
30
0.004 247 995.61
0.030 415 125.73 2555.5 2429.8 0.436 75 8.4520 8.0152
35
0.005 629 993.99
0.039 674 146.63 2564.5 2417.9 0.505 13 8.3517 7.8466
40
0.007 385 992.18
0.051 242 167.53 2573.5 2406.0 0.572 40 8.2555 7.6831
45
0.009 595 990.17
0.065 565 188.43 2582.4 2394.0 0.638 61 8.1633 7.5247
50
0.012 352 988.00
0.083 147 209.34 2591.3 2381.9 0.703 81 8.0748 7.3710
55
0.015 762 985.66
0.104 56
230.26 2600.1 2369.8 0.768 02 7.9898 7.2218
60
0.019 946 983.16
0.130 43
251.18 2608.8 2357.7 0.831 29 7.9081 7.0769
t = temperature
hL = liquid enthalpy
sL = liquid entropy
p, MPa = pressure
hV = vapor enthalpy
sV = vapor entropy
ρL = liquid density
ρV = vapor density
∆h = enthalpy of vaporization
∆s = entropy of vaporization
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ISA Handbook of Measurement Equations and Tables
t, °C p, MPa
Density, kg/m3 ρL ρV
Enthalpy, kJ/kg ∆h hL hV
Entropy, kJ/(kg·K) ∆s sL sV
65
0.025 042 980.52
0.161 46
272.12 2617.5 2345.4 0.893 65 7.8296 6.9359
70
0.031 201 977.73
0.198 43
293.07 2626.1 2333.0 0.955 13 7.7540 6.7989
75
0.038 595 974.81
0.242 19
314.03 2634.6 2320.6 1.0158
7.6812 6.665
80
0.047 414 971.77
0.293 67
335.01 2643.0 2308.0 1.0756
7.6111 6.5355
85
0.057 867 968.59
0.353 88
356.01 2651.3 2295.3 1.1346
7.5434 6.4088
90
0.070 182 965.30
0.423 90
377.04 2659.5 2282.5 1.1929
7.4781 6.2853
95
0.084 608 961.88
0.504 91
398.09 2667.6 2269.5 1.2504
7.4151 6.1647
100 0.101 42
958.35
0.598 17
419.17 2675.6 2256.4 1.3072
7.3541 6.0469
105 0.120 90
954.70
0.705 03
440.27 2683.4 2243.1 1.3633
7.2952 5.9318
110 0.143 38
950.95
0.826 93
461.42 2691.1 2229.6 1.4188
7.2381 5.8193
115 0.169 18
947.08
0.965 40
482.59 2698.6 2216.0 1.4737
7.1828 5.7091
120 0.198 67
943.11
1.1221
503.81 2705.9 2202.1 1.5279
7.1291 5.6012
125 0.232 24
939.02
1.2987
525.07 2713.1 2188.0 1.5816
7.0770 5.4955
130 0.270 28
934.83
1.4970
546.38 2720.1 2173.7 1.6346
7.0264 5.3918
135 0.313 23
930.54
1.7190
567.74 2726.9 2159.1 1.6872
6.9772 5.2900
140 0.361 54
926.13
1.9667
589.16 2733.4 2144.3 1.7392
6.9293 5.1901
145 0.415 68
921.62
2.2423
610.64 2739.8 2129.2 1.7907
6.8826 5.0919
150 0.476 16
917.01
2.5481
632.18 2745.9 2113.7 1.8418
6.8371 4.9953
155 0.543 50
912.28
2.8863
653.79 2751.8 2098.0 1.8924
6.7926 4.9002
160 0.618 23
907.45
3.2596
675.47 2757.4 2082.0 1.9426
6.7491 4.8066
165 0.700 93
902.51
3.6707
697.24 2762.8 2065.6 1.9923
6.7066 4.7143
170 0.792 19
897.45
4.1222
719.08 2767.9 2048.8 2.0417
6.6650 4.6233
175 0.892 60
892.28
4.6172
741.02 2772.7 2031.7 2.0906
6.6241 4.5335
180 1.0028
887.00
5.1588
763.05 2777.2 2014.2 2.1392
6.5840 4.4448
185 1.1235
881.60
5.7504
785.19 2781.4 1996.2 2.1875
6.5447 4.3571
190 1.2552
876.08
6.3954
807.43 2785.3 1977.9 2.2355
6.5059 4.2704
195 1.3988
870.43
7.0976
829.79 2788.8 1959.0 2.2832
6.4678 4.1846
200 1.5549
864.66
7.8610
852.27 2792.0 1939.7 2.3305
6.4302 4.0996
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Chapter 2/Pressure
t, °C p, MPa
Density, kg/m3 ρL ρV
Enthalpy, kJ/kg ∆h hL hV
49
Entropy, kJ/(kg·K) ∆s sL sV
205
1.7243
858.76
8.6898
874.88 2794.8 1919.9
2.3777
6.3930 4.0154
210
1.9077
852.72
9.5885
897.63 2797.3 1899.6
2.4245
6.3563 3.9318
215
2.1058
846.54
10.562
920.53 2799.3 1878.8
2.4712
6.3200 3.848
220
2.3196
840.22
11.615
943.58 2800.9 1857.4
2.5177
6.2840 3.7663
225
2.5497
833.75
12.755
966.80 2802.1 1835.4
2.5640
6.2483 3.6843
230
2.7971
827.12
13.985
990.19 2802.9 1812.7
2.6101
6.2128 3.6027
235
3.0625
820.33
15.314
1013.8 2803.2 1789.4
2.6561
6.1775 3.5214
240
3.3469
813.37
16.749
1037.6 2803.0 1765.4
2.7020
6.1423 3.4403
245
3.6512
806.22
18.297
1061.5 2802.2 1740.7
2.7478
6.1072 3.3594
250
3.9762
798.89
19.967
1085.8 2800.9 1715.2
2.7935
6.0721 3.2785
255
4.3229
791.37
21.768
1110.2 2799.1 1688.8
2.8392
6.0369 3.1977
260
4.6923
783.63
23.712
1135.0 2796.6 1661.6
2.8849
6.0016 3.1167
265
5.0853
775.66
25.809
1160.0 2793.5 1633.5
2.9307
5.9661 3.0354
270
5.5030
767.46
28.073
1185.3 2789.7 1604.4
2.9765
5.9304 2.9539
275
5.9464
759.00
30.520
1210.9 2785.2 1574.3
3.0224
5.8944 2.8720
280
6.4166
750.28
33.165
1236.9 2779.9 1543.0
3.0685
5.8579 2.7894
285
6.9147
741.25
36.028
1263.2 2773.7 1510.5
3.1147
5.8209 2.7062
290
7.4418
731.91
39.132
1290.0 2766.7 1476.7
3.1612
5.7834 2.6222
295
7.9991
722.21
42.501
1317.3 2758.7 1441.4
3.2080
5.7451 2.5371
300
8.5879
712.14
46.168
1345.0 2749.6 1404.6
3.2552
5.7059 2.4507
305
9.2094
701.64
50.167
1373.3 2739.4 1366.1
3.3028
5.6657 2.3629
310
9.8651
690.67
54.541
1402.2 2727.9 1325.7
3.3510
5.6244 2.2734
315
10.556
679.18
59.344
1431.8 2715.1 1283.2
3.3998
5.5816 2.1818
320
11.284
667.09
64.638
1462.2 2700.6 1238.4
3.4494
5.5372 2.0878
325
12.051
654.33
70.506
1493.5 2684.3 1190.8
3.5000
5.4908 1.9908
330
12.858
640.77
77.050
1525.9 2666.0 1140.2
3.5518
5.4422 1.8903
335
13.707
626.29
84.407
1559.5 2645.4 1085.9
3.6050
5.3906 1.7856
340
14.601
610.67
92.759
1594.5 2621.8 1027.3
3.6601
5.3356 1.6755
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ISA Handbook of Measurement Equations and Chapter Tables 3/Pressure
t, °C p, MPa
Density, kg/m3 ρL ρV
Enthalpy, kJ/kg ∆h hL hV
Entropy, kJ/(kg·K) ∆s sL sV
345
15.541
593.63 102.36
1631.5 2594.9
963.4
3.7176
5.2762 1.5586
350
16.529
574.71 113.61
1670.9 2563.6
892.7
3.7784
5.2110 1.4326
355
17.570
553.14 127.09
1713.7 2526.6
812.9
3.8439
5.1380 1.294
360
18.666
527.59 143.90
1761.7 2481.5
719.8
3.9167
5.0536 1.1369
365
19.821
495.74 166.35
1817.8 2422.9
605.2
4.0014
4.9497 0.9483
370
21.044
451.43 201.84
1890.7 2334.5
443.8
4.1112
4.8012 0.6901
tc
22.064
322.00 322.00
2084.3 2084.3
0.
4.4070
4.4070 0.
(tc = 373.946 °C)
50
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Chapter 2/Pressure
51
Thermodynamic Properties of Saturated Water and Steam as a Function of Pressure Density, kg/m3
Enthalpy, kJ/kg
Entropy, kJ/(kg·K)
p, MPa ρL
t, °C
ρV
hL
hV
∆h
sL
∆s
sV
611.657 Pa 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020
0.01 3.761 6.970 9.654 11.969 14.010 15.837 17.495
999.79 999.92 999.86 999.68 999.46 999.20 998.93 998.64
0.004 855 0.006 264 0.007 741 0.009 202 0.010 650 0.012 086 0.013 511 0.014 928
0.00 15.81 29.30 40.57 50.28 58.83 66.49 73.43
2500.9 2507.8 2513.7 2518.6 2522.8 2526.5 2529.9 2532.9
2500.9 2492.0 2484.4 2478.0 2472.5 2467.7 2463.4 2459.4
0.000 00 0.057 48 0.105 91 0.145 95 0.180 15 0.210 04 0.236 62 0.260 56
9.1555 9.0567 8.9749 8.9082 8.8521 8.8035 8.7608 8.7226
9.1555 8.9992 8.8690 8.7623 8.6719 8.5935 8.5241 8.4620
0.0025 0.0030 0.0035 0.0040 0.0045 0.0050
21.077 24.079 26.672 28.960 31.012 32.874
997.93 997.24 996.56 995.92 995.30 994.70
0.018 437 0.021 904 0.025 338 0.028 743 0.032 122 0.035 480
88.42 100.98 111.82 121.39 129.96 137.75
2539.4 2544.8 2549.5 2553.7 2557.4 2560.7
2451.0 2443.9 2437.7 2432.3 2427.4 2423.0
0.311 82 0.354 29 0.390 61 0.422 39 0.450 69 0.476 20
8.6420 8.5764 8.5211 8.4734 8.4313 8.3938
8.3302 8.2221 8.1305 8.0510 7.9806 7.9176
0.0060 0.0070 0.0080 0.0090 0.010
36.159 39.000 41.509 43.761 45.806
993.59 992.55 991.59 990.69 989.83
0.042 135 0.048 722 0.055 252 0.061 731 0.068 166
151.48 163.35 173.84 183.25 191.81
2566.6 2571.7 2576.2 2580.2 2583.9
2415.2 2408.4 2402.4 2397.0 2392.1
0.520 82 0.559 03 0.592 49 0.622 30 0.649 20
8.3290 8.2745 8.2273 8.1858 8.1488
7.8082 7.7154 7.6348 7.5635 7.4996
0.012 0.014 0.016 0.018 0.020
49.419 52.547 55.313 57.798 60.058
988.26 986.82 985.50 984.28 983.13
0.080 917 0.093 535 0.106 04 0.118 44 0.130 75
206.91 219.99 231.57 241.96 251.42
2590.3 2595.8 2600.6 2605.0 2608.9
2383.4 2375.8 2369.1 2363.0 2357.5
0.696 28 0.736 64 0.772 01 0.803 55 0.832 02
8.0849 8.0311 7.9846 7.9437 7.9072
7.3887 7.2945 7.2126 7.1402 7.0752
0.025 0.030 0.035 0.040 0.045 0.050
64.963 69.095 72.681 75.857 78.715 81.317
980.54 978.25 976.19 974.30 972.56 970.94
0.161 21 0.191 26 0.220 99 0.250 44 0.279 65 0.308 64
271.96 289.27 304.30 317.62 329.62 340.54
2617.4 2624.5 2630.7 2636.1 2640.9 2645.2
2345.5 2335.3 2326.4 2318.4 2311.2 2304.7
0.89319 0.94407 0.98774 1.0261 1.0603 1.0912
7.8302 7.7675 7.7146 7.6690 7.6288 7.5930
6.9370 6.8234 6.7269 6.6429 6.5686 6.5018
0.06 0.07 0.08 0.09 0.10
85.926 89.932 93.486 96.687 99.606
967.99 965.34 962.93 960.70 958.63
0.366 07 0.422 87 0.479 14 0.534 94 0.590 34
359.91 376.75 391.71 405.20 417.50
2652.9 2659.4 2665.2 2670.3 2674.9
2292.9 2282.7 2273.5 2265.1 2257.4
1.1454 1.1921 1.2330 1.2696 1.3028
7.5311 7.4790 7.4339 7.3943 7.3588
6.3857 6.2869 6.2009 6.1246 6.0561
0.12 0.14 0.16 0.18 0.20
104.784 109.292 113.297 116.911 120.210
954.86 951.49 948.41 945.57 942.94
0.700 10 0.808 69 0.916 29 1.0230 1.1291
439.36 458.42 475.38 490.70 504.70
2683.1 2690.0 2696.0 2701.4 2706.2
2243.7 2231.6 2220.7 2210.7 2201.5
1.3609 1.4110 1.4551 1.4945 1.5302
7.2977 7.2461 7.2014 7.1621 7.1269
5.9367 5.8351 5.7463 5.6676 5.5967
t = temperature
hL = liquid enthalpy
sL = liquid entropy
p, MPa = pressure
hV = vapor enthalpy
ρL = liquid density
∆h = enthalpy of vaporization
sV = vapor entropy
ρV = vapor density
∆s = entropy of vaporization
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Density, kg/m3
Enthalpy, kJ/kg
Entropy, kJ/(kg·K)
p, MPa t, °C
ρL
ρV
hL
hV
∆h
sL
sV
∆s
0.22 0.24 0.26 0.28 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.0
123.250 126.072 128.708 131.185 133.522 138.857 143.608 147.903 151.831 155.456 158.826 161.980 164.946 167.749 170.406 172.936 175.350 177.661 179.878
940.47 938.13 935.93 933.83 931.82 927.15 922.89 918.96 915.29 911.85 908.59 905.51 902.56 899.74 897.04 894.43 891.92 889.48 887.13
1.2345 1.3393 1.4436 1.5474 1.6508 1.9077 2.1627 2.4161 2.6680 2.9189 3.1687 3.4177 3.6660 3.9137 4.1608 4.4074 4.6536 4.8995 5.1450
517.63 529.64 540.87 551.44 561.43 584.26 604.65 623.14 640.09 655.76 670.38 684.08 697.00 709.24 720.86 731.95 742.56 752.74 762.52
2710.6 2714.6 2718.3 2721.7 2724.9 2732.0 2738.1 2743.4 2748.1 2752.3 2756.1 2759.6 2762.8 2765.6 2768.3 2770.8 2773.0 2775.1 2777.1
2193.0 2185.0 2177.4 2170.3 2163.5 2147.7 2133.4 2120.2 2108.0 2096.6 2085.8 2075.5 2065.8 2056.4 2047.4 2038.8 2030.5 2022.4 2014.6
1.5628 1.5930 1.6210 1.6471 1.6717 1.7274 1.7765 1.8205 1.8604 1.8970 1.9308 1.9623 1.9918 2.0195 2.0457 2.0705 2.0940 2.1165 2.1381
7.0951 7.0661 7.0394 7.0146 6.9916 6.9401 6.8955 6.8560 6.8207 6.7886 6.7592 6.7322 6.7071 6.6836 6.6616 6.6409 6.6213 6.6027 6.5850
5.5323 5.4731 5.4184 5.3675 5.3199 5.2128 5.1190 5.0356 4.9603 4.8916 4.8284 4.7699 4.7153 4.6641 4.6160 4.5704 4.5272 4.4862 4.4470
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
184.062 187.957 191.605 195.039 198.287 201.370 204.307 207.112 209.798 212.377
882.62 5.6354 878.35 6.1251 874.28 6.6144 870.39 7.1034 866.65 7.5924 863.05 8.0815 859.58 8.5708 856.22 9.0606 852.96 9.5508 849.80 10.042
781.03 798.33 814.60 829.97 844.56 858.46 871.74 884.47 896.71 908.50
2780.6 2783.7 2786.5 2788.8 2791.0 2792.8 2794.5 2795.9 2797.2 2798.3
1999.6 1985.4 1971.9 1958.9 1946.4 1934.4 1922.7 1911.4 1900.5 1889.8
2.1785 2.2159 2.2508 2.2835 2.3143 2.3435 2.3711 2.3975 2.4227 2.4468
6.5520 6.5217 6.4936 6.4675 6.4430 6.4199 6.3981 6.3775 6.3578 6.3390
4.3735 4.3058 4.2428 4.1839 4.1286 4.0765 4.0270 3.9800 3.9351 3.8923
2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.8
217.249 221.789 226.046 230.057 233.853 237.459 240.897 244.182 247.330 250.354 253.264 256.070 258.780 261.402 263.941 266.403 268.795 271.120 273.382 275.585 277.733 279.829 281.875 283.874
843.72 837.92 832.37 827.04 821.90 816.92 812.10 807.41 802.83 798.37 794.00 789.73 785.53 781.42 777.37 773.39 769.46 765.59 761.77 758.00 754.27 750.58 746.93 743.31
930.87 951.87 971.67 990.46 1008.3 1025.4 1041.8 1057.6 1072.8 1087.5 1101.7 1115.5 1128.9 1141.9 1154.6 1167.0 1179.1 1191.0 1202.6 1213.9 1225.1 1236.0 1246.7 1257.3
2800.1 2801.4 2802.3 2802.9 2803.2 2803.1 2802.9 2802.4 2801.7 2800.8 2799.8 2798.6 2797.3 2795.8 2794.2 2792.5 2790.7 2788.7 2786.7 2784.6 2782.4 2780.1 2777.7 2775.2
1869.2 1849.6 1830.7 1812.4 1794.8 1777.7 1761.0 1744.8 1728.9 1713.3 1698.1 1683.1 1668.4 1653.9 1639.6 1625.5 1611.5 1597.8 1584.1 1570.7 1557.3 1544.1 1530.9 1517.9
2.4921 2.5343 2.5736 2.6106 2.6455 2.6787 2.7102 2.7403 2.7691 2.7968 2.8234 2.8490 2.8738 2.8978 2.9210 2.9435 2.9654 2.9868 3.0075 3.0278 3.0476 3.0669 3.0858 3.1043
6.3038 6.2712 6.2409 6.2124 6.1856 6.1602 6.1360 6.1129 6.0908 6.0696 6.0491 6.0293 6.0102 5.9917 5.9737 5.9561 5.9391 5.9224 5.9061 5.8901 5.8745 5.8592 5.8441 5.8293
3.8116 3.7369 3.6672 3.6018 3.5400 3.4815 3.4258 3.3726 3.3217 3.2728 3.2257 3.1803 3.1364 3.0939 3.0527 3.0126 2.9736 2.9356 2.8985 2.8623 2.8269 2.7923 2.7583 2.7250
11.026 12.013 13.004 14.000 15.001 16.006 17.018 18.036 19.059 20.090 21.127 22.172 23.224 24.284 25.351 26.427 27.512 28.605 29.707 30.818 31.940 33.070 34.211 35.363
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Chapter 2/Pressure
Density, kg/m3
Enthalpy, kJ/kg
Entropy, kJ/(kg·K)
p, MPa t, °C
ρL
ρV
hL
hV
∆h
sL
∆s
sV
7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 9.6 9.8 10.0
285.829 287.741 289.614 291.448 293.245 295.008 296.737 298.434 300.100 301.737 303.345 304.926 306.481 308.010 309.516 310.997
739.72 736.17 732.64 729.14 725.66 722.20 718.76 715.34 711.93 708.54 705.16 701.80 698.44 695.09 691.76 688.42
36.525 37.698 38.883 40.079 41.287 42.507 43.740 44.985 46.244 47.517 48.804 50.105 51.421 52.753 54.100 55.463
1267.7 1277.9 1287.9 1297.9 1307.7 1317.3 1326.8 1336.3 1345.6 1354.8 1363.9 1372.9 1381.8 1390.6 1399.4 1408.1
2772.6 2770.0 2767.3 2764.5 2761.6 2758.7 2755.7 2752.6 2749.4 2746.2 2742.9 2739.6 2736.2 2732.7 2729.1 2725.5
1505.0 1492.1 1479.3 1466.6 1454.0 1441.4 1428.8 1416.3 1403.9 1391.5 1379.1 1366.7 1354.4 1342.0 1329.7 1317.4
3.1224 3.1402 3.1576 3.1747 3.1915 3.2081 3.2243 3.2403 3.2561 3.2717 3.2870 3.3021 3.3170 3.3317 3.3463 3.3606
5.8148 5.8004 5.7863 5.7723 5.7586 5.7450 5.7316 5.7183 5.7051 5.6921 5.6791 5.6663 5.6536 5.6410 5.6284 5.6160
2.6924 2.6603 2.6287 2.5976 2.5671 2.5369 2.5072 2.4779 2.4490 2.4204 2.3922 2.3642 2.3366 2.3092 2.2822 2.2553
10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0
314.603 318.079 321.433 324.675 327.813 330.854 333.803 336.666 339.449 342.155 344.789 347.355 349.855 352.293 354.671 356.992 359.259 361.473 363.636 365.749 367.813 369.827 371.791 373.705
680.11 58.946 671.81 62.541 663.51 66.257 655.18 70.106 646.81 74.097 638.37 78.245 629.85 82.563 621.22 87.069 612.45 91.783 603.52 96.727 594.38 101.93 584.99 107.42 575.29 113.25 565.21 119.46 554.66 126.12 543.54 133.30 531.70 141.13 519.00 149.76 505.25 159.43 490.19 170.50 473.34 183.63 453.41 200.16 426.11 223.54 369.77 274.16
1429.4 1450.4 1471.1 1491.5 1511.6 1531.5 1551.3 1571.0 1590.6 1610.2 1629.9 1649.7 1669.7 1690.0 1710.8 1732.1 1754.1 1777.2 1801.4 1827.2 1855.3 1887.6 1929.5 2011.3
2716.1 2706.3 2696.1 2685.4 2674.3 2662.7 2650.5 2637.9 2624.6 2610.7 2596.1 2580.8 2564.6 2547.5 2529.3 2509.8 2488.8 2466.0 2440.8 2412.3 2379.2 2338.6 2283.1 2173.1
1286.7 1255.9 1225.0 1194.0 1162.7 1131.2 1099.3 1066.9 1034.0 1000.5 966.2 931.1 894.9 857.5 818.5 777.7 734.7 688.9 639.4 585.1 523.9 451.0 353.6 161.7
3.3959 3.4303 3.4638 3.4967 3.5290 3.5608 3.5921 3.6232 3.6539 3.6846 3.7151 3.7457 3.7765 3.8077 3.8394 3.8718 3.9053 3.9401 3.9767 4.0156 4.0579 4.1064 4.1698 4.2945
5.5851 5.5545 5.5241 5.4939 5.4638 5.4336 5.4032 5.3727 5.3418 5.3106 5.2788 5.2463 5.2130 5.1787 5.1431 5.1061 5.0670 5.0256 4.9808 4.9314 4.8753 4.8079 4.7181 4.5446
2.1892 2.1242 2.0603 1.9972 1.9348 1.8728 1.8111 1.7495 1.6879 1.6260 1.5636 1.5006 1.4364 1.3710 1.3038 1.2342 1.1618 1.0855 1.0041 0.9158 0.8174 0.7015 0.5482 0.2501
22.064
373.946
322.00 322.00
2084.3
2084.3
0.
4.4070 4.4070 0.
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3 Flow Measurement
Principles of Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Basic Flow Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Inferential Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Velocity Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Magnetic Flowmeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Vortex Shedding Flowmeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Turbine Meters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Ultrasonic Flowmeters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Mass Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Volumetric Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Positive Displacement Meters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Physical Properties of Fluids & Gases . . . . . . . . . . . . . . . . . . . . . . . . 61 English & SI Units of Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . 61 Fundamental Constants & Conversion Factors. . . . . . . . . . . . . . . . . 62 Flow Conversion Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Gas Compressibility Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Critical Values for Some Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Head Losses in Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Specific Heats of Fluids and Gases . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Volume Flow Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Reynolds Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Flowmeter Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
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Compensation of Linear Volumetric Meter Signals . . . . . . . . . . . . . 77 Compensation of Rotameter Signals . . . . . . . . . . . . . . . . . . . . . . . . . 78 Compensation of Differential Pressure Meters . . . . . . . . . . . . . . . . . 79 Differential Pressure Flowmeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Head Type Flowmeter Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Open Channel Flow Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Magnetic Flowmeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Ultrasonic Flowmeters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 ANSI/ISA Standard Flow Equations for Sizing Control Valves . . . 101 An ‘Old Timer’s’ Tips for Approximate Plant Calculations . . . . . . . 116
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Chapter 3/Flow Measurement
Principles of Flow Basic Flow Equation Vfr = A v where Vfr = volumetric flow rate
A = cross-sectional area of flow v– = average flow velocity This equation applies in all cases. If flow is in a pipe, the cross-sectional area can be found in piping handbooks. Flow is laminar or turbulent, depending on the flow rate and viscosity. This can be predicted by calculating the Reynolds number, which is the ratio of inertial forces to viscous forces:
Re = 123.9 pVD/u where: Re = Reynolds number p = density in lbs./ft.3 V = average velocity in ft/sec. D = pipe diameter in inches u = viscosity in centipoises Reynolds numbers below 2,000 indicate laminar flow; above 4,000, turbulent flow. However, some velocity meters require values above 20,000 to be absolutely certain the flow is truly turbulent and a good average velocity profile is established that can be measured from a single point on the flow profile. Most liquid flows are turbulent, while highly viscous flows like
57
polymers or very low flow rates are laminar. Typical flow measurements can determine: average velocity, velocity at one point, volume of material flowing, and/or the mass of material. Velocity measurements, in particular, require the flow stream velocity to be relatively consistent across the diameter of the pipe. Less than fully turbulent flow creates lower velocities near the pipe wall. Fittings, valves—anything other than straight, open pipe upstream of the sensor—will cause velocity variations across the diameter of the pipe. To achieve uniform flow, different types of flowmeters require straight pipe runs upstream and downstream of the measurement. These run requirements are expressed as a certain number of straight, open pipe diameters. For example, for a 6-inch pipe, 20 diameters would be 10 feet. There are no consistent recommendations even for a particular flowmeter type; it is best to follow the manufacturer’s recommendations. Recommendations vary from 1 to 20, or even more, upstream diameters and a smaller number of downstream diameters. Flow measurements can grouped into four categories: 1. Inferential methods 2. Velocity methods 3. Mass methods 4. Volumetric methods
be
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Inferential Methods Placing an obstruction in the flow path causes the velocity to increase and the pressure to drop. The difference between this pressure and the pressure in the pipe can be used to measure the flow rate of most liquids, gases, and vapors, including steam. In turbulent flow, the differential pressure is proportional to the square of flow rate. An orifice plate is the most common type of obstruction, and, in fact, differential pressure across an orifice is used more than any other type of flow measurement. The installed base of orifice meters is probably as great as all other flow meters combined. The orifice plate is a metal disc with typically a round hole in it, placed between flanges in the pipe. Differential pressure can be measured at the pipe flanges directly upstream and downstream of the orifice or further upstream and downstream. The calculation formulas of differential pressure for a given orifice size and given location of the pressure taps are well developed, so no field calibration based on actual flow is needed (although the dP cell may have to be calibrated). Orifice flow measurements are relatively cheap to purchase but have relatively high installation costs. They have high operating costs because they create a fairly large unrecoverable pressure loss. Also, they have low turndown, in part due to the squared relationship.
Orifices are suitable for high temperature and pressure, and are best for clean liquids, gases, and low velocity steam flows. They require long straight runs upstream and downstream. They are subject to a number of errors, such as flow velocity variations across the pipe and wear or buildup on the orifice plate. Because of these error sources, they are not generally very accurate even when highly accurate differential pressure transmitters are used. Other types of obstructions include venturis and flow tubes which have less unrecoverable flow loss. A pitot tube is a device that can be inserted in large pipes or ducts to measure a differential pressure. Inferential Mass Flow Measurement Density of an Ideal Gas
Di =
PM RT
where Di = density of an ideal gas P = pressure M = molecular weight R = the universal gas constant T = temperature
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Density of an Imperfect Gas
Pim=
PM RTZ
where Pim = density of an imperfect gas P = pressure M = molecular weight R = the universal gas constant T = temperature Z = compressibility
Velocity Methods Magnetic Flowmeters Magnetic flowmeters depend on the principle that motion between a conductor (the flowing fluid) and a magnetic field develops a voltage in the conductor proportional to the velocity of the fluid. Coils outside the pipe generate a pulsed DC magnetic field. Material to be measured flows through the meter tube, which is lined with a non-conductive material such as Teflon, polyurethane, or rubber. Measuring electrodes protrude through the liner and contact the fluid and sense the generated voltage. The flowing fluid must be conductive, but there are very few other restrictions; most aqueous fluids are suitable. There are fewer Reynolds number limitations. The instrument is the full diameter of the pipe, so there is no pressure
59
loss. A wide range of sizes are available—from very small (1/8 inch, for example) up to 10 feet in diameter. The flowing material can be liquids, slurries and suspended solids, and there are minimum straight run requirements. Vortex Shedding Flowmeters Vortex shedding flowmeters measure the frequency of vortices shed from a blunt obstruction, called a “bluff body,” placed in the pipe. As the flow divides to go around the bluff body, vortices are created on each side of the divided stream. The rate of vortex creation is proportional to the stream velocity. Since each vortex represents an area of low pressure, the presencethen-absence of low pressures is counted and the count is proportional to the velocity. Vortex flowmeters provide good measurement accuracy with liquids, gases, or steam and are tolerant of fouling. They have high accuracy at low flow rates; the measurement is independent of material characteristics. They require long runs of straight pipe. Even though the accuracy of vortex meters is often stated as a percent of flow rate rather than of full scale which does indicate higher accuracies, below a certain flow rate they cannot measure at all. At some low flow rate the Reynolds number will be low enough so no vortices will be shed.
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Turbine Meters Turbine meters use a multi-bladed rotor supported by bearings in the pipe. The flowing fluid drives the rotor at a speed proportional to the fluid velocity. Movement of the rotor blades is sensed by a magnetic pickup outside the pipe. The number of blade tips passing the pickup is counted to get rotor speed.
Ultrasonic meters are non-invasive but are relatively low accuracy. Because clamp-on ultrasonic meters are easy to install, they can be used temporarily to verify another flowmeter permanently installed in the pipe. Since the same meter can do a variety of sizes, they are particularly cost effective in large sizes.
Mass Methods These meters have high accuracy for a defined viscosity. They are suitable for very high and low temperatures and high pressures. However, they are sensitive to viscosity changes, and the rotor is easily damaged by going too fast a speed. Because of the relatively high failure rate of their moving parts, they are not used as much as in the past. Ultrasonic Flowmeters Ultrasonic flowmeters send sound waves through the flowing stream. They can measure either the Doppler shift as ultrasonic waves are bounced off particles in the flow stream, or the time differential of ultrasonic waves with the flow stream compared to against the flow stream. Either method gives a signal which is proportional to flow velocity. The Doppler method works with liquids with suspended solids, and the Transit time method works with liquids and gases. In both methods, the signal is proportional to flow velocity.
Mass flowmeters measure actual mass flow. While it is possible to calculate mass flow from a velocity or inferential measurement and other variables like temperature for known fluids, only one meter type commonly measures liquid mass directly, the Coriolis meter. This meter used to be applied only for when highly accurate, mass flow was required. Now with lower prices, a wider range of configurations and easier installation, it is being applied more routinely. The heart of a Coriolis meter is a tube(s) that is vibrated at resonant frequency by magnetic drive coils. When fluid flows into the tube during the tube’s upward movement, the fluid is forced to take on the vertical momentum of the vibrating tube. Therefore, as the tube moves upwards in the first half of the vibration cycle, the fluid entering the tube resists the motion of the tube and exerts a downward force. Fluid in the discharge end of the meter has momentum in the opposite direction, and the difference in forces causes the tube to twist. This
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tube twist is sensed as a phase difference by sensors located on each end of the tube arrangement, and twist is directly proportional to mass flow rate.
1. Temperature
In addition to having high accuracy and a true mass flow measurement, Coriolis meters have no upstream and downstream straight run requirements, are independent of fluid properties, are low maintenance, and have a turndown ratio of as much as one hundred. While the meters originally were only available in a double U-shape, they are now available in a variety of configurations and sizes.
5. Density
61
2. Pressure 3. Liquid State 4. Gaseous State
6. Viscosity 7. Specific Gravity Depending on the type flowmeter used, and application, the following properties may also be important: 1. Vapor Pressure 2. Boiling Point 3. Electrical Conductivity
Volumetric Methods Positive Displacement Meters This type of meter separates the flow stream into known volumes by vanes, gears, pistons or diaphragms, then counts the segmented volumes. They have goodto-excellent accuracy, can measure viscous liquids, and have no straight run requirements. However, they do have a non-recoverable pressure loss, and their moving parts subject to wear. Physical Properties of Fluids & Gases When measuring flow, physical properties of fluids and gases are significant when designing systems and measuring performance. Properties of fundamental importance include:
4. Sonic Conductivity 5. Velocity 6. Specific Heat
English & SI units of Measurement Many manufacturers publish their data in both the English system (which uses inches, pounds, degrees Fahrenheit, and related units) and Système Internationale d’Unités (SI), an improved metric system (which uses centimeters, meters, grams, degrees Celsius, and related units). Degrees Celsius is also called degrees Centigrade, a French word. Celsius and Centigrade are completely interchangeable terms.
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The equation to convert degrees Fahrenheit to degrees Celsius is: tc =
t − 32 1 .8
The equation to convert degrees Celsius to degrees Fahrenheit is: t = 1.8 tc + 32
where tc = temperature in degrees Celsius
English Metric Flow Units Quantity
English
Metric
Volume
ft3/min
m3/sec
Mass
lb/min
kg/sec
Pressure
psig
kPa, bar
Temp.
°F
°C, K
Density
lb/ft3
kg/m3
Fundamental Constants and Conversion Factors 1 psi = 6.895 kPa 1 kPa = 0.1450 psi 1 bar = 100 kPa
Volume Flow Rate a=
dV dt
where a = volume flow rate d = distance V = measured volume t = time in seconds
1 bar = 14.50 psi 1 MPa = 145.0 psi 1 psi = 27.73 inches of water at °F or C 1 psi = 2.310 feet of water at °F or C 1 kPa = 7.5 mm of water at °F or C 1 kPa = 4.019 inches of water at °F or C 1 lb/ft3 = 16.026 kg/m3
Mass Flow Rate a=
dM dt
where a = mass flow rate d = distance M = measured mass t = time in seconds
1 lb/ft3 = 0.016026 kg/liter 1 kg/l = 0.0624 lb/ft3 1 lb/ft-sec = 0.000672 centipoise Fluid Pressure Absolute pressure is the actual pressure of the fluid with respect to a perfect vacuum, regardless of the atmospheric pressure on the outside of the container. Gauge pressure is the fluid pressure with respect to the atmospheric pressure outside its container.
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Differential pressure is the difference between two pressures. Note that gauge pressure is actually a differential pressure between fluid pressure and atmospheric pressure. Fluid Density Density is defined as the mass of the fluid per unit volume (ρ = m/V). In the English system, density is typically expressed in pounds per cubic foot, where the pounds represent mass rather than force. In the metric system, density is typically expressed in kilograms per cubic meter or kilograms per liter. Equivalence formulas are: 1 lb/ft3 = 16.026 kg/m3 1 lb/ft3 = 0.016026 kg/l 1 kg/l = 0.0624 lb/ft3 Temperature changes have a significant effect on liquid densities. The effect of pressure is normally so small it can be ignored. In general, liquids expand as temperature increases, and thus the density decreases. Gases can greatly vary in density with both pressure and temperature changes, as well as differences in molecular weight. The Ideal Gas Law incorporates both Charles’ Law, which states that the density of a gas at constant temperature is directly proportional to its absolute pressure, and Boyle’s Law, which states the density of a gas of constant pressure is inversely propor-
63
tional to its absolute temperature. The Ideal Gas Law is:
PV = nRT where P = absolute pressure V = volume n = mass/molecular weight R = Universal Gas Constant T = absolute temperature
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Flow Conversion Table To Convert from
To
Multiply by:
cm3
ft3
0.00003531467
cm3
in3
0.06102374
cm3
m3
0.0000001
cm3
mm3
1000
cm3
gallon
0.0002641721
cm3
quart (liquid)
0.001056688
cm3/sec
ft3/min
0.00211888
cm3/sec
liter/hr
3.6
ft3
cm3
28,316.847
ft3
in3
1728
ft3
m3
0.028316847
ft3
gallon
7.480519
ft3
liter
28.316847
ft3/hr
cm3/sec
7.865791
ft3/hr
liter/min
0.4719474
ft3min
cm3/sec
471.9474
ft3/min
gallon/sec
0.1246753
ft3/sec
m3/hr
101.9406
ft3/sec
gallon/min
448.8312
ft3/sec
liter/min
1699.011
in3
cm3
16.387064
in3
ft3
0.0005787037
in3
m3
0.000016387064
in3
gallon
0.004329004
in3
liter
0.016387064
cm3/min
cm3/sec
0.2731177
m3
cm3
100,000
m3
ft3
35.31467
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Chapter 3/Flow Measurement
Flow Conversion Table (cont.) To Convert from
To
Multiply by:
m3
in3
61,023.74
m3
gallon
264.1721
m3
liter
1000
m3/kg
ft3/lb
16.01846
mm3
cm3
0.001
mm3
in3
0.00006102374
°F
°C
0.5555556
°F
K
0.5555556
Dram (fluid)
cm3
3.696691
Dram (fluid)
in3
0.2255859
Dram (fluid)
milliliter
3.696691
Dram (fluid)
oz (fluid)
0.125
ft/hr
m/sec
0.00008466667
ft/min
km/hr
0.018288
ft/min
m/sec
0.00508
ft/sec
km/hr
1.09728
ft/sec
m/min
18.288
ft/sec
m/sec
0.3048
ft/poundal
Joule
0.0421401
ft/poundal
kg/m
0.00429740
ft/poundal
liter/atm
0.000415891
gallon
cm3
3785.412
gallon
ft3
0.13368056
gallon
in3
231
gallon
Dram (fluid)
1024
gallon
liter
3.785412
gallon
oz
128
gallon/min
ft3/hr
8.020834
65
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Flow Conversion Table (cont.) To Convert from
To
Multiply by:
gallon/min
ft3/sec
0.002228009
gallon/min
m3/hr
0.2271247
gallon/min
liter/sec
0.06309020
gram
Dram
0.56438339
gram
grain
15.432358
gram
kgm
0.001
gram
milligram
1000
gram
oz (liquid)
0.035273962
gram
lb
0.002046226
gram/cm3
kgm/m3
1000
gram/cm3
kgm/liter
1
gram/cm3
lb/ft3
62.42796
gram/cm3
lb/in3
0.03612729
gram/cm3
lb/gallon
8.345404
gram/liter
gram/cm3
0.001
gram/liter
kgm/m
1
gram/liter
lb/ft3
0.0624280
gram/liter
lb/gallon
0.0083454
gram/force
Dyne
980.665
gram/force
Newton
0.00980665
Joule
ft-lb force
0.737562
Joule
kg-force-meter
0.101972
Joule
Newton-meter
1
Kelvin
°F
1.8
Kelvin
°C
1
Kelvin
°Rankin
1.8
kg
oz (fluid)
35.273962
kg
lb
2.2046226
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Chapter 3/Flow Measurement
Flow Conversion Table (cont.) To Convert from
To
Multiply by:
kg/m3
gram/liter
1
kg/m3
lb/ft3
0.06242796
kg/m3
lb/in3
0.00003612729
kg/force
Dyne
0.0000980665
kg/force
Newton
9.80665
kg/force
lb/force
2.20462
kg/force
Poundal
70.9316
kPa
lb/ft2
20.8854
kPa
lb/in2
0.1450377
liter
cm3
1000
liter
ft3
0.03531467
liter
in3
61.02374
liter
m3
0.001
liter
Dram
270.5122
liter
gallon
0.26417205
liter
oz (fluid)
33.81402
liter
quart (fluid)
1.056688
liter/min
ft3//hr
2.118880
liter/min
ft3/sec
0.0005885778
liter/min
gallon/hr
15.85032
liter/min
gallon/sec
0.004402868
liter/sec
ft3//hr
127.1328
liter/sec
ft3/min
2.118880
liter/sec
gallon/hr
951.0194
liter/bar
Joule
100
MPa
bar
10
MPa
Newton/mm3
1
meter
ft
3.2808399
67
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Flow Conversion Table (cont.) To Convert from
To
Multiply by:
meter
in
39.37007874
millibar
Pa
100
milligram
Dram
0.0005643834
milligram
oz (fluid)
0.00003527396
milligram
lb
0.00000220462
milligram/liter
lb/ft3
0.00006242796
milligram/force
Dyne
0.980665
milligram/force
Newton
0.00000980665
milligram/force/cm
Dyne/cm
0.980665
milligram/force/cm
Newton/m
0.000980665
milligram/force/in
Dyne/cm
0.386089
milligram/force/in
Newton/m
0.000386089
mm
in
0.03937008
Newton
Dyne
0.00001
Newton
kg/force
0.1019716
Newton
Poundal
7.23301
Newton
lb/force
0.224809
Newton/meter
ft/lb force
0.737562
Newton/meter
Joule
1
Newton/meter
kg/meter force
0.1019716
oz (fluid)
Dram
8
oz (fluid)
gallon
0.0078125
oz (fluid)
lb
0.0625
oz (fluid)
cm3
29.57353
oz (fluid)
in3
1.8046875
oz (fluid)
milliliter
29.57353
oz (fluid)
quart
0.03125
Pascal
Newton/m2
1
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Chapter 3/Flow Measurement
Flow Conversion Table (cont.) To Convert from
To
Multiply by:
Pascal
Newton/mm2
0.000001
Pascal
Poundal/ft2
0.671969
Pascal
lb/ft2
0.0208854
Pascal
lb/in2 force
0.000145038
pint
cm3
473.1765
pint
in3
28.875
pint
liter
0.4731765
pint
oz (fluid)
16
lb
Dram
256
lb
gram
7000
lb
kg
0.45359237
lb
ton (U.S.)
0.0005
lb/ft3
kg/m3
16.01846
lb/ft3
lb/in3
0.0005787037
lb/in3
gram/cm3
27.679905
lb/in3
lb/ft3
1,728
lb/ft
kg/m
1.488164
lb/ft/hr
Pascal/sec
0.0004133789
lb/ft/sec
Pascal/sec
1.488164
lb/gallon
gram/cm3
0.1198264
lb/gallon
gram/liter
119.8264
lb/gallon
kg/m3
119.8264
lb/gallon
lb/ft3
7.480519
Poundal
gram/force
14.0981
Poundal
Newton
0.1382550
Poundal
lb/force
0.031081
psi
lb/in2 force
1
quart (fluid)
liter
0.94635295
quart (fluid)
in3
57.75
quart (fluid)
cm3
946.35295
ton (U.S.)
kg
907.18474
ton (U.S.)
ton (metric)
0.90718474
69
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Gas Compressibility Factors
Normalized pressure and temperature values (Z)
The True Gas (or “Real Gas”) Law (Non-Ideal Gas Law) PV = ZnRT
where P = absolute pressure V = volume Z = normalized compressibility n = mass/molecular weight R = universal gas constant T = absolute temperature
Tr =
T Tc
Pr =
P Pc
where Tr = reduced temperature Pr = reduced pressure T = absolute temperature P = absolute pressure Tc = critical temperature Pc = critical pressure
Values of the Universal Gas Constant (R) Mass
Pressure
Volume
Temperature
R Value
lb
psia
ft3
°Rankine
10.73
lb
psfa
ft3
°Rankine
1554
kg
kPa (abs)
m3
Kelvin
8.314
kg
kPa (abs)
liter
Kelvin
8.314
kg
kg/cm3
liter
Kelvin
84.78
kg
bars
liter
Kelvin
83.14
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71
Critical Values for Some Gases Gas
Mol. Wt.
Tc-°F
Pc-psia
Tc-°C
Pc-kPa
Acetic Acid
60
1071
840
595
5792
Acetylene
26
556
911
309
6280
Ammonia
17
730
1640
405
11,310
Argon
40
272
705
151
4860
Benzene
78
1011
702
562
4840
Butane
58
765
551
425
3800
Carbon Dioxide
44
548
1072
304
7390
Carbon Monoxide
28
239
507
133
3500
Carbon Tetrachloride
154
1001
661
556
4560
Chlorine
71
751
1118
417
7709
Cyclohexane
84
997
594
554
4100
Decane
142
1115
312
619
2150
Ethane
30
550
708
305
4880
Ethanol
46
929
927
516
6390
Ethyl Chloride
64.5
829
764
460
5270
Ethyl Either
74
839
522
466
3600
Ethylene
28
509
748
283
5160
Helium*
4
(24)
(151)
(13.3)
(1050)
Heptane
100
972
377
540
2600
Hexane
86
914
436
508
3010
Hydrogen*
2
(74)
(306)
(41)
(2110)
Hydrogen Chloride
36.5
584
1200
324
8270
Hydrogen Cyanide
27
822
735
457
5070
Methane
16
343
673
191
4640
Methanol
32
924
1450
513
10,000
Methyl Chloride
50.5
749
967
416
6670
Neon*
20
(95)
(498)
(52)
(3430)
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Critical Values for Some Gases (cont’d.) Gas
Mol. Wt.
Tc-°F
Pc-psia
Tc-°C
Pc-kPa
Nitric Oxide
30
323
955
179
6590
Nitrogen
28
227
492
126
3390
Nonane
128
1072
336
596
2320
Octane
114
1025
362
569
2500
Oxygen
32
278
730
154
5030
Pentane
72
847
486
470
3350
Propane
44
666
617
370
4250
Propanol
76
914
779
508
5370
Propylene
42
658
662
365
4562
Sulfur Dioxide
64
775
1142
430
7870
Sulfur Trioxide
80
885
1228
491
8470
Toluene
92
1069
612
594
4220
Water
18
1165
3206
647
22,100
*Pseudo-critical values shown.
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Chapter 3/Flow Measurement
Head Losses in Pipes Head loss consists of two primary components: friction losses, caused by the walls of a pipe, and minor losses. A fluid’s viscosity and flow turbulence both contribute to friction loss. The Darcy-Weisbach formula can be used to calculate friction losses in circular pipes:
hf =
f L V2 d 2g
where f = friction factor L = pipe length V = average velocity d = internal diameter g = gravity Friction factor can be determined by knowing the relative roughness of the pipe, solving for the Reynolds number, and using the Moody Chart found in most fluid mechanics books. To determine the Reynolds number, use the following equation: Re =
Vd v
where v = viscosity Minor losses are caused by a change in flow pattern, caused by bends in a pipe, a sudden change in a pipe diameter, valves, etc. Tables in many fluid mechanics books provide minor head loss val-
73
ues for different types of bends, valves, elbows, tees etc. Minor changes (hm) are small when compared to friction losses in large pipelines. They can be calculated using this equation: hm =
KV 2 2g
where hm = minor change K = minor head loss coefficient
Influence of Viscosity on Flowmeter Performance Reynolds number for flow in a pipe. Re =
4Mf Dv = πDv a Kv
where D = pipe diameter v– = average flow velocity Kv = Kinematic viscosity Mf = mass flow va = absolute viscosity
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Specific Heats of Fluids and Gases Specific heat is the amount of energy required to increase the temperature of one unit of mass of a material by one degree. Common units are calories/gram – °C, joules/gram – °C, and BTU/pound – °F. Specific heat is important when computing heat flow from a mass flow measurement and differential temperature. The equation is: Q = W Cp ∆T
where: Q = heat flow rate W = mass flow rate Cp = specific heat ∆T = temperature difference (for example, inlet and outlet of a heater) Liquids have only one form of specific heat (Cp). Gases have two forms: Cp, measured at constant pressure, and Cv, measured at constant volume. The ratio of Cp/Cv is important when designing differential pressure flowmeters for gas flow. Differential pressure meters use an equation based on velocity change. Velocities are inversely proportional to the inlet cross-sectional area and the restriction throat area: Vfr = A 1 v 1 = A 2 v 2
where Vfr = volumetric flow rate A1 and A2 = cross-sectional areas of inlet and throat v1 and v2 = velocities at inlet and throat The preceding equation is true for liquids. Gases, however, will expand due to lower pressure at the throat. As a result, a correction factor, Y, is included in gas flow equations. Called the Gas Expansion Factor, it depends on line pressure, differential pressure, meter geometry and the isentropic exponent for the particular gas at operating conditions.
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Chapter 3/Flow Measurement
Volume Flow Rate Vfr = Av
where Vfr = volumetric flow rate A = area of tube v– = average velocity of fluid Reynolds Numbers Reynolds Number Re =
pvD µ
where Re = Reynolds number p = fluid density v– = average velocity of fluid D = a dimension µ = absolute fluid viscosity
75
Pipe Reynolds Number ReD =
3160VgpmG µcP Din
where ReD = Pipe Reynolds Number Vgpm = volume flow rate, gallons per minute G = liquid specific gravity µcp= fluid viscosity, centipoise Din = inside pipe diameter, inches
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Flowmeter Accuracy Percent of Actual Flow Rate % of Rate = ±
Flow Uncertainty x 100 Instantaneous Flow Rate
Q D1
V1
D2
V2
D3 V3
Total Head v12 Velocity Head
v22 2g
P1
Pressure Head
w
P2 w
Flow
Z2 = Z1 Z1 Datam
Head Due to Elevation
P Head
Pv v
1
2
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Chapter 3/Flow Measurement
Percent of Full Scale Flow % of Full Scale = ±
Flow Uncertainty x 100 Full Scale Flow Rate
Percent of Maximum Differential Pressure (dP) % of Maximum dP = ±
dP Uncertainty x 100 Maximum dP
Compensation of Linear Volumetric Meter Signals Volumetric Flow Q=
(signal) KFt
where Q = the volumetric flow rate K = the factor which scales the signal to flow rate Ft = the thermal expansion of the meter due to temperature Mass Flow W =ρxQ=
(signal )(ρ) KFt
where W = mass flow ρ = fluid density Q = volumetric flow rate K = the factor which scales the signal to flow rate Ft = the thermal expansion of the meter due to temperature Gas Expansion Factor (Y) ∆P Y = 1 − (constant) P
where Y = gas expansion factor ∆P = the differential pressure P = absolute pressure
77
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Compensation of Rotameter Signals
Gases W = K(signal) ρ
Liquids
where W = mass flow K = a flow coefficient ρ = fluid density
ρ W = K (signal) (ρf − ρ) ρ f
where W = mass flow K = a flow coefficient ρ = fluid density ρ = float density f
Average Coefficient Selected by Manufacturer for Meter Total Range
Flowmeter Range
± 5% Rate
± 1% Rate
Meter Coefficient
Recommended Average Coefficient for Actual Flow Range
Flow Range Over Which Meter Will be Used Process Minimum
Process Maximum
Flow Rate Flowmeter Minimum
Flowmeter Maximum
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Compensation for Differential Pressure Meters Fa = 1 + 2α(Tb )
where Fa = expansion factor for meters calibrated at 60°F α = coefficient of expansion of the flow restriction material Tb =base temperature Effect of Fluid Properties on Flowmeter Accuracy Volumetric Meters Change
Liquid
Gas
Density up 1%
-1.0
-1.0
Temp. up to 10°C at -100°C
*
+6.0
Temp. up 10°C at 20°C
+0.2*
+3.4
Temp. up 10°C at 200°C
+.06*
+2.0
Press. up 1 psig at -10 psig
0.0
-20.0
Press. up 1 psig at 0.0 psig
0.0
-7.0
Press. up 1 psig at 35.0 psig
0.0
-2.0
Press. up 1 psig at 85.0 psig
0.0
-1.0
Meter Expansion, T up 100°C
-0.2
-0.2
Meter Factor changes up 1%
+1.0
+1.0
*Values shown are for water; may be higher for other liquids.
Differential Pressure Meters Change
Liquid
Gas
Density up 1%
-0.5
-0.5
Temp. up 10°C at -100°C
*
+3.0
Temp. up 10°C at 20°C
+0.1*
+1.7
Temp. up 10°C at 200°C
+0.6*
+1.0
Press. up 1 psig at -10 psig
0.0
-10.0
Press. up 1 psig at 0.0 psig
0.0
-3.5
Press. up 1 psig at 35.0 psig
0.0
-1.0
Press. up 1 psig at 85.0 psig
0.0
-0.5
Meter Expansion, T up 100°C
-0.2
-0.2
Meter Factor changes up 1%
+1.0
+1.0
*Values shown are for water; may be higher for other liquids.
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Rotameters Change
Liquid
Gas
Density up 1%
-.04
-.05
Temp. up 10°C at -100°C
*
+3.0
Temp. up 10°C at 20°C
+0.2*
+1.7
Temp. up 10°C at 200°C
+0.6*
+1.0
Press. up 1 psig at -10 psig
0.0
-10.0
Press. up 1 psig at 0.0 psig
0.0
-3.5
Press. up 1 psig at 35.0 psig
0.0
-1.0
Press. up 1 psig at 85.0 psig
0.0
-0.5
Meter Expansion, T up 100°C
-0.2
-0.2
Meter Factor changes up 1%
+1.0
+1.0
* Values shown are for water; may be higher for other liquids.
Differential Pressure Flowmeters Differential pressure (DP) flowmeters—also known as “head-type meters”—are widely applied when accurate fluid flow measurements in pipes are required at reasonable costs. DP devices have a flow restriction in the line that causes a differential pressure, or “head,” between the two measurement locations. Of all the head-type meters, the orifice flowmeter is the most widely applied device. Head Type Flowmeter Elements Head type flowmeters are based on the energy exchange which occurs when the flow area changes between the velocity (kinetic) energy and the pressure energy found in the flowing fluid. The
“Bernoulli Equation” states that the total energy in a flowing fluid is conserved after accounting for the mechanical work done by the fluid (such as with a turbine) or on the fluid (by a pump) along with any heat lost or gained from the system. This means that any of the three energy forms normally considered in this context; potential (elevation), kinetic, and pressure can be converted into any of the other forms. The increase in flow velocity is converted into a decrease in the pressure. This pressure difference is called ‘head’ and is used to infer the flow rate. When the flow area returns to the original size then most of the pressure is converted back into velocity except for the losses due to turbulence (see Figure 3-1). The figure is an attempt to show the relationship
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between velocity changes and the resulting pressure pattern. Note the pressure change is proportional to the velocity change squared. This means that at lower flow rates the pressure difference is less sensitive to flow changes. Any analysis of errors must consider the effects of this. The most common head type flow element is the orifice plate (see Figure 3-2). Most commonly this is a round flat plate with a round hole bored in the center. There are several reasons for this: 1. The physics of the orifice plate are well known and there is a large research database.
81
2. The geometry of a sharp edge round orifice in a round plate in a round pipe is easily to replicate and measure. 3. International and national standards exist. 4. Many purchase and custody contracts specify orifice meters. 5. It is inexpensive to make significant changes in the meter calibration by replacing the orifice plate with one of a different bore. The orifice meter can be very accurate, but only if the design, installation, and maintenance are done very well and closely adhere to the
Figure 3-1: Velocity and Pressure Profiles across Orifice Plate
Figure 3-2: Orifice Plate
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standards. For custody transfer (sale) of fluids this is justified. Many other orifice meter applications are used for less demanding applications and are installed with the understanding that uncertainties are increased by compromised but less expensive installation. The key to decisions around this is “the value of the measurement.” The orifice equation, (simplified): Q = d 2 •C • h • ρ
The orifice plate is installed between “orifice flanges” with pressure taps (see Figure 3-3). Orifice installations differ depending on the application and size. Some special orifice fittings allow the orifice plate to be removed and replaced without stopping flow. Note also that even when reporting flow in terms of volume the differential pressure signal is a function of the fluid density and that uncertainty increase as a function of the density uncertainty.
where Q is flow rate d is orifice bore C is the orifice coefficient h is head across orifice ρ flowing fluid density C for the orifice plate is defined in an equation as a complex function of Beta and Reynolds number. An average value of 0.61 can be used for preliminary designs and approximations. This approximation is valid only for Beta ratio (ratio of bore to pipe inside diameter) in the range of 0.2 to 0.5 and for Reynolds numbers between 10,000 and 100,000. For larger bore diameters, larger Beta ratio (β), it is necessary to compensate for the velocity of approach, and the equation used is: 1 2 Q= d •C • h • ρ 1 − β 4 The effect of Beta is less than 5% for Beta less than 0.55.
Figure 3-3: Orifice Plate Installation Other “tappings” are used. “Corner taps” measure the pressures at the faces of the orifice plate. “Radius” or “D, D/2” taps sense the pressures at one pipe diameter upstream and one half pipe diameters downstream. The orifice coefficient is different for each type of tapping. For calculation details, see standards. For mechanical details, see manufacturers’ catalogs.
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The venturi tube (Figure 3-4) is another head meter element shown in the standards. Because the inlet and the outlet provide a smooth change in flow path it has the characteristic of a smaller total pressure loss for a given flow. It is also thought to be less sensitive to wear and to upstream flow disturbances. Most venturis are made to the geometries shown in the standards. A number of standard designs are made and each has a specific flow coefficient. It is more complex to fabricate than a simple orifice run and thus tends to be more expensive. The orifice equations are used with coefficients on the order of 0.9 to 0.98. The flow nozzle (Figure 3-5) is another head type flow element. It is available in a number of constructions. Permanent flow pressure losses are less than for the orifice plate and greater than for a venturi. Most often the designs
83
shown in the standards are used. The orifice equations apply, with the appropriate coefficient. Several standard designs are available.
Figure 3-5: Flow Nozzle Installation
The Pitot tube (Figure 3-6) converts all the velocity energy at one point into pressure head. Since the flow is measured at only one point any variations in the flow pattern
Figure 3-4: Venturi Tube
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across the pipe are not discovered. The Averaging Pitot Tube has multiple sensing points and averages the pressure. The head developed is less than the orifice plate. Some commercial designs have higher coefficients.
A number of other designs for head flow elements are available commercially. See the catalogs. These all are based on the same physics. Some are more tolerant to solids in the flowing stream. At least one design has a body in the stream which moves as the flow changes. Bernoulli’s Equation at Each Flow Cross-section P v2 + + z = constant ρ 2g
Figure 3-6: Pitot Tube The Elbow Meter (Figure 3-7) measures the difference in pressure on the inside radius of an elbow compared to the outside. The differential generated is relatively small unless the velocity and the fluid density are both relatively high.
where P = static pressure (force per unit area) ρ = fluid density v– = average fluid velocity g = acceleration due to gravity z = elevation head of the fluid from a reference datum Incompressible Fluids The relationship between velocity and fluid flows for incompressible fluid in a close conduit is: Q = A1 × v 1 = A2 × v 2
where subscripts refer to sections 1 and 2 Flow Rate for Compressible Fluids
Figure 3-7: Elbow Meter
Particularly for gases, versus liquids, a change in temperature and pressure results in a change in volume, so flow rate units are expressed in actual volume or stan-
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dard volumetric flow rates. In the U.S., cubic foot is the most commonly used unit for gas volume. In ISO 5024 for natural gas or petroleum gas, standard pressure and temperature are 14.696 psia and 59°F (15°C). For ANSI/API 2530 the base pressure and temperature are 14.73 psia and 60°F (15.5°C). Base pressures and temperatures can vary by industry, country, and mutually agreed contractual terms. When gas densities at the flowing condition and base condition are known, flow rates in actual and base conditions are: Q = AC
2gh
where (Qscf)b = flow rate in standard cubic feet per second at the selected base condition Qacfs = volumetric flow rate in actual cubic feet per second ρf = density of fluid at the flowing condition ρb = density of fluid at the base condition
85
Open Channel Flow Measurement Triangular or V-Notch Weir Q = KH 2.5
where Q = flow rate H = head on the weir K = a constant for cfs, K = 2.50 tan
α 2
for mgd, K = 1.62 tan for gpm, K = 1120 tan
α 2 α 2
where α = angle of triangular opening cfs = ft3 per second mgd = million gallons per day gpm = gallon per minute 2Hmax Minimum
Hmax
Flow Rate Through a Hole of a Tank Q = AC
2Hmax Minimum
2gh
where Q = flow rate A = cross-section area of the hole C = flow coefficient (typical 0.60) g = acceleration due to gravity h = height of liquid
Triangular (V-Notch) Sharp Crest Weir
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Minimum Recommended Flow Rates for Triangular Weirs V-Notch Angle
Minimum Head, ft.
cfs
mgd
gpm
22.5°
0.2
0.009
0.006
4.04
30.0°
0.2
0.012
0.008
5.39
45.0°
0.2
0.019
0.012
8.53
60.0°
0.2
0.26
0.017
11.70
90.0°
0.2
0.045
0.029
20.20
120.0°
0.2
0.077
0.050
34.80
Maximum Recommended Flow Rates for Triangular Weirs V-Notch Angle
Maximum Head, ft.
cfs
mgd
gpm
22.5°
2.0
2.81
1.82
1260
30.0°
2.0
3.82
2.47
1710
45.0°
2.0
5.85
3.78
2630
60.0°
2.0
8.16
5.28
3660
90.0°
2.0
14.10
9.14
6330
120.0°
2.0
24.50
15.80
11,000
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Rectangular Weir with End Contractions
2Hmax Minimum
87
L Crest Length
Q = K(L - 0.2H1.5 )
where Q = flow rate H = head on weir L = crest length of weir K = a constant for cfs, Q = 3.33(L - 0.2H)H1.5 for mgd, Q = 2.15(L - 0.2H)H1.5 for gpm, Q = 1500(L - 0.2H)H1.5
Hmax 2Hmax Minimum
L Crest Length
Rectangular Weir W/O End Contractions Q = KLH1.5
where for cfs, Q = 3.33LH1.5 for mgd, Q = 2.15LH1.5 for gpm, Q = 1500LH1.5
Hmax
2Hmax Minimum
Rectangular Sharp-Crested Weir
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Minimum Recommended Flow Rates for Rectangular Weirs with End Contractions Crest Length, ft Minimum Head, ft
cfs
mgd
gpm
1.0
0.2
0.286
0.185
128
1.5
0.2
0.435
0.281
195
2.0
0.2
0.584
0.377
262
2.5
0.2
0.733
0.474
329
3.0
0.2
0.882
0.570
396
4.0
0.2
1.180
0.762
530
5.0
0.2
1.480
0.955
664
6.0
0.2
1.770
1.150
794
8.0
0.2
2.370
1.530
1060
10.0
0.2
2.970
1.920
1330
Maximum Recommended Flow Rates for Rectangular Weirs with End Contractions Crest Length, ft Maximum Head, ft
cfs
mgd
gpm
1.0
0.50
1.06
0.685
476
1.5
0.75
2.92
1.890
1310
2.0
1.00
5.99
3.870
2690
2.5
1.25
10.50
6.770
4710
3.0
1.50
16.50
10.70
7410
4.0
2.00
33.90
21.90
15,200
5.0
2.50
59.20
38.30
26,600
6.0
3.00
93.40
60.40
41,900
8.0
4.00
192.00
124.00
86,200
10.0
5.00
335.00
217.00
150,000
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89
Minimum Recommended Flow Rates for Rectangular Weirs Without End Contractions Crest Length, ft
Minimum Head, ft
cfs
mgd
gpm
1.0
0.2
0.298
0.192
134
1.5
0.2
0.447
0.289
201
2.0
0.2
0.596
0.385
267
2.5
0.2
0.745
0.481
334
3.0
0.2
0.894
0.577
401
4.0
0.2
1.190
0.770
534
5.0
0.2
1.490
0.962
669
6.0
0.2
1.790
1.160
803
8.0
0.2
2.380
1.540
1070
Maximum Recommended Flow Rates for Rectangular Weirs without End Contractions Crest Length, ft
Maximum Head, ft
cfs
mgd
gpm
1.0
0.50
1.18
0.761
530
1.5
0.75
3.24
2.10
1450
2.0
1.00
5.66
4.30
2990
2.5
1.25
11.60
7.52
5210
3.0
1.50
18.40
11.90
8560
4.0
2.00
37.70
24.30
16,900
5.0
2.50
65.80
42.50
29,500
6.0
3.00
140.00
67.10
46,700
8.0
4.00
213.00
138.00
95,600
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Minimum Recommended Flow Rates for Cipolletti Weirs Crest Length, ft
Minimum Head, ft
cfs
mgd
gpm
1.0
0.2
0.301
0.195
135
1.5
0.2
0.452
0.292
203
2.0
0.2
0.602
0.389
270
2.5
0.2
0.753
0.487
338
3.0
0.2
0.903
0.584
405
4.0
0.2
1.200
0.778
539
5.0
0.2
1.510
0.973
678
6.0
0.2
1.810
1.170
812
8.0
0.2
2.410
1.560
1080
10.0
0.2
3.010
1.950
1350
Maximum Recommended Flow Rates for Cipolletti Weirs Crest Length, ft
Minimum Head, ft
cfs
mgd
gpm
1.0
0.50
1.19
0.789
534
1.5
0.75
3.28
2.120
1470
2.0
1.00
6.73
4.350
3020
2.5
1.25
11.80
7.600
5300
3.0
1.50
18.60
12.000
8350
4.0
2.00
38.10
24.600
17,100
5.0
2.50
66.50
43.000
29,800
6.0
3.00
105.00
67.800
47,100
8.0
4.00
214.00
139.000
96,000
10.0
5.00
375.00
243.000
168,000
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Trapezoidal or Cipolletti Weir Q = KLH1.5
91
2Hmax Minimum
where for cfs, Q = 3.37LH1.5 for mgd, Q = 2.18LH1.5 for gpm, Q = 1510LH1.5
Hmax 2Hmax Minimum
Flumes Triangular (V-Notch) Sharp Crest Weir
Q = KH1.5
where Q = flow rate H = head pressure, point Ha n = constant power, dependent on throat width and units K = a constant, dependent on throat width
Discharge Equations for Parshall Flumes (W = Throat Width in Feet) Width
Cubic Feet/ Second
Million Gallon/Day
Gallon/Minute
1 in
Q = 0.338H1.55
Q = 0.3218H1.55
Q = 152H1.55
2 in
Q = 0.676H1.55
Q = 0.437H1.55
Q = 303H1.55
3 in
Q = 0.992H1.547
Q = 0.641H1.547
Q = 445H1.547
6 in
Q = 2.06H1.58
Q = 1.33H1.547
Q = 925H1.58
9 in
Q = 3.07H1.53
Q = 1.98H1.53
Q = 138H1.53
10 to 50 feet
Q= (3.69W+2.5)H1.65
Q= (2.39W+ 1.61)H1.6
Q= (1660W+1120)H1.6
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2/3 A
Ha Hb P
D Flow
W
R
C
H
A
General Flume Configuration
Minimum Recommended Flow Rates for H Flumes H Flume Size, ft
Minimum Head, ft
cfs
mgd
gpm
.50
0.2
0.0004
0.0003
0.180
.75
0.2
0.0006
0.0004
0.269
1.00
0.2
0.0007
0.0005
0.314
1.50
0.2
0.0011
0.0007
0.494
2.00
0.2
0.0014
0.0009
0.628
2.50
0.2
0.0018
0.0012
0.808
3.00
0.2
0.0021
0.0014
0.942
4.50
0.2
0.0031
0.0020
1.390
Maximum Recommended Flow Rates for H Flumes H Flume Size, ft
Minimum Head, ft
cfs
mgd
gpm
.50
0.50
0.375
0.224
156
.75
0.75
0.957
0.619
430
1.00
1.00
1.970
1.270
884
1.50
1.50
5.420
3.500
2430
2.00
2.00
11.100
7.170
4980
2.50
2.50
19.300
12.500
8660
3.00
3.00
30.700
19.800
13,800
4.50
4.50
84.500
54.600
37,900
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93
Minimum Recommended Flow Rates for Trapezoidal Flumes Flume Type
Minimum Head, ft
cfs
mgd
gpm
Large 60° V
0.14
0.010
0.006
4.37
2 in., 45° WSC
0.10
0.023
0.015
10.30
12 in., 45° SRCRC
0.20
0.160
0.103
71.80
Maximum Recommended Flow Rates for Trapezoidal Flumes Flume Type
Minimum Head, ft
cfs
mgd
gpm
Large 60° V
0.45
0.198
0.128
88.8
2 in., 45° WSC
0.77
1.820
1.180
817.0
12 in., 45° SRCRC
1.29
7.080
4.580
3180.0
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Target Flowmeters Mass Flow Rate in Terms of Target Force D − d τ2 π ρFτ x 2 d
M = (constant) x = (constant) x
1 − Bτ2 π PFτ x D 2 Bτ
= KD ρFτ
where F = target force ρ = fluid density D, dτ = pipe and target diameters, respectively K = constant that includes target blockage Bτ = d τ D Pipe
Target
d D
Force
Idealized Flow Streamlines Past a Circular Disc
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95
Rate of Heat Loss Flowmeter ∆T
qt = ∆T [k + 2(kCv ρπdv )1 / 2 ]
where qt = rate of heat loss per unit time ∆T = mean temperature elevation of wire d = diameter of wire k = thermal conductivity of fluid stream Cv = specific heat of fluid stream at constant volume ρ = density of fluid stream v = average velocity of fluid stream
H T2
T1 Thomas Flowmeter
T1
T2
H
Laub Flowmeter
Temperature Rise Flowmeter H W = ∆T * Cp
where W = mass flow H = heat(power) input ∆T = temperature change Cp = specific heat at constant temperature
Thermocouple
AC DC AC
+ +
Rate of Heat Loss Flowmeter
Flow Out
Section 2 Float Tube Section 1 Flow In
Fundamental Operation of a Variable Area Flowmeter
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Typical Range of Tube Flow Rates Size Inches
Water
Air
1/8
0.5-200 cc/min
50-7500 scc/min
1/4
100-2000 cc/min
4000-34000 scc/min
3/8
0.13-0.55 gpm
0.75-2.4 scfm
1/2
0.25-4.0 gpm
1-20 scfm
3/4
1.9-5.0 gpm
8-20 scfm
1
4.0-20 gpm
20-45 scfm
1 1/2
9.0-50 gpm
38-112 scfm
Typical Pressure Ratings for Glass Tube Meters Size Inches
psig
kPa
1/16-1/4
250-500
1724-3448
1/2
300
2069
3/4
200
1379
1
180
1241
1 1/2
130
896
2
100
690
3
70
483
Note: 1/16 to 1/2 in. glass tube meters with ANSI class 150 flanged connections would be limited to a rating of 270 psig (1826 kPa) at 100°F by the ANSI code rating. Warning: Do not use glass in hazardous applications. Derate gas pressure ratings due to damage and deterioration in use. Even a very small scratch on the end of a glass tube increases the chance of breakage due to stress and leads to failures.
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Magnetic Flowmeters Because they have no protrusions into the flow stream, magnetic flowmeters offer the advantage of not obstructing flow – unless their size is less than that of the pipeline itself. Improvements in ease-ofuse/installation and reduced costs have made miniature DC magnetic flowmeters more popular.
Principle of Operation: Faraday’s Law of Electromagnetic Induction is the underlying principle of many electrical devices and also applied to electrical power generation. It states that the magnitude of the voltage induced in a conductive medium moving through a magnetic field, and at a right angle to the field, is directly proportional to the product of the magnetic flux density (B), the velocity of the medium (v–), and path length (L) between the probes. E = constant x B x L x v
97
Magnetic flowmeters apply Faraday’s law, as follows: when a conductive liquid passes through a homogenous field, a voltage is generated along a path between two electrodes positioned within the magnetic field on opposite sides of the pipe. The path length is the distance between the two electrodes. If the magnetic field (B) is constant and the distance (D) between the electrodes is fixed, the induced voltage is directly propor–) of the liquid. tional to the velocity (v E = constant x B x D x v For a more detailed explanation of magnetic flowmeters, see ISA’s book, Industrial Flow Measurement, 3rd Edition, edited by David W. Spitzer.
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Electrical Conductivity of Aqueous Solutions, in Microsiemens/cm Chemical Name
Formula
Temp., °C Conductivity in Microsiemens/ cm
Acetic Acid
CH3CO2H
18
1.08 x 103 4.00 x 10-2*
Ammonia
NH3
15
8.67 x 102 1.93 x 102
Calcium Chloride
CaCl2
18
6.43 x 104 1.37 x 105
Hydrochloric Acid
HCl
15
3.95 x 105 6.62 x 105
Hydrofluoric Acid
HF
18
1.98 x 104 3.41 x 105
Nitric Acid
HNO3
18
3.12 x 105 4.90 x 105
Phosphoric Acid
H3PO4
15
5.66 x 104 9.79 x 104
Sodium Carbonate
Na2CO3
18
4.51 x 104 8.36 x 104
Sodium Hydroxide
NaOH
18
4.65 x 104 8.20 x 104
Sulfuric Acid
H2SO4
18
2.09 x 105 1.07 x 105
*Conductivity too low for magnetic flowmeter
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99
Electrical Conductivity of Pure Liquids Chemical Name
Temp., °C
Conductivity in Microsiemens/cm
Carbon Tetrachloride
18
4.0 x 10-2*
Ethyl Alcohol
25
0.0013*
Furfural
25
1.5**
Glycol
25
0.3**
Methyl Alcohol
18
0.44**
*Conductivity too low for magnetic flowmeter **Low conductivity application
Conductivities of Miscellaneous Liquids Name
Temp., °C
Conductivity in Microsiemens/cm
Black Liquor
93
5000
Fuel Oil
–
<10-7*
Water, New York City
25
72
*Conductivity too low for magnetic flowmeter
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Ultrasonic Flowmeters Primarily a flowmeter technology for liquid and some gas applications, ultrasonic flowmeters use acoustic waves, or vibrations, to measure flow traveling through a pipeline. Some designs permit measurements external to the pipe, while other designs require the sensor to be in contact with the flowstream. Doppler and TransitTime are two of the more popular ultrasonic flowmeter types.
Principle of Operation – Doppler Flowmeter: In 1842, the Austrian physicist Christian Johann Doppler first predicted frequencies of received sound waves depend on the motion of the source, relative to the receiver. For example, an approaching fire engine’s siren sounds higher pitched than after the siren passes by. That’s because an approaching fire engine’s velocity packs the sound waves more closely together, while the sound waves move further apart as the fire engine speeds away. To measure flow in a pipe, one transducer typically transmits an ultrasonic beam of approximately 0.5 MHz into the flow stream of a liquid containing sonically reflective materials such as solid particles or bubbles. These moving materials alter the frequency of the beam received at a second transducer. The frequency can be used to develop an analog or digital signal proportional to flow rate.
Basic equations for a Doppler flowmeter are: ∆f = 2fT sinθ
VF VS
Snell’s law: SinθT Sinθ = VT VS Therefore: VF =
VT ∆f X = K ∆f fT SinθT
where: VT = Sonic velocity of transmitter material θT = Angle of transmitter sonic beam K = Calibration factor VF = Flow velocity ∆F = Doppler frequency change VS = Sonic velocity of fluid fT = Trasmitted frequency θ = Angle of fT entry in liquid Principle of Operation – Transit-Time Flowmeter: Also called “time of flight” and “time of travel,” transit-time flowmeters measure the difference in travel time between pulses transmitted along and against the fluid flow. Pulses are typically beamed at a 45° angle in the pipe, with one clamp-on transducer located upstream of the other. Each transducer alternately transmits and receives bursts of ultrasonic energy. The difference in the transit times in the upstream (TU) versus
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the downstream (TD) directions can be used to calculate the flow through the pipe. TU =
L CO − VF cos θ
TD =
L CO + VF cos θ
VF =
k ⋅ (TU − TD ) TU ⋅TD
where: TU = Upstream transit time TD = Downstream transit time VF = Liquid flow velocity CO = Velocity of sound in fluid. Flow Equations for Sizing Control Valves ANSI/ISA–75.01.01–2002 (IEC 60534-2-1 Mod) Scope ANSI/ISA-75.01.01-2002 includes equations for predicting the flow coefficient of compressible and incompressible fluids through control valves. The equations for incompressible flow are based on standard hydrodynamic equations for Newtonian incompressible fluids. They are not intended for use when non-Newtonian fluids, fluid mixtures, slurries, or liquid-solid conveyance systems are encountered. At very low ratios of pressure differential to absolute inlet pressure (∆P/P1), compressible fluids
101
behave similarly to incompressible fluids. Under such conditions, the sizing equations for compressible flow can be traced to the standard hydrodynamic equations for Newtonian incompressible fluids. However, increasing values of ∆P/P1 result in compressibility effects that require that the basic equations be modified by appropriate correction factors. The equations for compressible fluids are for use with gas or vapor and are not intended for use with multiphase streams such as gas-liquid, vapor-liquid or gassolid mixtures. For compressible fluid applications, this part of ANSI/ISA75.01.01-2002 is valid for all valves. However, manufacturers of some valves with xT ≥ 0.84 have reported minor inaccuracies. Caution must also be exercised when applying the equations for compressible fluids to gaseous mixtures of compounds, particularly near phase boundaries. The accuracy of results computed with the equations in this standard will be governed by the accuracy of the constituent coefficients and the process data supplied. Methods of evaluating the coefficients used in the equations presented here are given in ANSI/ISA-75.02-1996. The stated accuracy associated with the coefficients in that document is ± 5% when Cv/d2 <0.047 N18. Reasonable accuracy can only be maintained for control valves if Cv/d2 <0.047 N18.
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Symbols Symbol Description
C CI d D D1 D2 Do Fd FF FL
Flow coefficient (Kv, Cv)
FLP
Combined liquid pressure recovery factor and piping geometry factor of a control valve with attached fittings
FP FR Fγ Gg
Piping geometry factor
M N P1 P2 PC Pr Pv ∆P
Molecular mass of flowing fluid
Q Rev T1 Tc Tr
Volumetric flow rate (see note 5)
Assumed flow coefficient for iterative purposes Nominal valve size Internal diameter of the piping Internal diameter of upstream piping Internal diameter of downstream piping Orifice diameter Valve style modifier Liquid critical pressure ration factor Liquid pressure recovery factor of a control valve without attached fittings
Reynolds number factor Specific heat ratio factor Gas specific gravity (ratio of density of flowing gas to density of air with both at standard conditions, which is considered in this practice to be equal to the ratio of the molecular weight of gas to molecular weight of air Numerical constants Inlet absolute static pressure measured at point A Outlet absolute static pressure measured at point B Absolute thermodynamic critical pressure Reduced pressure (P1,P2) Absolute vapor pressure of the liquid at inlet temperature Differential pressure between upstream and downstream pressure taps (P1 - P2) Valve Reynolds number Inlet absolute temperature Absolute thermodynamic critical temperature Reduced temperature (T1/Tc)
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103
ts W x xT
Absolute reference temperature for standard cubic meter
xTP
Pressure differential ratio factor of a control valve with attached fittings at choked flow
Y Z ν ρ1 ρ1ρ0 γ ζ
Expansion Factor
ζ1 ζ2 ζB1 ζB2 Note 1
Upstream velocity head loss coefficient of fitting
Note 2
1 bar = 102 kPa = 105 Pa
Note 3
1 centistoke = 10-6 m2/s
Note 4
These values are travel-related and should be stated by the manufacturer.
Note 5
Volumetric flow rates in cubic meters per hour, identified by the symbol Q, refer to standard conditions. The standard cubic meter is taken at 1013.25 mbar and either 273 K or 288 K (see Table 1).
Mass flow rate Ration of pressure differential to inlet absolute pressure (∆P/ P1) Pressure differential ratio factor of a control valve without attached fittings at choked flow
Compressibility factor Kinematic viscosity Density of fluid at P1 and T1
Relative density (ρ1ρ0 = 1.0 for water at 15°C) Specific heat ratio Velocity head loss coefficient at a reducer, expander or other fitting attached to a control valve or valve trim Downstream velocity head loss coefficient of fitting Inlet Bernoulli coefficient Outlet Bernoulli coefficient To determine the units for the numerical constants, dimensional analysis may be performed on the appropriate equations using the units given in Table 1
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Normative references
Definitions
The following normative documents contain provisions which, through reference in this text, constitute provisions of this part of ANSI/ISA-75.01.01-2002. All normative documents are subject to revision, and parties to agreements based on this part of ANSI/ISA75.01.01-2002 are encouraged to investigate the possibility of applying the most recent editions of the normative documents indicated below. Members of IEC and ISO maintain registers of currently valid International Standards.
For the purpose of ANSI/ISA75.01.01-2002, definitions given in IEC 60534-2-1 apply with the addition of the following:
IEC 60534-1:1987, Industrialprocess control valves – Part 1: Control valve terminology and general considerations IEC 60534-2-3:1997, Industrialprocess control valves – Part 2: Flow capacity – Section 3: Test procedures ANSI/ISA-75.02-1996, Control Valve Capacity Test Procedures ANSI/ISA-75.05.01-2001, Control Valve Terminology /1
Pressure tap
Flow
3.1 valve style modifier Fd the ratio of the hydraulic diameter of a single flow passage to the diameter of a circular orifice, the area of which is equivalent to the sum of areas of all identical flow passages at a given travel. It should be stated by the manufacturer as a function of travel. Installation In many industrial applications, reducers or other fittings are attached to the control valves. The effect of these types of fittings on the nominal flow coefficient of the control valve can be significant. In sizing control valves, using the relationships presented herein, the flow coefficients calculated are assumed to include all head losses between points A and B, as shown below.
/2
Pressure tap
B
A
Control valve with or without fittings /1 = two nominal pipe diameters /2 = six nominal pipe diameters
Reference pipe section for sizing
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105
Sizing equations for incompressible fluids
The flow coefficient shall be determined as follows:
The equations listed below identify the relationships between flow rates, flow coefficients, related installation factors, and pertinent service conditions for control valves handling incompressible fluids. Flow coefficients may be calculated using the appropriate equation selected from the ones given below.
Eq. 2 C =
Turbulent flow
Choked turbulent flow without attached fittings [Applicable if ] ∆P ≥ (FLP / FP )2 (P1 − FF Pv )
The equations for the flow rate of a Newtonian liquid through a control valve when operating under nonchoked flow conditions are derived from the basic formula as given in IEC 60534-2-1.
Non-choked turbulent flow Non-choked turbulent flow without attached fittings: [Applicable if ∆P < F 2 (P1 − FF Pv ) ] L The flow coefficient shall be determined by Eq. 1
C = N1
ρ1 / ρ0 ∆P
NOTE 1: The numerical constant N1 depends on the units used in the general sizing equation and the type of flow coefficient: Kv or Cv.
Non-choked turbulent flow with attached fittings [Applicable if ] ∆P < (FLP / FP )2 (P1 − FF Pv )
Q N1FP
ρ1 / ρ2 ∆P
Choked turbulent flow The maximum rate at which flow will pass through a control valve at choked flow conditions shall be calculated from the following equations:
The flow coefficient shall be determined as follows: Eq. 3
C=
Q N1FL
ρ1 / ρ0 P1 − FF Pv
Choked turbulent flow with attached fittings [Applicable if ∆P ≥ (FLP / FP )2 (P1 − FF Pv )
]
The following equation shall be used to calculate the flow coefficient: Eq. 4
C=
Q N1FLP
ρ1 / ρ0 P1 − FF Pv
Non-turbulent (laminar and transitional) flow The equations for the flow rate of a Newtonian liquid through a control valve when operating under nonturbulent flow conditions are
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derived from the basic formula as given in IEC 60534-2-1. This equation is applicable if Rev < 10,000.
Non-turbulent flow without attached fittings The flow coefficient shall be calculated as follows: Eq. 5
C=
Q N1FR
ρ1 / ρ0 ∆P
Non-turbulent flow with attached fittings For non-turbulent flow, the effect of close-coupled reducers or other flow disturbing fittings is unknown. While there is no information on the laminar or transitional flow behavior of control valves installed between pipe reducers, the user of such valves is advised to utilize the appropriate equations for line-sized valves in the calculation of the FR factor. This should result in conservative flow coefficients since additional turbulence created by reducers and expanders will further delay the onset of laminar flow. Therefore, it will tend to increase the respective FR factor for a given valve Reynolds number.
ids. Flow rates for compressible fluids may be encountered in either mass or volume units and thus equations are necessary to handle both situations. Flow coefficients may be calculated using the appropriate equations selected from the following. The flow rate of a compressible fluid varies as a function of the ratio of the pressure differential to the absolute inlet pressure (∆P/P1), designated by the symbol x. At values of x near zero, the equations in this section can be traced to the basic Bernoulli equation for Newtonian incompressible fluids. However, increasing values of x result in expansion and compressibility effects that require the use of appropriate factors. Turbulent flow:
Non-choked turbulent flow Non-choked turbulent flow without attached fittings [Applicable if x
C=
Eq. 7
C=
Sizing equations for compressible fluids The equations listed below identify the relationships between flow rates, flow coefficients, related installation factors, and pertinent service conditions for control valves handling compressible flu-
W N 6Y xP1 ρ1 W N 8P1Y
T1Z xM
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Eq. 8a C =
Q N 9FP P1Y
Q Eq. 8b C = N 7P1Y
MT1Z x GgT1Z
107
The flow coefficient shall be calculated from one of the following equations: Eq. 12 C =
x
W 0.667N6 Fγ xT P1ρ1
Non-choked turbulent flow with attached fittings [Applicable if x < Fγ xTP]
Eq. 13 C =
T1Z W 0.667N 8P1 Fγ x1M
The flow coefficient shall be determined from one of the following equations:
Eq. 14a C =
MT1Z Q 0.667N 9P1 Fγ xT
Eq. 14b C =
GgT1Z Q 0.667N 7P1 Fγ xT
Eq. 9
C=
W N6FPY xP1ρ1
Eq. 10 C =
W N 8FP P1Y
T1Z xM
Eq. 11a C =
Q N 9FP P1Y
MT1Z x
Eq. 11b C =
Q N 7FP P1Y
GgT1Z x
Choked turbulent flow with attached fittings [Applicable if x ≥ Fγ xTP] The flow coefficient shall be determined using one of the following equations: Eq. 15 C =
Choked turbulent flow The maximum rate at which flow will pass through a control valve at choked flow conditions shall be calculated as follows:
Choked turbulent flow without attached fittings [Applicable if x ≥ Fγ xT]
W 0.667N6FP Fγ xTP P1ρ1
Eq. 16 C =
T1Z W 0.667N 8FP P1 Fγ xTP M
Eq. 17a C =
MT1Z Q 0.667N 9FP P1 Fγ xTP
Eq. 17b C =
GgT1Z Q 0.667N 7FP P1 Fγ xTP
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Non-turbulent (laminar and transitional) flow The equations for the flow rate of a Newtonian fluid through a control valve when operating under nonturbulent flow conditions are derived from the basic formula as given in IEC 60534-2-1. These equations are applicable if Rev < 10,000 (see Equation 28). In this subclause, density correction of the gas is given by (P1 + P2)/2 due to nonisentropic expansion. Non-turbulent attached fittings
flow
without
The flow coefficient shall be calculated from one of the following equations: Eq. 18 C =
W N 27FR
T1 ∆P (P1 + P2 )M
Eq. 19 C =
Q N 22FR
MT1 ∆P (P1 + P2 )
Non-turbulent flow with attached fittings For non-turbulent flow, the effect of close-coupled reducers or other flow-disturbing fittings is unknown. While there is no information on the laminar or transitional flow behavior of control valves installed between pipe reducers, the user of such valves is advised to utilize the appropriate equations for line-sized valves in the calculation of the FR
factor. This should result in conservative flow coefficients since additional turbulence created by reducers and expanders will further delay the onset of laminar flow. Therefore, it will tend to increase the respective FR factor for a given valve Reynolds number.
Determination of Correction Factors Piping geometry factor (FP) The piping geometry factor (FP) is necessary to account for fittings attached upstream and/or downstream to a control valve body. The FP factor is the ratio of the flow rate through a control valve installed with attached fittings to the flow rate that would result if the control valve was installed without attached fittings and tested under identical conditions which will not produce choked flow in either installation. To meet the accuracy of the FP factor of ±5%, the FP factor shall be determined by test in accordance with ANSI/ISA-75.021996. When estimated values are permissible, the following equation shall be used: Eq. 20 FP =
1 Σξ C1 1+ N 2 d 2
2
In this equation, the factor Σ ξ is the algebraic sum of all of the effective velocity head loss coefficients of all
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fittings attached to the control valve. The velocity head loss coefficient of the control valve itself is not included. Eq. 21
∑ ξ = ξ1 + ξ2 + ξB1 − ξB 2
In cases where the piping diameters approaching and leaving the control valve are different, the ξB coefficients are calculated as follows: Eq. 22
d ξB = 1 − D
4
If the inlet and outlet fittings are short-length, commercially available, concentric reducers, the ξ1 and ξ2 coefficients may be approximated as follows: Eq. 23 Inlet reducer: d 2 ξ1 = 0.5 1 − D1
2
Eq. 24 Outlet reducer (expander): d 2 ξ1 = 1.0 1 − D2
109
tion requires iteration. Proceed by calculating the flow coefficient C for non-choked turbulent flow. NOTE: Choked flow equations and equations involving FP are not applicable. Next, establish C1 as follows: Eq. 26 C1 = 1.3C Using C1 from Equation 26, determine FP from Equation 20. If both ends of the valve are the same size, FP may instead be determined from Figure 2. Then, determine if Eq. 27
C ≤ C1 FP
If the condition of Equation 27 is satisfied, then use the C1 established from Equation 26. If the condition of Equation 27 is not met, then repeat the above procedure by again increasing C1 by 30%. This may require several iterations until the condition required in Equation 27 is met.
2
Reynolds Number Factor (FR)
Eq. 25 Inlet and outlet reducers of equal size: d 2 ξ1 + ξ2 = 1.5 1 − D
2
The FP values calculated with the above ξ factors generally lead to the selection of valve capacities slightly larger than required. This calcula-
The Reynolds number factor FR is required when non-turbulent flow conditions are established through a control valve because of a low pressure differential, a high viscosity, a very small flow coefficient, or a combination thereof. The FR factor is determined by dividing the flow rate when non-turbulent flow conditions exist by the flow rate measured in the same installation under turbulent conditions.
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Liquid Pressure Recovery Factors (FL) or (FLP) Liquid pressure recovery factor without attached fittings (FL) FL is the liquid pressure recovery factor of the valve without attached fittings. This factor accounts for the influence of the valve internal geometry on the valve capacity at choked flow. It is defined as the ratio of the actual maximum flow rate under choked flow conditions to a theoretical, non-choked flow rate which would be calculated if the pressure differential used was the difference between the valve inlet pressure and the apparent vena contracta pressure at choked flow conditions. The factor FL may be determined from tests in accordance with ANSI/ISA-75.02-1996. Combined liquid pressure recovery factor and piping geometry factor with attached fittings (FLP) FLP is the combined liquid pressure recovery factor and piping geometry factor for a control valve with attached fittings. It is obtained in the same manner as FL . To meet a deviation of ±5% for FLP, FLP shall be determined by testing. When estimated values are permissible, the following equation shall be used: FL
FLP = 1+
2
FL C (∑ ξ1) 2 d N2
2
Here Σξ1 is the velocity head loss coefficient, ξ1 + ξB1, of the fitting attached upstream of the valve as measured between the upstream pressure tap and the control valve body inlet.
Liquid critical pressure ratio factor (FF) FF is the liquid critical pressure ratio factor. This factor is the ratio of the apparent vena contracta pressure at choked flow conditions to the vapor pressure of the liquid at inlet temperature. At vapor pressures near zero, this factor is 0.96. Values of FF may be approximated from the following equation: FL
FLP = 1+
FL 2 C (∑ ξ1) 2 d N2
2
Expansion Factor Y The expansion factor Y accounts for the change in density as the fluid passes from the valve inlet to the vena contracta (the location just downstream of the orifice where the jet stream area is a minimum). It also accounts for the change in the vena contracta area as the pressure differential is varied. Theoretically, Y is affected by all of the following: a) ratio of port area to body inlet area; b) shape of the flow path; c) pressure differential ratio x ;
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d) Reynolds number; and e) specific heat ratio γ. The influence of items a), b), c), and e) is accounted for by the pressure differential ratio factor xT, which may be established by air test. The Reynolds number is the ratio of inertial to viscous forces at the control valve orifice. In the case of compressible flow, its value is generally beyond the range of influence, except where the flow rate or the CV is very low or a combination of both exist. The pressure differential ratio xT is influenced by the specific heat ratio of the fluid.
Y may be calculated using the following equation: Y = 1−
x 3FT xT
The value of x for calculation purposes shall not exceed FγXT. If x > FγXT, then the flow becomes choked and Y = 0.667.
Pressure Differential Ratio Factor (xT) or (xTP). Pressure differential ratio factor without fittings (xT) xT is the pressure differential ratio factor of a control valve installed without reducers or other fittings. If the inlet pressure P1 is held constant and the outlet pressure P2 is progressively lowered, the mass flow rate through a valve will
111
increase to a maximum limit, a condition referred to as choked flow. Further reductions in P2 will produce no further increase in flow rate. This limit is reached when the pressure differential x reaches a value of FγXT. The limiting value of x is defined as the critical differential pressure ratio. The value of x used in any of the sizing equations and in the relationship for Y shall be held to this limit even though the actual pressure differential ratio is greater. Thus, the numerical value of Y may range from 0.667, when x = FγXT, to 1.0 for very low differential pressures. The values of xT may be established by air test. The test procedure for this determination is covered in ANSI/ISA-75.02-1996.
Pressure differential ratio factor with attached fittings (xTP) If a control valve is installed with attached fittings, the value of xT will be affected. To meet a deviation of ±5% for xTP , the valve and attached fittings shall be tested as a unit. When estimated values are permissible, the following equation shall be used: xT FP
xTP = 1+
xT ξi C1 2 N5 d 2
NOTE: Values for N5 are given in Table 1 at end of Flow chapter, page 113.
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In the above relationship, xT is the pressure differential ratio factor for a control valve installed without reducers or other fittings. ξ1 is the sum of the inlet velocity head loss coefficients (ξ1 + ξB1) of the reducer or other fitting attached to the inlet face of the valve. If the inlet fitting is a short-length, commercially available reducer, the value of ξ may be estimated using Equation 23.
Specific Heat Ratio Factor Fγγ The factor xT is based on air near atmospheric pressure as the flowing fluid with a specific heat ratio of 1.40. If the specific heat ratio for the flowing fluid is not 1.40, the factor Fγ is used to adjust xT . Use the following equation to calculate the specific heat ratio factor: Fγ =
γ 1.40
Compressibility Factor Z Several of the sizing equations do not contain a term for the actual density of the fluid at upstream conditions. Instead, the density is inferred from the inlet pressure and temperature based on the laws of ideal gases. Under some conditions, real gas behavior can deviate markedly from the ideal. In these cases, the compressibility factor Z shall be introduced to compensate for the discrepancy. Z is a function of both the reduced pressure and reduced temperature (see appropriate reference books to deter-
mine Z ). Reduced pressure Pr is defined as the ratio of the actual inlet absolute pressure to the absolute thermodynamic critical pressure for the fluid in question. The reduced temperature Tr is defined similarly. That is Pr =
P1 PC
Tr =
T1 TC
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113
Table 1 - Numerical constants N Flow coefficient C
Formulae unit
∆P P,∆
ρ
T
d, D
ν
gpm
kPa bar psia
kg/m3 kg/m3 lbm/ft3
-
-
-
-
-
-
-
mm in
-
-
m3/h gpm scfh
-
-
-
-
m2/s cS cS
-
-
-
-
-
mm in
-
2.73 kg/h 2.73 x 101 kg/h 6.33 101 lbm/h 4.17 m3/h 4.17 x 102 m3/h scfh 1.36 x 103
kPa bar psia kPa bar psia
kg/m3 kg/m3 lbm/ft3 -
-
-
-
-
kPa bar psia
-
K K R
-
-
W
Q
1
-
m3/h m3/h
N2
1.60 x 10-3
2.14 x 10-3 8.90 x 102
-
N4
7.07 x 10-2 7.60 x 10-2 1.73 x 104 2.153 x 103
N5
1.80 x 10-3 2.41 x 10-3 1.00 x 103
N6
3.16 3.16 x 101
Constant
Kv
Cv
N1
1 x 10-1
8.65 x 10-2 8.65 x 10-1
1
N7 4.82 (t = 15.6°C) 4.82 x 102 N8
1.10 1.10 x 102
9.48 x 10-1 kg/h 9.48 x 101 kg/h 1.93 101 lbm/h
N9 (t = 0°C)
2.46 x 101 2.46 x 103
2.12 x 101 2.12 x 103 6.94 x 103
-
m3/h m3/h scfh
kPa bar psia
-
K K R
-
-
N9 2.60 x 101 (ts = 15°C) 2.60 x 103
2.25x 101 2.25 x 103 7.32 x 103
-
m3/h m3/h scfh
kPa bar psia
-
K K R
-
-
N18
8.65 x 10-1
1.00 6.45 x 102
-
-
-
-
-
mm in
-
N19
2.5
2.3 9.06 x 10-2
-
-
-
-
-
mm in
-
N22 (ts = 0°C)
1.73 x 101 1.73 x 103
1.50 x 101 1.50 x 103 4.92 x 103
-
m3/h m3/h scfh
kPa bar psia
-
K K R
-
-
N22 1.84 x 101 (ts = 15°C) 1.84 x 103
1.59 x 101 1.59 x 103 5.20 x 103
-
m3/h m3/h scfh
kPa bar psia
-
K K R
-
-
7.75 x 10-1 6.70 x 10-1 kg/h 7.75 x 10-1 6.70 x 10-1 kg/h 1.37 x 101 lbm/h
-
kPa bar psia
-
K K R
-
-
1.40 x 102
-
-
-
-
mm in
-
N27 (ts = 0°C) N32
1.27 x 102 1.70 x 101
-
NOTE: Use of the numerical constants provided in this table together with the practical metric and U.S. units specified in the table will yield flow coefficients in the units in which they are defined.
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Table 2 - Physical Contants1) Symbol
M
γ
Fγ
Acetylene
C2H2
26.04
1.30
0.929
Air
NH3
28.97
1.40
17.03
1.32
39.948
Benzene
A C6H6
Isobutane
C4H9
n-Butane
Pc2)
Tc3)
6,140
309
1.000
3,771
133
0.943
11,400
406
1.67
1.191
4,870
151
78.11
1.12
0.800
4,924
562
58.12
1.10
0.784
3,638
408
C4H10
58.12
1.11
0.793
3,800
425
Isobutylene
C4H8
56.11
1.11
0.790
4,000
418
Carbon dioxide
CO2
44.01
1.30
0.929
7,387
304
Carbon monoxide
CO Cl2
28.01
1.40
1.000
3,496
133
70.906
1.31
0.934
7,980
417
Ethane
C2H6
30.07
1.22
0.871
4,884
305
Ethylene
C2H4
28.05
1.22
0.871
5,040
283
Fluorine
F2
18.998
Gas or vapor
Ammonia Argon
Chlorine
1.36
0.970
5,215
144
Freon 11 (trichloromonofluormethane)
CCl3F
137.37
1.14
0.811
4,409
471
Freon 12
(dichlorodifluoromethane)
CCl2F2 120.91
1.13
0.807
4,114
385
Freon 13
(chlorotrifluoromethane)
CClF
104.46
1.14
0.814
3,869
302
(chlorodifluoromethane)
CHClF2
80.47
1.18
0.846
4,977
369
1.66
1.186
,229
5.25
1.05
0.750
2,736
540
1.41
1.007
1,297
33.25
Freon 22 Helium
n-Heptane
He C7H16
Hydrogen
H2
Hydrogen chloride
HCl
36.46
1.41
1.007
8,319
325
Hydrogen fluoride
HF CH4
20.01
0.97
0.691
6,485
461
16.04
1.32
0.943
4,600
191
CH3Cl
50.49
1.24
0.889
6,677
417
-
17.74
1.27
0.907
4,634
203
Neon
Ne
20.179
1.64
1.171
2,726
44.45
Nitric oxide
NO N2
63.01
1.40
1.000
6,485
180
28.013
1.40
1.000
3,394
126
Octane
C8H18
114.23
1.66
1.186
2,513
569
Oxygen
O2
32.00
1.40
1.000
5,040
155
Pentane
C5H12
72.15
1.06
0.757
3,374
470
Propane
C3H8
44.10
1.15
0.821
4,256
370
Propylene
C3H6
42.08
1.14
0.814
4,600
365
Methane Methyl chloride Natural gas 4)
Nitrogen
4.003 100.20 2.016
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Chapter 3/Flow Measurement
115
Saturated steam
-
18.016
1.25 1.32 4)
0.893 0.943 4)
22,119
647
Sulphur dioxide
SO2
64.06
1.26
0.900
7,822
430
-
18.016
1.315
0.939
22,119
647
Superheated steam
1) Constants are for fluids (except for steam) at ambient temperature and atmospheric
pressure. 2) Pressure units are kPa (absolute). 3) Temperature units are in K. 4) Representative values; exact characteristics require knowledge of exact constituents.
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ISA Handbook of Measurement Equations and Tables
An ‘Old Timer’s’ Tips for Approximate Plant Calculations Cullen Langford, a self-described “Old Timer”, who provided considerable help with the Head Type Flowmeter Elements, portion of this chapter, has generously agreed to share with ISA Handbook readers the “approximate plant calculations, for preliminary design and checking” shown below. Dr. Langford advises that readers use them with care, however, because “these are valid only for normal situations.” Units, definitions W, pph
P, psi
h inwc
ρ, Lb/cuft
R=19.316
g=grav, 32.16 ft/s2
m, mol wt
D or d, inches
v, ft/s
Valve not corrected for fittings, choking, etc. Cv = W /(63.2 • ∆P • ρ )
W = 63.2 • Cv • ∆P • ρ
Orifice, approximate discharge coefficient Cd,=0.61 for 0.2<β<0.55 and 10,000
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Chapter 3/Flow Measurement
117
Hydraulic Horse Power, the power to pump, or the power lost to turbulence. HP = W • psid / (946 • ρ ) Hydraulic Head: in feet of fluid head H = v 2 / 2g K 0 = C 0 + 273.16
R 0 = F 0 + 459.69
Absolute temperature Gas Density, T in K, p in psia
ρ = mP / R • T
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4 Temperature Measurement
Principles of Temperature – ITS-90. . . . . . . . . . . . . . . . . . . . . . . . . . 121 Comparative Characteristics of Thermometers . . . . . . . . . . . . . . . 122 Temperature Differences Between ITS-90, IPTS-68 and EPT-76 . . 123 Temperature Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Temperature Conversion Equations . . . . . . . . . . . . . . . . . . . . . . . . . 125 Steady-State Heat Transfer Analysis . . . . . . . . . . . . . . . . . . . . . . . . 127 Convective Heat Transfer Coefficients . . . . . . . . . . . . . . . . . . . . . . . 127 °F to °C Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Temperature Conversion Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 °F to Kelvin Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 °C to °F Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Thermocouples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Thermocouple Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Type E – Thermoelectric Voltage in mV. . . . . . . . . . . . . . . . . . . . 139 Type J – Thermoelectric Voltage in mV . . . . . . . . . . . . . . . . . . . . 141 Type K – Thermoelectric Voltage in mV. . . . . . . . . . . . . . . . . . . . 143 Type T – Thermoelectric Voltage in mV. . . . . . . . . . . . . . . . . . . . 145 Limits of Error for Thermocouples. . . . . . . . . . . . . . . . . . . . . . . . 147 Upper Temperature Limits for Protected Thermocouples . . . . . 147 RTDs (Resistive Temperature Detectors) . . . . . . . . . . . . . . . . . . . . . 147 RTD Material Resistivity Levels . . . . . . . . . . . . . . . . . . . . . . . . . . 148 Resistance Versus Temperature for Platinum . . . . . . . . . . . . . . . 149
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Wheatstone Bridge – Effect of Bridge Nonlinearities . . . . . . . . . . . 154 Wheatstone Bridge – 3-wire Measurement . . . . . . . . . . . . . . . . . . . 154 Thermistor Temperature-Resistance Relationship . . . . . . . . . . . . . 154 Resistance Tolerance Percent for Thermistors . . . . . . . . . . . . . . . . 155 Thermistor Voltage Drop Across a Wheatstone Bridge . . . . . . . . . 155 Stem Correction for a Total Immersion Thermometer . . . . . . . . . . . 155 Vapor Pressure Thermometers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Radiation Pyrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Planck’s Radiation Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Wien’s Radiation Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Stefan-Boltzmann Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Wien’s Displacement Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Total Emissivities of Metals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Total Radiation Pyrometer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Brightness Pyrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Johnson Noise Thermometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
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Chapter 4/Temperature
Principles of Temperature – ITS-90 Shortly after adoption of the International Practical Temperature Scale of 1968 (IPTS-68), it was realized the scale had many deficiencies and limitations. Consequently, the Comité Consultatif de Thermométrie (CCT) – one of eight specialized technical subcommittees of the Comité International des Poids et Mesures (CIPM) – undertook the development of a new scale. On 2628 September 1989, the CCT recommended ITS-90 be adopted. Following approval by CIPM, ITS-90 became the official international temperature scale on 1 January 1990, when it also was implemented at the U.S. National Institute of Standards and Technology (NIST).
121
According to a detailed report by B.W. Mangum, of NIST’s Center for Chemical Technology, National Measurement Laboratory, and NIST guest scientist G.T. Furukawa, ITS-90 – when compared to IPTS-68 – extends upward from 0.65 K. Also, temperatures on the newer scale are in much better agreement with thermodynamic values. In addition, ITS-90’s continuity, nonuniqueness and reproducibility throughout its ranges are much improved over previous scales. The most complete and authoritative document on ITS-90 from NIST is Technical Note 1265 by Mangum and Furukawa. It is available as a pdf from NIST’s web site: http://www.cstl.nist.gov/div836/836.0 5/papers/magnum90ITS90guide.pdf
Temperature Defining Points – IPTS-68 vs. ITS-90 IPTS-68 Kelvin
ITPS-68°C
ITS-90 Kelvin
ITS-90°C
Triple Point of Hydrogen
13.81
-259.34
13.8033
-259.3467
Boiling (Vapor Pressure) Point of Hydrogen at 25/75 Standard Atmosphere
17.042
-256.108
~17.0
~ -256.15
Boiling Point of Hydrogen
20.28
-252.87
~20.3
~ -252.85
Boiling Point of Neon
27.102
-246.048
—
—
—
—
24.5561
-248.5939
Triple Point of Oxygen
54.361
-218.789
54.3584
-218.7916
Boiling Point of Oxygen
90.188
-182.962
—
—
Triple Point of Water
273.16
0.01
273.16
0.01
Boiling Point of Water
373.15
100.00
—
—
Freezing Point of Zinc
692.73
419.58
692.677
419.527
Freezing Point of Silver
1235.08
961.93
1234.93
961.78
Freezing Point of Gold
1337.58
1064.43
1337.77
1064.18
Temperature Defining Point
Triple Point of Neon
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Comparative Characteristics of Thermometers Thermometer Thermocouples, Sheathed
Range °C
Resolution Accuracy of °C Absolute, %
Drift in 20 khr, %
0-250
>0.1
0.3-0.8
1.3@650°C
Sheathed type K (C/A)
250-850
>0.1
1-1.5
Sheathed type S(Pt-Rh)
0-1600
>0.1
0.1
1.7@ 1300°C
Industrial
-200 to 650
0.01
0.5-0.1
0.02@ 650°C
Standard
-183 to 631
<0.01
0.0001-0.003
0.02@ 1063°C
Thermistors
-200 to 600
0.0005
0.03-1
0.02-0.03
Mercury-in-Glass
-38 to 400
0.01
0.002-0.25
0.05
700-3000
0.20
0.10
0
Johnson Noise Thermometer
-272 to 1500
0.10
0.01-1.30
0
Transistor Absolute Thermometer
-200 to 123
0.04
0.50
Nuclear Quadrupole Resonance Thermometer
-183 to 125
0.0002
0.0004
Ultrasonic Pulse Echo Thermometer
0-2000
1-2
1
Fluidic Thermometers
0-1200
0.00001
105
Quartz Crystal Thermometer
-40 to 230
0.0001
<0.005
Eddy Current Thermometer (sodium)
150-600
0.05
1-10
Microwave Resonator
1370
0.05
1
Platinum Resistance Thermometers
Optical Pyrometer
<0.01@ 100°C
0.003@ 100°C
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Chapter 4/Temperature
123
Differences Between ITS-90, IPTS-68 and EPT-76 where ITS-90 = T90 or t90 IPTS-68 = T68 or t68 EPT-76 = T76 (T90 – T76)/mK T90/K
0
1
2
3
4
0
5
6
7
8
9
-0.1
-0.2
-0.3
-0.4
-0.5
-1.8
-2.0
8
9
10
-0.6
-0.7
-0.8
-1.0
-1.1
-1.3
-1.4
-1.5
20
-2.2
-2.5
-2.7
-3.0
-3.2
-3.5
-3.8
-4.1
6
7
(T90 – T68)/K T90/K
0
1
2
3
4
5
10
-0.006 -0.003 -0.004 -0.006 -0.008 -0.008
20
-0.009 -0.008 -0.007 -0.007 -0.006 -0.005 -0.004 -0.004 -0.005 -0.006
30
-0.006 -0.007 -0.008 -0.008 -0.008 -0.007 -0.007 -0.007 -0.006 -0.006
40
-0.006 -0.006 -0.006 -0.006 -0.006 -0.007 -0.007 -0.007 -0.006 -0.006
50
-0.006 -0.005 -0.005 -0.004 -0.003 -0.002 -0.001 0.000 0.001 0.002
60
0.003 0.003 0.004 0.004 0.005 0.005 0.006 0.006 0.007 0.007
70
0.007 0.007 0.007 0.007 0.007 0.008 0.008 0.008 0.008 0.008
80
0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.008
90
0.008 0.008 0.008 0.008 0.008 0.008 0.008 0.009 0.009 0.009
T90/K
0
10
20
30
40
50
60
70
80
90
100
0.009 0.011 0.013 0.014 0.014 0.014 0.014 0.013 0.012 0.012
200
0.011 0.010 0.009 0.008 0.007 0.005 0.003 0.001
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(T90 – T68)/°C T90/°C
0
-10
-20
-30
-40
-50
-60
-70
-80
-90
-100
0.013 0.013 0.014
0.014
0.014
0.013
0.012
0.010
0.008
0.008
0
0.000 0.002 0.004
0.006
0.008
0.009
0.010
0.011
0.012
0.012
30
40
50
60
70
80
90
T90/°C
0
10
20
0
0.000 -0.002 -0.005 -0.007 -0.010 -0.013 -0.016 -0.018 -0.021 -0.024
100
-0.026 -0.028 -0.030 -0.032 -0.034 -0.036 -0.037 -0.038 -0.039 -0.039
200
-0.040 -0.040 -0.040 -0.040 -0.040 -0.040 -0.040 -0.039 -0.039 -0.039
300
-0.039 -0.039 -0.039 -0.040 -0.040 -0.041 -0.042 -0.043 -0.045 -0.046
400
-0.048 -0.051 -0.053 -0.056 -0.059 -0.062 -0.065 -0.068 -0.072 -0.075
500
-0.079 -0.083 -0.087 -0.090 -0.094 -0.098 -0.101 -0.105 -0.108 -0.112
600
-0.115 -0.118 -0.122 -0.125 -0.08
-0.03
0.02
0.06
0.11
0.16
700
0.20
0.24
0.28
0.31
0.33
0.35
0.36
0.36
0.36
0.35
800
0.34
0.32
0.29
0.25
0.22
0.18
0.14
0.10
0.06
0.03
900
-0.01
-0.03
-0.06
-0.08
-0.10
-0.12
-0.14
-0.16
-0.17
-0.18
1000
-0.19
-0.20
-0.21
-0.22
-0.23
-0.24
-0.25
-0.25
-0.26
-0.26
T90/°C
0
100
200
300
400
500
600
700
800
900
-0.26
-0.30
-0.35
-0.39
-0.44
-0.49
-0.54
-0.60
-0.66
1000 2000
-0.72
-0.79
-0.85
-0.93
-1.00
-1.07
-1.15
-1.24
-1.32
-1.41
3000
-1.50
-1.59
-1.69
-1.78
-1.89
-1.99
-2.10
-2.21
-2.32
-2.43
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Chapter 4/Temperature
˚F 1340
˚R
K
1800
125
˚C 1000
727
1000
538
˚F = 2(˚C) Approx.
˚Rea 500
960
533
Water Boils 212 Room Temp 70 Water Freezes 32
0 -40
460
Absolute Zero 0 Temperature -460 Fahrenheit Rankin
273 ˚C = ˚F
0 Kelvin
260
208
100
80
21 0 -40
17 0
-273 Celsius
-218 Reaumur
Relation of Temperature Scales Temperature Conversion Equations °Celsius to °Fahrenheit Degree F = (Degree C x 1.8) + 32 °Celsius to °Rankine Degree R = (Degree C + 273.15) x 1.8 °Celsius to Kelvin Kelvin = Degree C + 273.15
°Fahrenheit to °Celsius Degree C =
Degree F - 32 1.8
°Fahrenheit to °Rankine Degree R = Degree F + 459.67 °Fahrenheit to Kelvin Degree C =
Degree F - 32 + 273.1 1.8
°Rankine to °Fahrenheit Degree F = Degree R - 459.67
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°Rankine to Kelvin
°Fahrenheit
Add to °Celsius
Degree R Kelvin = 1 .8
1
0.5556
2
1.1111
3
1.6667
4
2.2222
5
2.7778
6
3.3334
7
3.8889
8
4.4445
9
5.0000
10
5.5556
20
11.1112
30
16.6668
40
22.2224
50
27.7780
60
33.3336
70
38.8892
80
44.4448
90
50.0004
Kelvin to °Celsius Degree C = Kelvin - 273.15 Kelvin to °Rankine Degree R = Kelvin x 1.8 Interpolation Values To interpolate for accurate temperatures between the various incremental changes in the following temperature conversion tables, the interpolation table below provides the values to add to the conversion table values. Note that these values are to four decimal places. To use these add-on values correctly, calculate the add-on value, and then round to two decimal places.
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Chapter 4/Temperature
Steady-State Heat Transfer Analysis The performance of temperature sensors can depend on all the modes of heat transfer – conduction, convection, and radiation.
In many applications, heat transfer along all the coordinate axes is not significant. In these cases the equations are: Cartesian (one-dimensional) ∂2T
The steady-state heat conduction equation is: ∇ ⋅ kVT = 0
∂x 2
where ∇ = geometry-dependent differential operator k = thermal conductivity For constant thermal conductivity, the conduction equation is:
∂r 2
+
1 ∂T =0 r ∂r
Cylinder (r,z) ∂2T ∂r 2
+
1 ∂T ∂2T + =0 r ∂r ∂z 2
Sphere (r only)
∇2T = 0 The differential operators for three geometries are: x,y,z (Cartesian) ∂2T ∂x 2
+
∂2T ∂y 2
+
∂2T ∂r 2
+
∇2T = =
∂2T ∂r
2
1 ∂ 2 ∂T r r 2 ∂r ∂r +
2 ∂T r ∂r
∂2T ∂z 2
r,z, θ (cylindrical) ∇2T =
=0
Cylinder (r only) ∂2T
∇2T =
1 ∂T 1 ∂2T ∂2T + 2 2 + 2 r ∂r r ∂θ ∂z
Convective Heat Transfer Coefficients Dimensionless Quantities for Sensors of Single Cylinders or Spheres Nusselt number (Nu) =
r, θ, φ (spherical) ∇2T =
1 ∂ r 2 ∂r
2 ∂T r + ∂r
∂ ∂T sin θ + ∂ ∂θ θ r sin θ ∂2T
1
r sin θ ∂φ2 2
hD k
Reynolds number (Re) = Du
1
2
2
127
Prandtl number (Pr) =
cµ k
ρ µ
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where h = film heat transfer coefficient D = diameter of sensor k = thermal conductivity of fluid ρ = fluid density u = fluid velocity µ = fluid viscosity c = fluid specific heat capacity General Form of the Correlations Nu = a1 + a2 Rea3 Pra4
where a = experimental data Nonmetals Flowing Normal to a Single Cylinder Nu = (0.35 + 0.47 Re0.52) Pr0.3 for 0.1
Nonmetals Flowing Across a Single Sphere
Nu = 2.0 + 0.60 Re1/2 Pr1/2 Metals Flowing Normal to a Single Cylinder
Nu = 0.8 Re0.5 Pr0.5 Metals Flowing Across a Single Sphere
Nu = 2.0 + 0.386 Re0.5 Pr0.5
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Chapter 4/Temperature
129
Conversion Tables, °F to °C °F
°C
°F
°C
°F
°C
-500
-295.556
0
-17.778
70
21.111
-480
-284.444
1
-17.222
80
26.667
-460
-273.333
2
-16.667
90
32.222
-440
-262.222
3
-16.111
100
37.778
-420
-251.111
4
-15.556
110
43.333
-400
-240.000
5
-15.000
120
48.889
-380
-228.889
6
-14.444
130
54.444
-360
-217.778
7
-13.889
140
60.000
-340
-206.667
8
-13.333
150
65.556
-320
-195.556
9
-12.778
160
71.111
-300
-184.444
10
-12.222
170
76.667
-280
-173.333
11
-11.667
180
82.222
-260
-162.222
12
-11.111
190
87.778
-240
-151.111
13
-10.556
200
93.333
-220
-140.000
14
-10.000
210
98.889
-200
-128.889
15
-9.444
220
104.444
-180
-117.778
16
-8.889
230
110.000
-160
-106.667
17
-8.333
240
115.556
-140
-95.556
18
-7.778
250
121.111
-120
-84.444
19
-7.222
260
126.667
-100
-73.333
20
-6.667
270
132.222
-80
-62.222
30
-1.111
280
137.778
-60
-51.111
40
4.444
290
143.333
-40
-40.000
50
10.000
300
148.889
-20
-28.889
60
15.556
310
154.444
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Conversion Tables, °F to °C (cont.) °F
°C
°F
°C
°F
°C
320
160.000
570
298.889
900
482.222
330
165.556
580
304.444
950
510.000
340
171.111
590
310.000
1000
537.778
350
176.667
600
315.556
1050
565.556
360
182.222
610
321.111
1100
593.333
370
187.778
620
326.667
1150
621.111
380
193.333
630
332.222
1200
648.889
390
198.889
640
337.778
1250
676.667
400
204.444
650
343.333
1300
704.444
410
210.000
660
348.889
1350
732.222
420
215.556
670
354.444
1400
760.000
430
221.111
680
360.000
1450
787.778
440
226.667
690
365.556
1500
815.556
450
232.222
700
371.111
1550
843.333
460
237.778
710
376.667
1600
871.111
470
243.333
720
382.222
1650
898.889
480
248.889
730
387.778
1700
926.667
490
254.444
740
393.333
1750
954.444
500
260.000
750
398.889
1800
982.222
510
265.556
760
404.444
1850
1010.000
520
271.111
770
410.000
1900
1037.778
530
276.667
780
415.556
1950
1065.556
540
282.222
790
421.111
2000
1093.333
550
287.778
800
426.667
2050
1121.111
560
293.333
850
454.444
2100
1148.889
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Chapter 4/Temperature
Temperature Conversion Table To Convert From
To
Multiply by:
°C heat unit
Btu
1.8
°C heat unit
Calorie
453.592
°C heat unit
Joule
1899.10
°C/hr-kilocalorie
°C / watt
0.859845
ft/°F
m/°C
0.548640
in/°F
mm/°C
45.72
Joule
Calorie
0.238846
Joule/°C
Btu/°F
0.000526565
kilocalorie
Btu
3.968320
kilocalorie
Joule
4186.80
liter-bar
Joule
100.0
°C-temperature interval
°F
1.8
°C-temperature interval
°Rankine
1.8
°F-temperature interval
°C
0.5555556
°F-temperature interval
°Rankine
1.0
°F-temperature interval
Kelvin
0.5555556
131
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ISA Handbook of Measurement Equations and Tables
Conversion Tables, °F to Kelvin
1
°F
K
°F
K
°F
K
-500
-22.406
0
255.372
70
294.261
-480
-11.294
1
255.928
80
299.817
-460
-0.183
2
256.483
90
305.372
-440
10.928
3
257.039
100
310.928
-420
22.039
4
257.794
110
316.483
-400
33.150
5
258.150
120
322.039
-380
44.261
6
258.706
130
327.594
-360
55.372
7
259.261
140
333.150
-340
66.483
8
259.817
150
338.706
-320
77.594
9
260.372
160
344.261
-300
88.706
10
260.928
170
349.817
-280
99.817
11
261.483
180
355.372
-260
110.928
12
262.039
190
360.928
-240
122.039
13
262.594
200
366.483
-220
133.150
14
263.150
210
372.039
-200
144.261
15
263.706
220
377.594
-180
155.372
16
264.261
230
383.150
-160
166.483
17
264.871
240
388.706
-140
177.594
18
265.372
250
394.261
-120
188.706
19
265.928
260
399.817
-100
199.817
20
266.483
270
405.372
-80
210.928
30
272.039
280
410.928
-60
222.039
40
277.594
290
416.483
-40
233.150
50
283.150
300
422.039
-20
244.261
60
288.706
310
427.594
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Chapter 4/Temperature
133
Conversion Tables, °F to Kelvin (cont.) °F
K
°F
K
°F
K
320
433.150
570
572.709
900
755.372
330
438.706
580
577.594
950
783.150
340
444.261
590
583.150
1000
810.928
350
449.817
600
588.706
1050
838.706
360
455.372
610
594.261
1100
866.483
370
460.928
620
599.817
1150
894.261
380
466.483
630
605.372
1200
922.039
390
472.039
640
610.928
1250
949.817
400
477.594
650
616.483
1300
977.594
410
483.150
660
622.039
1350
1005.372
420
488.706
670
627.594
1400
1033.150
430
494.261
680
633.150
1450
1060.928
440
499.817
690
638.706
1500
1088.706
450
505.372
700
644.261
1550
1116.483
460
510.928
710
649.817
1600
1144.261
470
516.483
720
655.372
1650
1172.039
480
522.039
730
660.928
1700
1199.817
490
527.594
740
666.438
1750
1227.594
500
533.150
750
672.039
1800
1255.372
510
538.706
760
677.594
1850
1283.150
520
544.261
770
683.150
1900
1310.928
530
549.817
780
688.706
1950
1338.706
540
555.372
790
694.261
2000
1366.483
550
560.928
800
699.817
2050
1394.261
560
566.483
850
727.594
2100
1422.039
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ISA Handbook of Measurement Equations and Tables
Conversion Tables, °C to °F °C
°F
°C
°F
°C
°F
-300
-508.0
-50
-58.0
20
68.0
-290
-490.0
-40
-40.0
25
77.0
-280
-472.0
-30
-22.0
30
86.0
-270
-454.0
-20
-4.0
40
104.0
-260
-436.0
-10
14.0
50
122.0
-250
-418.0
0
32.0
60
140.0
-240
-400.0
1
33.8
70
158.0
-230
-382.0
2
35.6
80
176.0
-220
-364.0
3
37.4
90
194.0
-210
-346.0
4
39.2
100
212.0
-200
-328.0
5
41.0
110
230.0
-190
-310.0
6
42.8
120
248.0
-180
-292.0
7
44.6
130
266.0
-170
-274.0
8
46.4
140
284.0
-160
-256.0
9
48.2
150
302.0
-150
-238.0
10
50.0
160
320.0
-140
-220.0
11
51.8
170
338.0
-130
-202.0
12
53.6
180
356.0
-120
-184.0
13
55.4
190
374.0
-110
-166.0
14
57.2
200
392.0
-100
-148.0
15
59.0
210
410.0
-90
-130.0
16
60.8
220
428.0
-80
-112.0
17
62.6
230
446.0
-70
-94.0
18
64.4
240
464.0
-60
-76.0
19
66.2
250
482.0
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Chapter 4/Temperature
135
Conversion Tables, °C to °F (cont.) °C
°F
°C
°F
°C
°F
260
500.0
510
950.0
760
1400.0
270
518.0
520
968.0
770
1418.0
280
536.0
530
986.0
780
1436.0
290
554.0
540
1004.0
790
1454.0
300
572.0
550
1022.0
800
1472.0
310
590.0
560
1040.0
810
1490.0
320
608.0
570
1058.0
820
1508.0
330
626.0
580
1076.0
830
1526.0
340
644.0
590
1094.0
840
1544.0
350
662.0
600
1112.0
850
1562.0
360
680.0
610
1130.0
860
1580.0
370
698.0
620
1148.0
870
1598.0
380
716.0
630
1166.0
880
1616.0
390
734.0
640
1184.0
890
1634.0
400
752.0
650
1202.0
900
1652.0
410
770.0
660
1220.0
910
1670.0
420
788.0
670
1238.0
920
1688.0
430
806.0
680
1256.0
930
1706.0
440
824.0
690
1274.0
940
1724.0
450
842.0
700
1292.0
950
1742.0
460
860.0
710
1310.0
960
1760.0
470
878.0
720
1328.0
970
1778.0
480
896.0
730
1346.0
980
1796.0
490
914.0
740
1364.0
990
1814.0
500
932.0
750
1382.0
1000
1832.0
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ISA Handbook of Measurement Equations and Tables
Thermocouples The thermocouple is the most popular type of sensor. Thermocouples are based on the principle that two wires made of dissimilar materials connected at either end will generate a potential between the two ends that is a function of the materials and temperature difference between the two ends. A number of material choices are in common use. Base metal thermocouples are useful for measuring temperatures under 1000 degrees C. This class includes iron/constantan (Type J), Chromel/Alumel (Type K) and a number of others. Nobel metal thermocouples are useful to about 2000 degrees C. This class includes tungsten-rhenium alloy thermocouples and others. The potential generated is in millivolts and is a nonlinear function of temperature. In practice, one end is placed near the material to be
measured and the other end is connected to the instrument. Since the thermocouple materials are not typically good materials for transmission, wires with similar characteristics are used when the transmitting instrument is remote. Thermocouple Types Thermocouples come in different combinations of metals and calibrations. Types J, K, T and E are the four most common calibrations. Types R, S, C and GB are high temperature calibrations. Each calibration has a different temperature range and environment. However, the maximum temperature varies with the diameter of the wire used in the thermocouple. The letter type, e.g., type J, identifies a specific temperature-voltage relationship, not a particular chemical composition. Thermocouples of a given type may have variations in composition as long as their
Thermocouples Type
Composition
Temperature range, °C
B
Pt-30% Rh versus Pt-6% Rh
0 to 1820
E
Ni-Cr alloy versus a Cu-Ni alloy
-270 to 1000
J
Fe versus a Cu-Ni alloy
-210 to 1200
K
Ni-Cr alloy versus Ni-Al alloy
-270 to 1372
N
Ni-Cr-Si alloy versus Ni-Si-Mg alloy
-270 to 1300
R
Pt-13% Rh versus Pt
-50 to 1768
S
Pt-10% Rh versus Pt
-50 to 1768
T
Cu versus a Cu-Ni alloy
-270 to 400
Courtesy: National Institute of Standards and Technology (NIST) ©1995 copyright by the U.S. Secretary of Commerce on behalf of the United States of America. All rights reserved.
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Chapter 4/Temperature
resultant temperature-voltage relationships remain within specified tolerances. All materials manufactured in compliance with the established thermoelectric voltage standards are equally acceptable. Thermocouple Circuit Analysis V = ∫ T2 (Sa − Sb )dT
137
where S=
∆V ∆T
V = voltage T = temperature The Basic Thermoelectric Voltage Element
T
1
Thermocouple Circuit Analysis
A Simple Thermocouple Circuit
where: V = open-circuit voltage T1 = Temperature at one end of wires T2 = temperature at other end of wires Sa = absolute Seebeck coefficient for material Sb = absolute Seebeck coefficient for material T = temperature Sa − Sb = Sab
S T2
T1
∆V
The Basic Thermoelectric Voltage Element
Sab = −Sba Sac = Sab − Scb Sac = Sab + Sbc Sa
where Sab = relative Seebeck coefficient for materials a and b
T1
T2
V
The Relation Between Temperature Difference and Voltage ∆V = S (T2 − T1)
T1 Sb A Simple Thermocouple Circuit
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ISA Handbook of Measurement Equations and Tables
Solutions also require specification of boundary conditions at interfaces. Interfaces occur between regions containing different materials or surfaces. Since notation becomes cumbersome if all geometries are considered, only the common boundary conditions for cylindrical (r only) geometry are given. Internal; Continuity of Temperature
Tr- = Tr+ Internal; Continuity of Heat Flux k1
∂T ∂r
r−=
k2
∂T ∂r
r+
Internal; Finiteness of Temperature T (r ) ≠ ∞
Surface; Convection −k
∂T ∂r
R=
h(TR − θ)
Surface: Fixed Surface Temperature
TR = TF Surface: Insulated Surface ∂T ∂r
R=
0
Surface: Radiation −k
∂T ∂r
4 R =∈ σ(TR
− θR4 )
where Tr- = temperature at r as approached from the interior Tr+ = temperature at r as approached from the exterior k = thermal conductivity k1 = thermal conductivity of material interior to the interface at r k2 = thermal conductivity of material exterior to the interface at r R = radius at the surface h = film heat transfer coefficient θ = temperature of fluid around sensor θR = temperature of medium exchanging radiative energy with the sensor TF = fixed temperature specified for surface ∈ = emissivity σ = Stefan-Boltzmann constant
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Chapter 4/Temperature
Type E - Thermoelectric Voltage in mV °C 270 -260 -250 -240 -230 -220 -210 -200 -190 -180 -170 -160 -150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100
mV -9.835 -9.797 -9.718 -9.604 -9.455 -9.274 -9.063 -8.825 -8.561 -8.273 -7.963 -7.632 -7.279 -6.907 -6.516 -6.107 -5.681 -5.237 -4.777 -4.302 -3.811 -3.306 -2.787 -2.255 -1.709 -1.152 -0.582 0.000 0.591 1.192 1.801 2.420 3.048 3.685 4.330 4.985 5.648 6.319
110
6.998
120
7.685
130
8.379
140
9.081
150
9.789
160
10.503
170
11.224
180
11.951
190
12.684
200
13.421
210
14.164
220
14.912
230
15.664
240
16.420
250
17.181
260
17.945
270
18.713
280
19.484
290
20.259
300
21.036
310
21.817
320
22.600
330
23.386
340
24.174
350
24.964
360
25.757
370
26.552
380
27.348
390
28.146
400
28.946
410
29.747
420
30.550
430
31.354
440
32.159
450
32.965
460
33.772
470
34.579
480
35.387
139
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ISA Handbook of Measurement Equations and Tables
Type E - Thermoelectric Voltage in mV (cont’d.) °C 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850
mV 36.196 37.005 37.815 38.624 39.434 40.243 41.053 41.862 42.671 43.479 44.286 45.093 45.900 46.705 47.509 48.313 49.116 49.917 50.718 51.517 52.315 53.112 53.908 54.703 55.497 56.289 57.080 57.870 58.659 59.446 60.232 61.017 61.801 62.583 63.364 64.144 64.922
860
65.698
870
66.473
880
67.246
890
68.017
900
68.787
910
69.554
920
70.319
930
71.082
940
71.844
950
72.603
960
73.360
970
74.115
980
74.869
990
75.621
1000
76.373
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Chapter 4/Temperature
110
5.814
120
6.360
mV
130
6.909
-210
-8.095
140
7.459
-200
-7.890
150
8.010
-190
-7.659
160
8.562
170
9.115
Type J - Thermoelectric Voltage in mV °C
-180
-7.403
-170
-7.123
-160
-6.821
-150
-6.500
-140
180
9.669
190
10.224
200
10.779
210
11.334
-6.159
220
11.889
-130
-5.801
230
12.445
-120
-5.426
240
13.000
-110
-5.037
250
13.555
-100
-4.633
260
14.110
-90
-4.215
270
14.665
280
15.219
290
15.773
300
16.327
310
16.881
320
17.434
330
17.986
-80
-3.786
-70
-3.344
-60
-2.893
-50
-2.431
-40
-1.961
-30
-1.482
340
18.538
-20
-0.995
350
19.090
-10
-0.501
360
19.642
0
0.000
370
20.194
10
0.507
380
20.745
20
1.019
390
21.297
400
21.848
410
22.400
420
22.952
430
23.504
440
24.057
450
24.610
30
1.537
40
2.059
50
2.585
60
3.116
70
3.650
80
4.187
460
25.164
90
4.726
470
25.720
100
5.269
480
26.276
141
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ISA Handbook of Measurement Equations and Tables
Type J - Thermoelectric Voltage in mV (cont’d.) °C
mV
490
26.834
830
47.431
840
48.074
850
48.715
860
49.353
870
49.989
880
50.622
890
51.251
900
51.877
910
52.500
920
53.119
930
53.735
940
54.347
950
54.956
960
55.561
970
56.164
980
56.763
990
57.360
1000
57.953
1010
58.545
500
27.393
510
27.953
520
28.516
530
29.080
540
29.647
550
30.216
560
30.788
570
31.362
580
31.939
590
32.519
600
33.102
610
33.689
620
34.279
630
34.873
640
35.470
1020
59.134
650
36.071
1030
59.721
660
36.675
1040
60.307
670
37.284
1050
60.890
680
37.896
1060
61.473
690
38.512
1070
62.054
700
39.132
1080
62.634
710
39.755
1090
63.214
720
40.382
1100
63.792
730
41.012
1110
64.370
740
41.645
1120
64.948
750
42.281
1130
65.525
760
42.919
1140
66.102
770
43.559
1150
66.679
780
44.203
1160
67.255
790
44.848
1170
67.831
800
45.494
1180
68.406
810
46.141
1190
68.980
820
46.786
1200
69.553
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Chapter 4/Temperature
Type K - Thermoelectric Voltage in mV
70
2.851
80
3.267
°C
mV
90
3.682
-270
-6.458
100
4.096
-260
-6.441
110
4.509
-250
-6.404
120
4.920
-240
-6.344
130
5.328
-230
-6.262
140
5.735
-220
-6.158
150
6.138
-210
-6.035
160
6.540
-200
-5.891
170
6.941
-190
-5.730
180
7.340
-180
-5.550
190
7.739
-170
-5.354
200
8.138
-160
-5.141
210
8.539
-150
-4.913
220
8.940
230
9.343
-140
-4.669
-130
-4.411
240
9.747
250
10.153
260
10.561
270
10.971
280
11.382
290
11.795
300
12.209
310
12.624
320
13.040
330
13.457
-120
-4.138
-110
-3.852
-100
-3.554
-90
-3.243
-80
-2.920
-70
-2.587
-60
-2.243
-50
-1.889
-40
-1.527
340
13.874
-30
-1.156
350
14.293
-20
-0.778
360
14.713
-10
-0.392
370
15.133
0
0.000
380
15.554
10
0.397
390
15.975
20
0.798
400
16.397
30
1.203
410
16.820
40
1.612
420
17.243
50
2.023
430
17.667
60
2.436
440
18.091
143
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ISA Handbook of Measurement Equations and Tables
Type K - Thermoelectric Voltage in mV (cont.) °C 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820
mV 18.516 18.941 19.366 19.792 20.218 20.644 21.071 21.497 21.924 22.350 22.776 23.203 23.629 24.055 24.480 24.905 25.330 25.755 26.179 26.602 27.025 27.447 27.869 28.289 28.710 29.129 29.548 29.965 30.382 30.798 31.213 31.628 32.041 32.453 32.865 33.275 33.685 34.093
830
34.501
840
34.908
850
35.313
860
35.718
870
36.121
880
36.524
890
36.925
900
37.326
910
37.725
920
38.124
930
38.522
940
38.918
950
39.314
960
39.708
970
40.101
980
40.494
990
40.885
1000
41.276
1010
41.665
1020
42.053
1030
42.440
1040
42.826
1050
43.211
1060
43.595
1070
43.978
1080
44.359
1090
44.740
1100
45.119
1110
45.497
1120
45.873
1130
46.249
1140
46.623
1150
46.995
1160
47.367
1170
47.737
1180
48.105
1190
48.473
1200
48.838
1210
49.202
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1220
49.565
1230
49.926
1240
50.286
1250
50.644
1260
51.000
1270
51.355
1280
51.708
1290
52.060
1300
52.410
1310
52.759
1320
53.106
1330
53.451
1340
53.795
1350
54.138
1360
54.479
1370
54.819
145
Type T - Thermoelectric Voltage in mV °C -270 -260 -250 -240 -230 -220 -210 -200 -190 -180 -170 -160 -150 -140 -130 -120 -110 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90
mV -6.258 -6.232 -6.180 -6.105 -6.007 -5.888 -5.753 -5.603 -5.439 -5.261 -5.070 -4.865 -4.648 -4.419 -4.177 -3.923 -3.657 -3.379 -3.089 -2.788 -2.476 -2.153 -1.819 -1.475 -1.121 -0.757 -0.383 0.000 0.391 0.790 1.196 1.612 2.036 2.468 2.909 3.358 3.814
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Type T - Thermoelectric Voltage in mV °C
mV
100
4.279
110
4.750
120
5.228
130
5.714
140
6.206
150
6.704
160
7.209
170
7.720
180
8.237
190
8.759
200
9.288
210
9.822
220
10.362
230
10.907
240
11.458
250
12.013
260
12.574
270
13.139
280
13.709
290
14.283
300
14.862
310
15.445
320
16.032
330
16.624
340
17.219
350
17.819
360
18.422
370
19.030
380
19.641
390
20.255
400
20.872
Source: NIST ITS-90 Database
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147
Limits of Error for Thermocouples Thermocouple Type
Temperature Range °C
Standarda Error Limit
Speciala Error Limit
T
-59 to 93
1.0°C
J
0 to 277
2.2°C
E
0 to 316
1.7°C
K
0 to 277
2.2°C
R or S
0 to 538
1.5°C
0.5°C 93 to 371 1.1°C 277 to 1260 1.0°C 316 to 817 1.1°C 277 to 1260 0.6°C 538 to 1482
B
871 to 1705
0.50%
n.a.
aLimits of error are expressed in percentage of Celsius temperature. Limits of error are material tolerances, not accuracies.
Recommended Upper Temperature Limits for Protected Thermocouples, °C (°F) Type
8 Gauge
T
14 Gauge
20 Gauge
24 Gauge
28 Gauge
370 (770)
260 (500)
200 (400)
200 (400)
J
760 (1400)
590 (1100)
480 (900)
370 (700)
370 (700)
E
870 (1600)
650 (1200)
540 (1100)
430 (800)
430 (800)
K
1260 (2300) 1090 (2000)
980 (1800)
870 (1600)
870 (1600)
R or S
1480 (2700)
B
1700 (3100)
RTDs (Resistive Temperature Detectors) RTDs are made of metal wire, fiber, or semiconductor material that responds to temperature change by changing its resistance. Platinum, nickel, tungsten and other metals are used that have high resistivity, good temperature coefficient of resistance, good ductile or tensile strength, and chemical inertness with packaging and insulation materials. When the material is a semiconductor, the sensor is called a thermistor.
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RTD Material Resistivity Levels Metal
Resistivity (Ohm/CMF) CMF = Circular Mil Foot)
Copper
9.26
Gold
13.00
Nickel
36.00
Platinum
59.00
Silver
8.8
Tungsten
30.00
Change in resistance can be determined using a bridge circuit. Since resistance changes in the connection wire due to ambient temperature changes can also affect the resistance reading, a third wire is used from another leg in the bridge to balance that change. RTDs are generally more accurate than thermocouples, but are less rugged and cannot be used at as high temperatures.
All types of temperature measuring devices suffer from slow response, since it is necessary for heat to conduct through the protective sheath, and through any installed well. Locating the well (or unprotected sensor) so it sees as high a velocity of process material as possible helps reduce this lag, as does having the sensor contact the well. A bare thermocouple touching the sheath and/or well, however, generates a ground and requires an isolated amplifier. The resistivity (r) is proportional to the length (L) and inversely proportional to the cross-section area (A). R=
r (L) A
where R = resistance, ohms r = resistivity, ohm cm L = length, cm A = cross-section area, cm2
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4.0 3.8 3.6 3.4
Basis: German Standard DIN 43760
3.2 3.0 2.8 Resistance/resistance ˚C
2.6 2.4 2.2 2.0 1.8 1.6 1.4
Linear approximation for -200 to 600˚C
1.2 1.0 0.8 0.6 0.4 0.2 0.0
-200
-100
0
100
200 300 Temperature ˚C
400
500
Resistance vs. Temperature for Platinum
600
149
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Resistance Versus Temperature and Tolerance for 100 Ohm Platinum RTDs According to DIN 43760 T°C
R Ohm
°C Temp. Tolerance
T°C
R Ohm
-220
10.41
1.8
30
111.67
-210
14.36
40
115.54
-200
18.53
50
119.40
-190
22.78
60
123.40
-180
27.05
70
127.07
-170
31.28
80
130.89
-160
35.48
90
134.70
-150
39.65
100
138.50
-140
43.80
110
142.28
-130
47.93
120
146.06
-120
52.04
130
149.82
-110
56.13
140
153.57
-100
60.20
150
157.32
-90
64.25
160
161.04
-80
68.28
170
164.76
-70
72.29
180
168.47
-60
76.28
190
172.16
-50
80.25
200
175.84
-40
84.21
210
179.51
-30
88.17
220
183.17
-20
92.13
230
186.82
-10
96.07
240
190.46
0
100.00
250
194.08
10
103.90
260
197.70
20
107.79
270
201.30
1.2
0.7
0.3
°C Temp. Tolerance
0.6
1.2
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151
Resistance Versus Temperature and Tolerance for 100 Ohm Platinum RTDs According to DIN 43760 (cont.) T°C
R Ohm
280
°C Temp. Tolerance
° Temp. Tolerance
T°C
R Ohm
204.88
530
290.87
290
208.46
540
294.16
300
212.03
550
297.43
310
215.58
560
300.70
320
219.13
570
303.95
330
222.66
580
307.20
340
226.18
590
310.43
350
229.69
600
313.65
360
233.19
610
316.86
370
236.67
620
320.05
380
240.15
630
323.24
390
243.61
640
326.41
400
247.06
650
329.57
410
250.50
660
332.72
420
253.93
670
335.86
430
257.34
680
338.99
440
260.75
690
342.10
450
264.14
700
345.21
460
267.52
710
348.30
470
270.89
720
351.38
480
274.25
730
354.45
490
277.60
740
357.51
500
280.93
750
360.55
510
284.26
800
375.61
4.8
520
287.57
850
390.38
5.1
1.8
2.4
3.0
3.6
4.2
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Resistance Versus Temperature for 100 Ohm (Nominal) Platinum RTD According to SAMA RC21-4-1966 T °C
R Ohm
T °C
R Ohm
-200
16.666
20
105.920
-190
20.972
30
109.799
-180
25.244
40
113.665
-170
29.483
50
117.521
-160
33.691
60
121.365
-150
37.871
70
125.197
-140
42.023
80
129.018
-130
46.151
90
132.827
-120
50.255
100
136.625
-110
54.337
110
140.412
-100
58.399
120
144.187
-90
62.441
130
147.950
-80
66.466
140
151.702
-70
70.474
150
155.442
-60
74.465
160
159.171
-50
78.442
170
162.889
-40
82.405
180
166.595
-30
86.355
190
170.289
-20
90.292
200
173.972
-10
94.216
210
177.644
0
98.129
220
181.304
10
102.030
230
184.953
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Resistance Versus Temperature for 100 Ohm (Nominal) Platinum RTD According to SAMA RC21-4-1966 (cont.) T °C
R Ohm
T °C
R Ohm
240
188.581
430
255.512
250
192.215
440
258.919
260
195.829
450
262.315
270
199.432
460
265.699
280
203.023
470
269.072
290
206.603
480
272.434
300
210.171
490
275.784
310
213.728
500
279.122
320
217.273
510
282.449
330
220.807
520
285.784
340
224.329
530
289.068
350
227.840
540
292.361
360
231.339
550
295.642
370
234.827
560
298.911
380
238.303
570
302.169
390
241.768
580
305.416
400
245.221
590
308.651
410
248.663
600
311.875
420
252.093
153
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Wheatstone Bridge – Effect of Bridge Nonlinearities
Thermistor TemperatureResistance Relationship
R RS E = Eo T − R + RT RS + R
1 1 R = β − Ro T To
where E = voltage drop Eo = output voltage RT = fixed resistor RS = adjustable resistor
where R = unknown resistance Ro = known resistance β = Kelvins T = unknown temperature To = known temperature
Wheatstone Bridge 3-Wire Measurement R RS E = Eo T − R + R R T S +R
1 = ao + a1(1n R ) + a3 (1n R )3 T where T = temperature R = resistance ao = 1.1252 x 10-3 K-1 a1 = 2.3476x10-4 K-1 a3 = 8.5262 x 10-8 K-1
Rs
R E
Eo R
RT Basic Wheatstone Bridge (2-wire)
Lead 1 Rs
R
RL Lead 2
E
Eo
RL R
RT
The Steinhart and Hart Equation for NTC Thermistors
Lead 3
Wheatstone Bridge for 3-Wire Measurements
Thermistor Temperature Error Due to Self-Heating ∆T =
I 2R 1000(DC )
where ∆T = temperature measurement error, °C I = sensing current, mA R = thermistor resistance, Ω DC = dissipation constant, mW/°C
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155
Resistance Tolerance Percent for Thermistors (MIL-T-23648A) Temperature °C
Type F + or -1%
Type G + or -2%
Type J + or -5%
Type K + or -10%
-55
10
12
15
20
-15
5
6
9
14
0
3
4
7
12
25
1
2
5
10
50
3
4
7
12
75
5
6
9
14
100
7
9
12
17
125
10
12
15
20
200°
15
18
25
30
275°
20
25
35
40
aThe percent tolerance indicated with each thermistor type is the resistance at 25°C.
Thermistor Voltage Drop Across a Wheatstone Bridge E = K + F (T ) Eo where K =−
R R + Rs 1
F (T ) = 1+
RT RTo RTo R
RTo = resistance at a reference temperature
Stem Correction for a Total Immersion Thermometer ∆T = Kn(TB − T )
where ∆T = temperature correction K = temperature correction factor n = number of degrees on scale between surface of fluid and end of fluid column in the capillary TB = bulb temperature T = average temperature of the portion of the thermometer between the fluid surface and end of fluid column in the capillary
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Vapor Pressure Thermometers
R
Rs E
Eo T
R Vapor Wheatstone Bridge for Thermistor Readout Volatile Liquid
Vapor Pressure Thermometers Cross Ambient Effect PG = PB + ∆PC
where PG = pressure on the Bourdon tube PB = pressure in the bulb PC = pressure in the capillary
Volatile Liquid
Vapor
Radiation Pyrometers Planck’s Radiation Law H (λT ) =
λ (e 5
C1 c2λT
− 1)
where H(λT) = radiant power density λ = wavelength, cm T = temperature, K C1 = 3.74 x 10-12, Wcm2 C2 = 1.44, cmK
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Wien’s Radiation Law (lower temperatures) H (λT ) =
C1e −C2 / λT
157
Wien’s Displacement Law T =
0.2898 λm
λ5
Stefan-Boltzmann Law (total radiation power) H (T ) = σT 4
where H(T) = total radiation power per unit area σ = 5.669 x 10-12, W/cm2 K4 T = temperature, K
where T = temperature, K λm = wavelength where maximum radiation power density occurs
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Location of Peak (see Wien's Displacement Law) 0.15 0.14 0.13
Relative Spectral Radiant Power
0.12 0.11
1300 K, 1880˚F
0.10
1200 K, 1700˚F
0.09
1100 K, 1520˚F
0.08 1000 K, 1340˚F
0.07 0.06
900 K, 1160˚F
0.05
800 K, 960˚F
0.04
700 K, 800˚F
0.03 0.02 0.01 0.00 0
1
2
3
4
5
6
Wavelength λ, microns
Radiation Power Density as a Function of Wavelength and Temperature (Plank’s Law for a Blackbody)
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159
Total Emissivities of Metals, Surface Unoxidized Material
25°C
100°C
500°C
Aluminum
0.022
0.028
0.060
Bismuth
0.048
0.061
Carbon
0.81
0.81
Chromium
1000°C 1500°C 2000°C
0.79
0.08
Cobalt
0.13
0.23
Columbium
0.19
Copper
0.02
Gold
0.02
Iron
0.06
Lead
0.05
Mercury
0.10
0.15 Liquid 0.03
0.12
Molybdenum
0.13
Nickel
0.045
0.06
0.12
0.19
Platinum
0.037
0.047
0.095
0.152
0.02
0.035
Silver
0.24
Tantalum Tin
0.043
0.05
Tungsten
0.024
0.032
Brass
0.035
0.035
0.071
0.15
0.19
0.24
0.191
0.21
0.26
0.23
0.28
Cast Iron
0.21
0.29 Liquid
Steel
0.08
0.28 Liquid
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Total Radiation Pyrometer
Johnson Noise Thermometer
True Temperature vs. Indicated Temperature
Relationship Between Noise Voltage and Absolute Temperature
T = TI (∈)1 / 4
V 2 = 4kTR ∆f
where T = true temperature TI = indicated temperature ∈ = material radiation emissivity
where V = noise voltage k = Boltzmann’s constant T = absolute temperature R = electrical resistance of sensor ∆f = frequency band-width over which the noise voltage is measured
Brightness Pyrometer True Temperature vs. Brightness Temperature T =
TB λTB 1+ 1n ∈ (λ) 1.44
where T = true temperature TB = brightness temperature
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5
Level Measurement
Principles of Level Measurement & Theory . . . . . . . . . . . . . . . . . . 163 Important Level Measurement Technologies . . . . . . . . . . . . . . . . . 164 • Differential Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 • Bubblers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 • Displacers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 • Floats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 • RF Admittance & Capacitance . . . . . . . . . . . . . . . . . . . . . . . . 165 • Ultrasonic/Sonic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 • Radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 • Nuclear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 • Table Comparing Level Measurement Technologies . . . . . 167 • Time Domain Reflectometry (TDR) . . . . . . . . . . . . . . . . . . . . 167 • Magnetostrictive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 • Hydrostatic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 • Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 • Float Switch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Level Measurement Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Dielectric Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Weight of Water versus Temperature . . . . . . . . . . . . . . . . . . . . . . . 177 Sound Absorption Coefficient of a Material . . . . . . . . . . . . . . . . . . 179 Radiation Field Intensity in Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
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Principles of Level Measurement Instrument suppliers offer more than 20 different level measurement technologies. All work, when properly applied. However, each has its strengths and its weaknesses, and some are not suitable for certain applications. Theory For a given acceleration of gravity, the liquid head in a tank or vessel generates a force per unit area or pressure (P) that is directly proportional to the liquid level (L) above the measurement point times the average density (ρ) of the liquid in the column. Solving for L: L = P/ρ While this formula is simple, its usage can be complicated. Virtually all applications using pressure transmitters for liquid level include one or more of the following issues: • Transmitter is not located at the zero level point • Transmitter is remote from the tank, above or below the primary pressure connection • Transmitter is isolated from process fluid with a flange or seal system • Tank is closed and, hence, subject to pressure or vacuum above the liquid • The fluid above the liquid may be the vapor of the liquid itself or an outside sourced fluid, such as a nitrogen blanket • Tank pressure reference connection is filled with a vapor (dry leg) • Tank pressure reference connection is filled with liquid (wet leg) • External wet legs can exist on both high and low pressure sides of the transmitter • Environmental conditions can be different for each of these external legs • Environmental conditions are usually different than tank conditions, e.g., a wet leg temperature might be very different from the in-tank temperature • Plus, changes in liquid and vapor densities. Reference: Dudley Harelson and Jonathan Rowe, Foxboro Division, Invensys, Multivariable Transmitters: A New Approach to Liquid Level Measurement. Copyright 2004 by ISA. Presented at ISA 2004.
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Important technologies used in level measurement include: Differential Pressure Among the most frequently used devices for measuring level, differential pressure (d/p) transmitters do not measure level by themselves. Instead, they measure the head pressure that a diaphragm senses due to the height of material in a vessel. That pressure measurement is multiplied by a second variable, the product’s density. That calculation shows the force being exerted on the diaphragm, which is then translated into a level measurement. Errors can occur, however, due to density variations of a liquid, caused by temperature or product changes. These variations must always be compensated for if accurate measurements are to be made. DPs are primarily used for clean liquids and should not be used with liquids that solidify as their concentrations increase, such as paper pulp stock. Bubblers This simple level measurement has a dip tube installed with the open end close to the bottom of the process vessel. A flow of gas (usually air) passes through the tube. When air bubbles escape from the open end, the air pressure in the tube corresponds to the hydraulic head of the liquid in the vessel. The air pressure in the bubble pipe varies proportionally with the change in head pressure. Calibration is directly affected by changes in product density, however. Because of this, it becomes a mass measurement. Displacers When a body is immersed in a fluid, it loses weight equal to the liquid weight displaced (Archimedes Principle). By detecting the apparent weight of the immersed displacer, a level instrument can be devised. If the cross sectional area of the displacer and the density of the liquid is constant, then a unit change in level will result in a reproducible unit change in displacer weight. Displacers also are affected by changes in product density. They should only be used for relatively non-viscous, clean fluids and work best for short spans. Floats Level measuring devices that use a float resting on the surface of the measured process fluid are legion. Many commodes use a simple, floatdriven, on/off switch, water-leveling apparatus. As the liquid in a process rises and falls in its vessel, the float rises and falls as well. Indicators advise the operator and/or the automation links as to the liquid’s level. The float may directly and mechanically trip a switch, push a magnet, pull a lever, or raise a pointer. Floats are made of brass, copper, stainless steel, and many types of plastics, among other materials.
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Float technology advantages include low cost, if remote reading is required; adaptability to wide variations in fluid densities; the ability to be used in extreme process conditions; unlimited tank height; and high accuracy. Disadvantages can include high maintenance requirements; vulnerability to particulate or product deposition; moving parts exposed to fluids; limited pressure rating; and not good for use in agitated vessels and for granular products. RF Admittance & Capacitance For applications permitting contact with what’s being measured, radio frequency (RF) is perhaps the most versatile technology for continuous level measurement. RF uses a constant voltage applied to a rod or cable (sensing element) in the process. The resulting RF current is monitored to infer the level of the process material. RF technologies handle a wide range of process conditions – from cryogenics to 1,000°F and from vacuum to 10,000 psi pressure. It can withstand severe service in harsh corrosive environments. RF also is the most preferred technology for point level measurement, able to achieve short span measurement accuracies many other technologies cannot achieve. As an intrusive technology, however, insulating granular measurements require special considerations, such as the moisture range and location of the sensing element to minimize errors caused by probe movement. Ultrasonic/Sonic Ultrasonic transmitters send a sound wave from a piezoelectric transducer to the contents of the vessel. The device measures the length of time it takes for the reflected sound wave to return to the transducer. A successful measurement depends on reflection from the process material in a straight line back to the transducer. Ultrasonic’s appeal is the transducer does not come in contact with the process material and does not contain any moving parts. Ultrasonic technology was the first industrially accepted non-contact level measurement in the process control market. Today’s ultrasonic devices typically require no calibration and can provide high accuracy level measurements in both liquid and solids applications. However, excessive process temperatures and pressure can be a limiting factor. And, since ultrasonic technology is based on a traveling sound pressure wave, a constant velocity via its media (air) is required to assure a high degree of accuracy. Material such as dust, heavy vapors, surface turbulence, foam and even ambient noise can affect the returning signal. Because sound travels at a constant known velocity at a given temperature, the time between the transmit burst and detection of the return echo
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will be proportional to the distance between the sensor and the reflecting object. The distance between the two can be calculated from: Distance = Rate x Time Radar Radar technology broadened non-contact level technology options. Radar’s inherent accuracy with its ability to have a more narrow beam angle avoided many vessel internal obstructions from reflecting false level signals. Radar is unaffected by vapors, steams, and many of the undesired affects of condensation that can affect ultrasonic devices. Properly applied, radar is completely capable of measuring most liquids and solids level applications. Frequency modulated continuous wave (FMCW) is fast enough for tank gauging, but normally too slow to measure the turbulent surfaces encountered in agitated process applications. Like ultrasonic, radar does not require calibration. Nuclear Nuclear level controls are used for continuous measurements, typically where most other technologies are unsuccessful. For example, they are extremely suitable for applications involving high temperatures and pressures, or corrosive materials within the vessel. No tank penetration is needed. Radiation from the source penetrates through the vessel wall and process fluid. A detector on the other side of the vessel measures the radiation field strength and infers the level in the vessel. The basic unit of radiation intensity is the curie, defined as that source intensity which undergoes 3.70 x 1010 disintegrations per second. For industrial applications, radiation field intensity is normally measured in milliroentgens per hour. Radiation field intensity in air can be calculated from: D = 1000
KMc d2
where D = radiation intensity in milliroentgens per hour (mR/hr) Mc = source strength in millicuries (MCi) d = distance to the source in inches K = source constant (0.6 for cesium 137; 2.0 for cobalt 60)
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Technology
Liquids
Granulars
Slurries
Interfaces
RF Admittance
O.K.
Use Caution
O.K.
O.K.
Ultrasonic
O.K.
Use Caution
O.K.
Not Practical
Radar
O.K.
Use Caution
O.K.
Not Practical
Differential Pressure
O.K.
Not Practical
Use Caution
Use Caution
Displacers
O.K.
Not Practical
Use Caution
Use Caution
Bubblers
O.K.
Not Practical
Use Caution
Not Practical
Nuclear
O.K.
Use Caution
O.K.
Use Caution
Courtesy of Ametek Drexelbrook. M. Bahner, A Practical Overview of Level Measurement Technologies. Reprinted with permission.
Other level measurement technologies include: Time Domain Reflectometry (TDR) Another contacting level measurement technology, TDR is also known by trade names such as “guided wire radar,” “radar on a rope,” “reflex radar,” etc. TDR is a pulse time of flight measurement much like ultrasonic and some radar techniques. Like radar, it transmits an electromagnetic pulse that travels at the speed of light to the surface of the material to be measured. It has a more narrow beam, or pulse width, than radar since it is completely focused on a flexible wire or rod. The measurement is determined by the transit time divided in half. TDR also does not require calibration. Magnetostrictive Magnetostrictive technology allows very high-accuracy level measurements of non-viscous liquids at ranges up to 50 feet. The technology is based on a float with embedded magnets that rides on a tube that contains magnetostrictive wire pulsed with a low voltage, high current electronic signal. When this signal intersects the magnetic field, generated by the float, a torsional pulse is reflected back to the electronics. This creates a time of flight measurement. Magnetostrictive devices require no calibration and no maintenance when properly applied. Hydrostatic Pressure A well-established level measurement method, hydrostatic pressure technology’s basic principle is measuring total head pressure above a pressure-sensing diaphragm. Measuring water in below-ground wells is a major application.
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Conductance Conductivity devices are primarily used for point level measurement. Materials being measured using conductivity switches must be conductive. Typically, conductivity switches are used to measure high and/or low level in liquids such as water, acids, conductive chemicals, etc. The conductivity electrodes are connected to a relay to provide control and require little or no calibration. Float Switch One of the oldest methods of level measurement, float devices continue to be used because they are simple to apply and cost effective on appropriate applications. Because floats are a mechanical level switch, it is important to use them in applications where coating build up will not occur. Clean, noncoating liquids are typically good applications for float measurement. Variable Displacement Measuring Devices V =
πD 2 (L) 4
where V = volume of the displacer D = diameter of the displacer L = length of displacer To Determine the Weight of the Displacer Ww =
V (Gw ) Gv
where Ww = weight of displacer V = volume of displacer Gv = volume of a gallon, H2O Gw = weight of a gallon, H2O References: 1. Ametek Drexelbrook brochure: Level Measurement Solutions …For Every Application. 2. Gillum, Donald R., Industrial Pressure, Level and Density Measurement , ISA—The Instrumentation, Systems, and Automation Society, 1995.
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Principles of Level Measuring Devices Hydrostatic Head Level Measurement p=
F A
where p = pressure on supporting surface F = weight, H2O A = area of supporting surface
F A G = specific gravity p=
h = vertical height of a column F = weight, H2O A = area of supporting surface Electrical Level Measurement, Total System Capacitance CE = C1 + C 2 + C 3
Open-Tank Head-Type Level Measurement P = pGh
where p = pressure corrected for atmosphere pressure
where C2 =
C3 =
0.614K a (L − 1) D log10 d 0.614(K p )(l ) D log10 d
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C1 = gland capacitance C2 = vapor phase capacitance C3 = liquid phase capacitance Ka = dielectric constant, vapor phase Kp = dielectric constant, liquid phase L = vessel height l = level height D = diameter of vessel d = probe diameter
Hydrostatic Level Measurement in an Open Tank
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Electrical Level Measurement C=
KA D
where C = capacitance in microfarads K = the dielectric constant A = the area of the plates D = the distance between plates
Equivalent Capacitance
Capacitor Probe in a Tank Probe in Nonconductive Fluid
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Dielectric Constants of Solids Acetic Acid (36°F)
4.1
Aluminum Phosphate
6.1
Asbestos
4.8
Asphalt
2.7
Bakelite
5.0
Barium Sulfate (60°F)
11.4
Calcium Carbonate
9.1
Cellulose
3.9
Cereals
3-5.0
Ferrous Oxide (60°F) Glass
14.2 3.7
Lead Oxide
25.9
Lead Sulfate
14.3
Magnesium Oxide
9.7
Mica
7.0
Napthalene
2.5
Nylon
45.0
Paper
45.0
Phenol (50°F)
2.0
Polyethylene
4-5.0
Polypropylene
1.5
Porcelain
5-7.0
Potassium Carbonate (60°F)
5.6
Quartz
4.3
Rice
3.5
Rubber (hard)
3.0
Sand (Silicon Dioxide)
3-5.0
Sulphur
3.4
Sugar
3.0
Urea
3.5
Zinc Sulfide
8.3
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Dielectric Constants of Granular and Powdery Materials Material
Loose
Packed
Fly Ash
1.7
2.0
Coke
65.3
70.0
Oatmeal
1.47
Molecular 5A, Sieve Dry
1.8
Polyethylene
2.2
Polyethylene, Powder
1.25
Reclaimed Foundry Sand
4.8
4.8
1.3 to 1.7
1.3 to 1.25
Laundry Detergent
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Dielectric Constants of Liquids Material
Temp. °F
Constant
Acetone
71
21.4
Ammonia
-30
22.0
Ammonia
68
15.5
Aniline
32
7.8
Aniline
68
7.3
Benzene
68
2.3
Bromine
68
3.1
Butane
30
1.4
Carbon Dioxide
32
1.6
Carbon Tetrachloride
68
2.2
Castor Oil
60
4.7
Chlorine
32
2.0
Chlorocyclohexane
76
7.6
Chloroform
32
5.5
Cumene
68
2.4
Cyclohexane
68
2.0
Dibromobenzene
68
8.8
Dibromohexane
76
5.0
Dowtherm
70
3.36
Ethanol
77
24.3
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Dielectric Constants of Liquids (cont.) Material
Temp. °F
Constant
Ethyl Acetate
68
6.4
Ethylene Chloride
68
10.5
Ethyl Ether
-40
5.7
Ethyl Ether
68
4.3
Formic Acid
60
58.5
Freon-12
70
2.4
Glycerine
68
47.0
Glycol
68
41.2
Heptane
68
1.9
Hexane
68
1.9
Hydrogen Chloride
82
4.6
Hydrogen Sulfide
48
5.8
Isobutyl Alcohol
68
18.7
Kerosine
70
1.8
Methyl Alcohol
32
37.5
Methyl Alcohol
68
33.1
Methyl Ether
78
5.0
Naphthalene
68
2.5
Octane
68
1.96
Oil, Transformer
68
2.2
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Dielectric Constants of Liquids (cont.) Material
Temp. °F
Constant
Pentane
68
1.8
Phenol
118
9.9
Phenol
104
15.0
Phosphorus
93
4.1
Propane
32
1.6
Styrene (Phenylethene)
77
2.4
Sulphur
752
3.4
Sulphuric Acid
68
84.0
Tetrachloroethylene
70
2.5
Toluene
68
2.4
Trichloroethylene
61
3.4
Urea
71
3.5
Vinyl Ether
68
3.9
Water
32
88.0
Water
68
80.0
Water
212
48.0
Xylene
68
2.4
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Weight of One Gallon (U.S.) of Water at Various Temperatures Temp. °C
Wt. in Vacuum Grams
Wt. in Vacuum Pounds
Wt. in Air Grams
Wt. in Air Pounds
0
3784.856
8.34417
3780.543
8.33467
1
3785.078
8.34466
3780.781
8.33518
2
3785.233
8.34500
3780.953
8.33556
3
3785.326
8.34520
3781.060
8.33580
4
3785.355
8.34527
3781.105
8.33590
5
3785.325
8.34520
3781.090
8.33587
6
3785.235
8.34500
3781.015
8.33570
7
3785.089
8.34468
3780.884
8.33541
8
3784.887
8.34424
3780.698
8.33500
9
3784.633
8.34368
3780.358
8.33447
10
3784.326
8.34300
3780.167
8.33383
11
3783.966
8.34221
3779.821
8.33307
12
3783.557
8.34130
3779.426
8.33220
13
3783.099
8.34030
3778.983
8.33122
14
3782.597
8.33919
3778.495
8.33014
15
3782.049
8.33798
3777.962
8.32897
16
3781.458
8.33668
3777.415
8.32770
17
3780.824
8.33528
3776.764
8.32633
18
3780.148
8.33379
3776.103
8.32487
19
3779.430
8.33221
3775.398
8.32332
20
3778.672
8.33054
3774.653
8.32167
21
3777.873
8.32877
3773.868
8.31994
22
3777.035
8.32693
3773.044
8.31813
23
3776.158
8.32499
3772.180
8.31622
24
3775.243
8.32298
3771.279
8.31424
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Weight of One Gallon (U.S.) of Water at Various Temperatures (cont.) Temp. °C
Wt. in Vacuum Grams
Wt. in Vacuum Pounds
Wt. in Air Grams
Wt. in Air Pounds
25
3774.291
8.32088
3770.340
8.31217
26
3773.320
8.31870
3769.364
8.31001
27
3772.277
8.31644
3768.352
8.30778
28
3771.218
8.31410
3767.306
8.30548
29
3770.123
8.31169
3766.224
8.30309
30
3768.995
8.30920
3765.109
8.30063
31
3768.995
8.30664
3763.961
8.29810
32
3766.641
8.30401
3762.780
8.29550
33
3765.416
8.30131
3761.568
8.29283
34
3764.160
8.29854
3760.324
8.29008
35
3762.874
8.29571
3759.050
8.28728
40
3756.018
8.28059
3752.255
8.27230
45
3748.41
8.2638
3744.42
8.2550
50
3740.19
8.2457
3736.22
8.2369
55
3731.34
8.2261
3727.37
8.2174
60
3721.91
8.2054
3717.95
8.1966
65
3711.88
8.1832
3707.93
8.1745
70
3701.35
8.1600
3697.42
8.1514
75
3690.30
8.1357
3686.38
8.1270
80
3678.72
8.1101
3674.81
8.1015
85
3666.68
8.0836
3662.78
8.0750
90
3654.15
8.0560
3650.27
8.0474
95
3641.21
8.0274
3637.34
8.0189
100
3627.81
7.9979
3623.95
7.9894
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Sonic and Ultrasonic Level Measurement Sound Absorption Coefficient of a Material d=
Sa Ss
where d = sound absorption coefficient Sa = sound energy absorbed Ss = sound energy incident upon the surface Radiation Used in Level Measurement Radiation Field Intensity in Air
D = 1000
where D = radiation intensity in mR/hr Mc = source strength in millicurie d = distance to the source, inches K = the source constant 1.3 for radium 226 0.6 for cesium 137 2.0 for cobalt 60
KMc d2
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6
Industrial Communications Buses Introduction and Network Topologies . . . . . . . . . . . . . . . . . . . . . . . 183 Industrial Networking Technologies . . . . . . . . . . . . . . . . . . . . . . . . 185 • • • • • • • • • • • • • • • • • • • •
ARCNet AS-i CANopen ControlNet DeviceNet Ethernet FOUNDATION fieldbus High Speed Ethernet FOUNDATION fieldbus H1 HART Interbus LonWorks Modbus Plus Modbus RTU/ASCII Profibus-DP/PA/FMS SERCOS Seriplex Smart Distributed System Time-Triggered Protocol (TTP/A/ TTP/C) Universal Serial Bus WorldFIP
Fieldbus Foundation Standard Unit Codes Table . . . . . . . . . . . . . 189 The Units Codes Table provides a standard set of globally defined scaling constants for Function Blocks and standard display strings for use in Electronic Device Descriptions.
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183
Introduction Early automation networks were called serial “buses.” The term fieldbus evolved from that thinking. Because each supplier's business model was different and focused on its own technology, one manufacturer's bus turned out to be different from another manufacturer's bus. This caused confusion among end-users, so standards committees attempted to fix the problem. However, standardizing on one or two technologies just didn't work, so today there are many industrial communications technologies. Ethernet, the clear winner in the information technology (IT) market, became the basis for the newest evolution of industrial automation networks—at least at the high-performance end. Lower-level networks connect sensors and actuators with different technologies. Exchanging information through any communications method requires both the transmission end and receivers to share a common agreement on the type of electrical signals used, the organization of the data, and the processes used to assure successful and error-free transmission of the information. Formalization of that agreement is called the communications protocol. All network architectures are described by the International Standards Organization (ISO) standard Open Systems Interconnection (OSI) basic reference model: standard ISO/IEC 7498-1:1994. Network Topology The network architecture, or wiring plan, is called the “topology” designed to interconnect network devices.
Star Topology Star is the most popular of all network topologies. It is used in practically all office networks, especially where Ethernet and Token Ring are used. Star networks usually have an active server, switch, or hub at the central location. The central server, switch, or hub allows easy reconfiguration of the network when devices are moved from one location to another. Multidrop Topology Some manufacturing equipment is built as a long sequence of machines organized in a straight line, with sensors and actuators positioned all along the line. A natural method to wire these devices is to
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use a “trunk cable” with “drops” to each device. Since many drops are required, this topology is called multidrop. A multidrop topology is sometimes used with a peer-to-peer protocol that allows direct communications between devices, but is often used with a master/slave protocol that only allows communications between the master and one slave device. Daisy-Chain Topology Similar to multidropped topology, a daisy-chain network is designed for devices laid out in a linear distributed pattern. However, each device needs must drive the signal on the wire only as far as the next device, often requiring less power than a multidropped topology. Data not intended for that device is always forwarded on to the next device. Ring Topology Ring networks, usually used where high reliability networking is desired, is very similar to the daisy-chain topology except the last device is always wired back to the first device or network master device. Mesh Topology Mesh networks provide more than one data path between network nodes in order to achieve path redundancy for purposes of reliability. However, mesh networks usually have an increased protocol burden called “routing.” Because they have alternative paths, mesh networks need to have the route defined by the destination address when a message enters the network. The Internet is a very large wired mesh network.
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185
Industrial Networking Technologies Fieldbus Name
Technology Developer
Year Introduced
Openness
Network Topology
Physical Media
ARCNet
Datapoint
1975
Chips, boards, ANSI docs
Star, bus distributed star
Coax, twisted pair, fiber
AS-i
AS-i Consortium
1993
800+ products, 150 vendors
Bus, ring, tree, star
2-wire cable
CANopen
CAN In Automation, Phillips
1995
17 chip vendors, 300 product vendors, open spec
Trunkline, dropline
Twisted pair, optional signal & power
ControlNet
Allen-Bradley
1996
Open spec, 2 chip vendors
Linear, tree, Coax, fiber star, or combination
DeviceNet
Allen-Bradley
1994
17 chip vendors
Trunkline, dropline
Twisted pair for signal & power
Ethernet
DEC, Intel, Xerox
1976
Many chip and product vendors
Bus, star, daisy chain
Thin coax, twisted pair, fiber; thick coax
FOUNDATION Fieldbus fieldbus FOUNDATION High Speed Ethernet
2000
Open standard
Star, Ring
Twisted pair, fiber 100 MBPS
FOUNDATION Fieldbus fieldbus H1 FOUNDATION
1995
Open standard
Bus, Tree
Twisted pair, fiber 31.25 KBPS
HART
Rosemount
1989
Open standard, 500 products, 130 suppliers
Point-topoint, digital multidrop
Twisted pair
Interbus
Phoenix Contact/ Interbus Club
1984
Products from 1,000+ vendors
Line, bus, tree
Twisted pair, fiber, slip ring, power line
LonWorks
Echelon
1991
Public doc on
Bus, ring, loop, star protocol
Twisted pair, fiber
Modbus Plus
Modicon
na
Proprietary, requires license/ ASICs
Linear
Twisted pair
Modbus RTU/ASCII
Modicon
1999
Open spec
Line, star, tree w/segments
Twisted pair
ProfibusDP/PA/FMS
German government
DP: 1994 PA: 1995 FMS: 1991
1,900 products from 300+ vendors
Line, star, ring
Twisted pair, fiber
SERCOS
German consortium
1989
IEC 61491, EN 61491
Ring/ Multiple rings
Plastic and glass fiber optic
Seriplex
APC
1990
Chips available w/ multiple interfaces
Tree, loop, ring, multidrop, star
4-wire shielded cable
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Industrial Networking Technologies (cont.) Fieldbus Name
Technology Developer
Year Introduced
Openness
Network Topology
Physical Media
Smart Distributed System
Honeywell
1994
17 chip vendors, 100+ products
Trunkline, dropline
Twisted pair for signal & power
TimeTriggered Protocol (TTP/A/ TTP/C)
Herman Kopetz TTTech AG
1998
Standardization under way
Bus, star, ring
2 Mbps, RS-485 to 5 Mbps, fiber at 25 Mbps
Universal Serial Bus
Compaq, Intel, 1996 HP, Lucent, Microsoft, NEC, Phillips
Royalty free for adopters
Point-topoint w/ hubs
Copper
World FIP
World FIP
Multiple chip vendors
Bus
Twisted pair, fiber
1988
Note: Wireless industrial networking control is imminent. Present installations exist using wireless access protocol (WAP) and the Bluetooth standard. Phone.com, Ericsson, and Nokia developed WAP. 3Com, Ericsson, Intel, IBM, Lucent, Microsoft, Motorola, Nokia, and Toshiba developed and continue to modify Bluetooth.
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Industrial Networking Technologies (cont.) Fieldbus Name
Maximum Devices (Nodes)
Maximum Distance
Communication Methods
Transmission Properties
Data Transfer Size
ARCNet
255 nodes
Coax 2,000 ft twisted pair 400 ft, fiber 6,000 ft
Peer-to-peer
19.53 Kbps to 10 Mbps
0-507 bytes
AS-i
62 slaves
100 m, 300 m w/repeater
Master/slave w/cyclic polling
EMI resistant,
4 bits
CANopen
127 nodes
25-1,000 m, depending on data rate
Master/slave, peer-to-peer, multicast, multimaster
10, 20, 50, 125, 250, 500, & 800 Kbps, 1 Mbps
8-byte variable
ControlNet
99 nodes
1,000 m on coaxial 2 nodes, 250 m with 48 nodes, 3-30 km fiber
Producer/ consumer, device object model
5 Mbps
0-510 bytes variable
DeviceNet
64 nodes
500 m, 6 km w/repeaters
Master/slave, multimaster, peer-to-peer
125, 250, 500 Kbps
8 bytes peerto-peer
Ethernet
1,024 nodes, expandable via routers
Thin coax Peer-to-peer 185 m, 10Base-T (twisted pair) 100 m, fiber 400 m, 50 km capability
10, 100 Mbps
46-1,500 bytes
FOUNDATION fieldbus High Speed Ethernet
IP addressing supports unlimited node count
100 m at 100 Mbps on twisted pair, 2,000 m at 100 Mbps on fiber 100 Mbps on fiber
Client/server, publisher/ subscriber event notification
100 Mbps
Varies, uses standard TCP/IP
FOUNDATION 240 nodes/ fieldbus H1 segment
1,900 m at 31.25 Kbps
Client/server, publisher/subscriber notification
31.25 Kbps
128 octets
HART
3 typical (w/masters 1 slave); 17 multidrop (2 masters 15 slaves)
3,000 m
Master/slave broadcast, multimaster
2-4 updates/ sec, continuous 4-20 mA current loop
Data byte structure has 11 bits, 15-50 bytes
Interbus
512 nodes
400 m/ segment, 12.8 km total
Master/slave w/total frame transfer
500 Kbps, 2 Mbps
0-246 bytes
LonWorks
32,000 nodes/ 2,000 m at domain 78 Kbps
Master/slave, peer-to-peer
1.25 Mbps full duplex
228 bytes
Modbus Plus
32 nodes/ 500 m/ segment, segment 64 maximum
Peer-to-peer
1 Mbps
Variable
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Industrial Networking Technologies (cont.) Fieldbus Name
Maximum Devices (Nodes)
Maximum Distance
Communication Methods
Transmission Properties
Data Transfer Size
Modbus RTU/ASCII
250 nodes/ segment
350 m
Master/slave
300 bps to 38.4 Kbps
0-254 bytes
ProfibusDP/PA/ FMS
126 nodes
DP: 100-1,200 m/segment PA: 1,900 m/ segment
Master/slave cyclic polling, master/master token passing or hybrid access
DP: 9.6, 19.2, 93.75, 187.5, 500 Kbps; 1.5, 3, 6, 12 Mbps PA: 31.25 Kbps
0-244
SERCOS
254 nodes/ ring
800 m node to node 200+ km total
na
2, 4, 8, 16 Mbps
na
Seriplex
500+ nodes
500+ ft
Master/slave, peer-to-peer
200 Mbps
7,680/transfer
Smart Distributed System
64 nodes, 126 addresses
500 m
Master/slave, peer-to-peer, multicast, multimaster
1 Mbps, 125, 250, & 500 Kbps
8-byte variable message
TimeTriggered Protocol (TTP/A/ TTP/C)
64/cluster, unlimited using gateways
20-100 m
TDMA, collision free, arbitration free, fully deterministic
Controlled by master node
1-240 byte/ transmission
Universal Serial Bus
127 per bus
5 m node to node
Packet protocol
Differential serial with NRZI encoding
1-1,000 bytes
WorldFIP
256 nodes
Up to 40 km
Peer-to-peer
31.25 Kbps, 1 & 2.5 Mbps, 6 Mbps fiber
No limit, variable, 128 bytes
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189
Fieldbus Foundation Standard Unit Codes Table This Standard Unit Codes Table, produced by the Fieldbus Foundation especially for the ISA Handbook of Measurement Equations and Tables, 2nd Edition, provides a standard set of globally defined scaling constants for Function Blocks and standard display strings for use in Electronic Device Descriptions. The list in the “Display” column is what the human interface device should display on the screen. The list under “Standard Dictionary Help String” is what the operator would see if he or she pressed the Help key for that parameter. Display
Description
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
K
Kelvin
SI
K
Kelvin
°C
degree Celsius
1°C = 1 K (delta);
°C
degree Celsius
°C(temperature) = °K(temperature) + 273.2” °F
degree Fahrenheit
1 °F = (5/9)°C (delta); °F(temperature) = (9/5) °C(temperature) +32”
°F
degree Fahrenheit
°R
degree Rankine
1°R = 1°F (delta); °R(temperature) = °F(temperature) - 459.69 °F(temperature) = (9/5) °C(temperature) +32”
°R
degree Rankine
r
radian
angle in which length of circular arc is equal to radius, (1/2π ) rev.1 r = 1 m/m = 1”
r
radian
°
degree
1° = (π /180)rad
°
degree
‘
minute
1 “ = (1°/60)
‘
minute
“
second
1 ‘’” = (1”/60)
\”
second
gon
gon (or grade)
1 gon = (π /200)rad
gon
gon (or grade)
rev
revolution
(2π ) r
rev
revolution
m
meter
SI
m
meter
km
kilometer
km
kilometer
cm
centimeter
cm
centimeter
mm
millimeter
mm
millimeter
µm
micrometer
µm
micrometer
nm
nanometer
nm
nanometer
pm
picometer
Å
angstrom
1 Å = 10-10m
pm
picometer
Å
angstrom
ft
feet
1 ft = 12 in
ft
feet
in
inch
1 in = 2.54 cm
in
inch
yd
yard
1 yd = 3 ft
yd
yard
mile
mile
1 mile = 5280 ft
mile
mile
nautical mile
nautical mile
1 nautical mile = 1852 meters
nautical mile
nautical mile
m2
square meter
m2
square meter
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
km2 cm2 dm2
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
square kilometer
km2
square kilometer
square centimeter
cm2
square centimeter
square decimeter
dm2
square decimeter
mm2
square millimeter
mm2
square millimeter
a
are
1 a = 1002 m2
a
are
ha
hectare
1 ha = 100004 m2
ha
hectare
in2
square inch
in2
square inch
ft2
square feet
ft2
square feet
yd2
square yard
yd2
square yard
mile2
square mile
mile2
square mile
m3
cubic meter
m3
cubic meter
dm3
cubic decimeter
dm3
cubic decimeter
cm3
cubic centimeter
cm3
cubic centimeter
mm3
cubic millimeter
mm3
cubic millimeter
L
liter
L
liter
cl
centiliter
cl
centiliter
ml
milliliter
ml
milliliter
hl
hectoliter
hl
hectoliter
in3
1 L = .00110-3 m3
cubic inch
in3
cubic inch
ft3
cubic feet
ft3
cubic feet
yd3
cubic yard
yd3
cubic yard
mile3
cubic mile
mile3
cubic mile
pint
pint
(1/2) quart
pint
pint
quart
quart
(1/4) gallon
quart
quart
gallon
US gallon
3.784 L
gallon
gallon
ImpGal
Imperial gallon
4.544 L
ImpGal
Imperial gallon
bushel
bushel
US Dry = 35.23808 liters; British = 35.99899 liters
bushel
bushel
bbl
barrel
1 bbl = 42 US gallons liquid bbl = 31.5 US Gallons; petroleum = 42 US Gallons; dry = 105 US Quarts
barrel
bbl (liq)
barrel liquid
1 liquid bbl = see bbl31.5 US gallons
bbl (liq)
barrel liquid
SCF
standard cubic foot
mass of a gas whose volume is one cubic foot at standard temperature and pressure
SCF
standard cubic foot
s
second
SI
s
second
ks
kilosecond
ks
kilosecond
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
ms
millisecond
ms
millisecond
µs
microsecond
µs
microsecond
min
minute
min
minute
h
hour
1 h = 60 min
h
hour
d
day
1 d = 24 h
d
day
m/s
meter per second
m/s
meter per second
mm/s
millimeter per second
mm/s
millimeter per second
1 min = 60 s
m/h
meter per hour
m/h
meter per hour
km/h
kilometer per hour
km/h
kilometer per hour
knot
knot
in/s
inch per second
1 knot = 1.852 km/h
knot
knot
in/s
inch per second
ft/s
feet per second
ft/s
feet per second
yd/s
yard per second
yd/s
yard per second
in/min
inch per minute
in/min
inch per minute
ft/min
feet per minute
ft/min
feet per minute
yd/min
yard per minute
yd/min
yard per minute
in/h
inch per hour
in/h
inch per hour
ft/h
feet per hour
ft/h
feet per hour
yd/h
yard per hour
yd/h
yard per hour
MPH
miles per hour
MPH
miles per hour
m/s2
meter per second per second
m/s2
meter per second per second
Hz
hertz
Hz
hertz
THz
terahertz
THz
terahertz
GHz
gigahertz
GHz
gigahertz
MHz
megahertz
MHz
megahertz
kHz
kilohertz
kHz
kilohertz
1/s
per second
1/s
per second
1/min
per minute
1/min
per minute
rev/s
revolutions per second
rev/s
revolutions per second
RPM
revolutions per minute
RPM
revolutions per minute
r/s
radian per second
r/s
radian per second
1/s2
per second per second
1/s2
per second per second
kg
kilogram
g
gram
frequency in cycles per second 1 Hz = 1 s-1
angular velocity, or frequency = (2π) Hz
SI
kg
kilogram
g
gram
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
mg
milligram
mg
milligram
Mg
megagram
Mg
megagram
t
metric ton
1 t = 103kg
t
metric ton
oz
ounce
US Fluid = 29.573 ml; British Fluid = 28.415 ml; Avoirdupois = 28.349 gm; Troy = 31.103 gm; Apothecary = 31.103 gm
oz
ounce
lb
pound (mass)
Avoirdupois = 0.453 kg; Troy = 0.373 kg; Apothecary = 0.373 kg
lb
pound (mass)
STon
short ton
1 Stonshort ton = 2000 lbpounds
STon
short ton
LTon
long ton
1 Ltonlong ton = 2240 lbpounds
LTon
long ton
kg/m3
kilograms per cubic meter
Mg/m3
megagrams per cubic meter
kg/m3
kilograms per cubic meter
Mg/m3
megagrams
Equivalence
Standard Dictionary Unit
per cubic meter
Standard Dictionary Help String
kg/dm3
kilograms per cubic decimeter
kg/dm3
kilograms per cubic decimeter
g/cm3
grams per cubic centimeter
g/cm3
grams per cubic centimeter
g/m3
grams per cubic meter
g/m3
grams per cubic meter
t/m3
metric tons per
t/m3
metric tons per cubic meter
cubic meter kg/L
kilograms per liter
kg/L
kilograms per liter
g/ml
grams per milliliter
g/ml
grams per milliliter
g/L
grams per liter
g/L
grams per liter
lb/in3
pounds per cubic inch
lb/in3
pounds per cubic Inch
lb/ft3
pounds per cubic foot
lb/ft3
pounds per cubic foot
lb/gal
pounds per US gallon
lb/gal
pounds per gallon
STon/yd3
short tons per cubic yard
1 STon = 2000 pounds
STon/yd3
short tons per cubic yard
degTwad
degrees Twaddell
degTwad = 200 SGU - 200
degTwad
degrees Twaddell
degBaume degrees Baume hv heavy
degBaume hv = 0 for 1 SGU, degBaume hv degrees Baume 66 for 1.842 SGU” heavy
degBaume degrees Baume lt light
degBaume lt = 145 (SGU-1) / SGU
degBaume lt degrees Baume light
degAPI
degAPI = (141.5 / SGU) 131.5
degAPI
degrees API
Copyright Fieldbus Foundation. Reprinted with permission.
degrees API
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
SGU
specific gravity units 1 SGU = 1 Kg/L
SGU
specific gravity units
kg/m
kilograms per meter
kg/m
kilograms per meter
mg/m
milligrams per meter
mg/m
milligrams per meter
tex
tex
tex
tex kilogram square meter kilogram meter per second
1 tex = 10-6kg/m = 1 g/km
kg-m2
kilogram square meter
kg-m2
kg-m/s
kilogram meter per second
kg-m/s
N
newton
N
newton
MN
meganewton
MN
meganewton
kN
kilonewton
kN
kilonewton
mN
millinewton
mN
millinewton
µN
micronewton
µN
micronewton
kg-m2/s
kilogram square meter per second
kg-m2/s
kilogram square meter per second
N-m
newton meter
N-m
newton meter
MN-m
meganewton meter
MN-m
meganewton meter
kN-m
kilonewton meter
kN-m
kilonewton meter
mN-m
millinewton meter
mN-m
millinewton meter
Pa
pascal
1 N = 1 kg-m/s2
1 Pa = 1 N/m2
Pa
pascal
GPa
gigapascal
GPa
gigapascal
MPa
megapascal
MPa
megapascal
kPa
kilopascal
kPa
kilopascal
mPa
millipascal
mPa
millipascal
µPa
micropascal
µPa
micropascal
hPa
hectopascal
hPa
hectopascal
bar
bar
1 bar = 100 kPa
bar
bar
mbar
millibar
1 mbar = 1 hPa
mbar
millibar
torr
torr
1 torr = 1mmHg
torr
torr
atm
atmospheres
14.7 psia; 760 mmHg
atm
atmospheres
psi
pounds per square inch
unreferenced or differential pressure
psi
pounds per square inch
psia
pounds per square inch absolute
referenced to a vacuum
psia
pounds per square inch absolute
psig
pounds per square inch gauge
referenced to atmosphere
psig
pounds per square inch gauge
g/cm2
gram per square centimeter
g/cm2
gram per square centimeter
kg/cm2
kilogram per square centimeter
kg/cm2
kilogram per square centimeter
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
Equivalence
inH2O
inches of water
1 inH2O = .0361 psi
inH2O (4°C)
inches of water at 4°C
inH2O (68°F)
inches of water at 68°F
inH2O (68°F) inches of water at 68°F
mmH2O
millimeters of water 1 mmH2O = .098 hPa
mmH2O
millimeters of water
mmH2O (4°C)
millimeters of water at 4°C
mmH2O (4°C)
millimeters of water at 4°C
mmH2O (68°F)
millimeters of water at 68°F
mmH2O (68°F)
millimeters of water at 68°F
ftH2O
feet of water
ftH2O
feet of water
ftH2O (4°C)
feet of water at 4°C
ftH2O (4°C)
feet of water at 4°C
ftH2O (68°F)
feet of water at 68°F
ftH2O (68°F)
feet of water at 68°F
inHg
inches of mercury
inHg (0°C)
inches of mercury at 0°C
mmHg
millimeters of mercury
mmHg (0°C)
millimeters of mercury at 0°C
mmHg (0°C) millimeters of mercury at 0°C
Pa-s
Pascal second
Pa-s
Pascal second
m2/s
square meter per second
m2/s
square meter per second
P
poise
P
poise
cP
centipoise
cP
centipoise
1 ftH2O = .433 psi
1 inHg = 13.6 inH2O
1 mmHg = 1.333 hPa
1 cP = 1 mPa-s absolute viscosity
Standard Dictionary Unit
Standard Dictionary Help String
inH2O
inches of water
inH2O (4°C)
inches of water at 4°C
inHg
inches of mercury
inHg (0°C)
inches of mercury at 0°C
mmHg
millimeters of mercury
St
stokes
cSt
centistokes
St
stokes
cSt
centistokes
N/m mN/m
newton per meter
N/m
newton per meter
millinewton meter
mN/m
millinewton per meter
J
joule
EJ
exajoules
PJ
petajoules
PJ
petajoules
TJ
terajoules
TJ
terajoules
1 cSt = 1 mm2/s kinematic viscosity
1 J = 1 N-m
J
joule
EJ
exajoules
GJ
gigajoules
GJ
gigajoules
MJ
megajoules
MJ
megajoules
kJ
kilojoules
kJ
kilojoules
mJ
millijoules
mJ
millijoules
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
WH
watt hour
1 W-h = 3.6 kJ
WH
watt hour
TWH
terawatt hour
TWH
terawatt hour
GWH
gigawatt hour
GWH
gigawatt hour
MWH
megawatt hour
MWH
megawatt hour
KWH
kilowatt hour
KWH
kilowatt hour
cal
calorie
kcal
kilocalorie
cal
calorie
kcal
kilocalorie
1 cal = 4.184 J
Mcal
megacalorie
Btu
British thermal unit
decatherm ft-lb W
watt
TW
terawatt
GW
gigawatt
GW
gigawatt
MW
megawatt
MW
megawatt
KW
kilowatt
KW
kilowatt
mW
milliwatt
mW
milliwatt
µW
microwatt
µW
microwatt
nW
nanowatt
nW
nanowatt
pW
picowatt
pW
picowatt
Mcal/h
megacalorie per hour
Mcal/h
megacalorie per hour
MJ/h
megajoule per hour
MJ/h
megajoule per hour
Btu/h
British thermal unit per hour
Btu/h
British thermal unit per hour
hp
horsepower
hp
horsepower
W/(m-K)
watt per meter kelvin
W/(m-K)
watt per meter kelvin
W/(m2-K)
watt per square meter kelvin
W/(m2-K)
watt per square meter kelvin
m2-K/W
square meter kelvin per watt
m2-K/W
square meter kelvin per watt
Mcal
megacalorie
Btu
British thermal unit
decatherm
decatherm
decatherm
foot-pound
ft-lb
foot-pound
W
watt
TW
terawatt
1 Btu = 0.2519958 kcal
1 W = 1 J/s
1 hp = 746 W
J/K
joule per kelvin
J/K
joule per kelvin
kJ/K
kilojoule per kelvin
kJ/K
kilojoule per kelvin
J/(kg-K)
joule per kilogram kelvin
J/(kg-K)
joule per kilogram kelvin
kJ/(kg-K)
kilojoule per kilogram kelvin
kJ/(kg-K)
kilojoule per kilogram kelvin
J/kg
joule per kilogram
J/kg
joule per kilogram
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
MJ/kg kJ/kg
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
megajoule per kilogram
MJ/kg
megajoule per kilogram
kilojoule per kilogram
kJ/kg
kilojoule per kilogram
A
ampere
A
ampere
kA
kiloampere
SI
kA
kiloampere
mA
milliampere
mA
milliampere
µA
microampere
µA
microampere
nA
nanoampere
nA
nanoampere
pA
picoampere
pA
picoampere
C
coulomb
C
coulomb
MC
megacoulomb
MC
megacoulomb
kC
kilocoulomb
kC
kilocoulomb
µC
microcoulomb
µC
microcoulomb
nC
nanocoulomb
nC
nanocoulomb
pC
picocoulomb
pC
picocoulomb
1 C = 1 A-s
A-h
ampere hour
A-h
ampere hour
C/m3
coulomb per cubic meter
1 A-h = 3.6 kC
C/m3
coulomb per cubic meter
C/mm3
coulomb per cubic millimeter
C/mm3
coulomb per cubic millimeter
C/cm3
coulomb per cubic centimeter
C/cm3
coulomb per cubic centimeter
kC/m3
kilocoulomb per cubic meter
kC/m3
kilocoulomb per cubic meter
mC/m3
millicoulomb per cubic meter
mC/m3
millicoulomb per cubic meter
µC/m3
microcoulomb per cubic meter
µC/m3
microcoulomb per cubic meter
C/m2
coulomb per square meter
C/m2
coulomb per square meter
C/mm2
coulomb per square millimeter
C/mm2
coulomb per square millimeter
C/cm2
coulomb per square centimeter
C/cm2
coulomb per square centimeter
kC/m2
kilocoulomb per square meter
kC/m2
kilocoulomb per square meter
mC/m2
millicoulomb per square meter
mC/m2
millicoulomb per square meter
µC/m2
microcoulomb per square meter
µC/m2
microcoulomb per square meter
V/m
volt per meter
V/m
volt per meter
MV/m
megavolt per meter
MV/m
megavolt per meter
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
kV/m
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
kilovolt per meter
kV/m
kilovolt per meter
V/cm
volt per centimeter
V/cm
volt per centimeter
mV/m
millivolt per meter
mV/m
millivolt per meter
µV/m
microvolt per meter
µV/m
microvolt per meter
V
volt
V
volt
1 V = 1 W/A
MV
megavolt
MV
megavolt
KV
kilovolt
KV
kilovolt
mV
millivolt
mV
millivolt
µV
microvolt
µV
microvolt
F
farad
F
farad
mF
millifarad
mF
millifarad
µF
microfarad
µF
microfarad
nF
nanofarad
nF
nanofarad
pF
picofarad
pF
picofarad
F/m
farad per meter
F/m
farad per meter
µF/m
microfarad per meter
µF/m
microfarad per meter
nF/m
nanofarad per meter
nF/m
nanofarad per meter
pF/m
picofarad per meter
pF/m
picofarad per meter
C-m
coulomb meter
C-m
coulomb meter
A/m2
ampere per square meter
A/m2
ampere per square meter
MA/m2
megampere per square meter
MA/m2
megampere per square meter
A/cm2
ampere per square centimeter
A/cm2
ampere per square centimeter
kA/m2
kiloampere per square meter
kA/m2
kiloampere per square meter
1 F = 1 C/V
A/m
ampere per meter
A/m
ampere per meter
kA/m
kiloampere per meter
kA/m
kiloampere per meter
A/cm
ampere per centimeter
A/cm
ampere per centimeter
T
tesla
T
tesla
mT
millitesla
mT
millitesla
µT
microtesla
µT
microtesla
nT
nanotesla
Wb
weber
mWb
milliweber
1 T = 1 Wb/m2
1 Wb = 1 V-s
nT
nanotesla
Wb
weber
mWb
milliweber
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ISA Handbook of Measurement Equations and Tables
Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
Wb/m
weber per meter
Wb/m
weber per meter
kWb/m
kiloweber per meter
kWb/m
kiloweber per meter
H
henry
H
henry
mH
millihenry
mH
millihenry microhenry
1 H = 1 Wb/A
µH
microhenry
µH
nH
nanohenry
nH
nanohenry
picoH
picohenry
pH
picohenry
H/m
henry per meter
H/m
henry per meter
µH/m
microhenry per meter
µH/m
microhenry per meter
nH/m
nanohenry per meter
nH/m
nanohenry per meter
A-m2
ampere square meter
A-m2
ampere square meter
N-m2/A
newton square meter per ampere
N-m2/A
newton square meter per ampere
Wb-m
weber meter
Ohm
Ohm
1 ohmΩ = 1 V/A
Wb-m
weber meter
Ohm
Ohm
GOhm
gigaOhm
GOhm
gigaOhm
MOhm
megaOhm
MOhm
megaOhm
kOhm
kiloOhm
kOhm
kiloOhm
mOhm
milliOhm
mOhm
milliOhm
µOhm
microOhm
µOhm
microOhm
S
siemens
S
siemens
kS
kilosiemens
kS
kilosiemens
mS
millisiemens
mS
millisiemens
µS
microsiemens
µS
microsiemens
Ohm-m
Ohm meter
Ohm-m
Ohm meter
GOhm-m
gigaOhm meter
GOhm-m
gigaOhm meter
MOhm-m
megaOhm meter
MOhm-m
megaOhm meter
kOhm-m
kiloOhm meter
kOhm-m
kiloOhm meter
Ohm-cm
Ohm centimeter
Ohm-cm
Ohm centimeter
1 S = 1 /ohm Ω -1
mOhm-m
milliOhm meter
mOhm-m
milliOhm meter
µOhm-m
microOhm meter
µOhm-m
microOhm meter
nOhm-m
nanoOhm meter
nOhm-m
nanoOhm meter
S/m
siemens per meter
S/m
siemens per meter
MS/m
megasiemens per meter
MS/m
megasiemens per meter
kS/m
kilosiemens per meter
kS/m
kilosiemens per meter
mS/cm
millisiemens per centimeter
mS/cm
millisiemens per centimeter
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
µS/mm
microsiemens per millimeter
1/H
per henry
sr
steradian
W/sr
watt per steradian
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
mS/mm
micorsiemens per millimeter
1/H 1 sr = conical angle which sr encloses a surface area on a sphere equal to square of the radius of sphere1 sr = 1 m2/m2 = 1
per henry steradian
W/sr
watt per steradian
W/(sr-m2) watt per steradian square meter
W/(sr-m2)
watt per steradian square meter
W/(m2)
W/(m2)
watt per square meter
watt per square meter
lm
lumen
lm-s
lumen second
lm-h
lumen hour
lm/m2
1 lm = 1 cd-sr
1 lm-h = 3600 lm-s
lumen per square meter
lm
lumen
lm-s
lumen second
lm-h
lumen hour
lm/m2
lumen per square meter
lm/W
lumen per watt
lx
lux
lm/W
lumen per watt
lx
lux
lx-s
lux second
lx-s
lux second
cd
candela
cd/m2
candela per square meter
cd
candela
cd/m2
candela per square meter
g/s g/min
gram per second
g/s
gram per second
gram per minute
g/min
gram per minute
g/h
gram per hour
g/h
gram per hour
g/d
gram per day
g/d
gram per day
kg/s
kilogram per second
kg/s
kilogram per second
kg/min
kilogram per minute
kg/min
kilogram per minute
kg/h
kilogram per hour
kg/h
kilogram per hour
kg/d
kilogram per day
kg/d
kilogram per day
t/s
metric ton per second
t/s
metric ton per second
t/min
metric ton per minute
t/min
metric ton per minute
t/h
metric ton per hour
t/h
metric ton per hour
t/d
metric ton per day
t/d
metric ton per day
lb/s
pound per second
lb/s
pound per second
lb/min
pound per minute
lb/min
pound per minute
lb/h
pound per hour
lb/h
pound per hour
lb/d
pound per day
lb/d
pound per day
1 lx = 1 lm/m2
SI
1 t = 103 kg
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
STon/s
short ton per second
1 Ston = 2000 pounds
STon/s
short ton per second
STon/min short ton per minute
STon/min
short ton per minute
STon/h
STon/h
short ton per hour
short ton per hour
STon/d
short ton per day
LTon/s
long ton per second
1 Lton = 2240 pounds
STon/d
short ton per day
LTon/s
long ton per second
LTon/min long ton per minute
LTon/min
long ton per minute
LTon/h
LTon/h
long ton per hour
long ton per hour
LTon/d
long ton per day
LTon/d
long ton per day
%
percent
%
percent
% sol/wt
percent solids per weight
% sol/wt
percent solids per weight
% sol/vol percent solids per volume
% sol/vol
percent solids per volume
% stm qual
percent steam quality
% stm qual
percent steam quality
% plato
percent plato
% plato
percent plato cubic meter per second
% sugar by wt.
m3/s
cubic meter per second
m3/s
m3/min
cubic meter per minute
m3/min
cubic meter per minute
m3/h
cubic meter per hour
m3/h
cubic meter per hour
m3/d
cubic meter per day
m3/d
cubic meter per day
L/s
liter per second
L/s
liter per second
L/min
liter per minute
L/min
liter per minute
L/h
liter per hour
L/h
liter per hour
L/d
liter per day
L/d
liter per day
ML/d
megaliter per day
ML/d
megaliter per day
CFS
cubic feet per second
CFS
cubic feet per second
CFM
cubic feet per minute
CFM
cubic feet per minute
CFH
cubic feet per hour
CFH
cubic feet per hour
ft3/d
cubic feet per day
ft3/d
cubic feet per day
SCFM
standard cubic feet per minute
SCFM
standard cubic feet per minute
SCFH
standard cubic feet per hour
SCFH
standard cubic feet per hour
gal/s
US gallon per second
gal/s
gallon per second
GPM
US gallon per minute
GPM
gallon per minute
gal/h
US gallon per hour
gal/h
gallon per hour
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
gal/d
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
US gallon per day
gal/d
gallon per day
Mgal/d
mega US gallon per day
Mgal/d
megagallon per day
ImpGal/s
Imperial gallon per second
ImpGal/s
Imperial gallon per second
ImpGal/ min
Imperial gallon per minute
ImpGal/min
Imperial gallon per minute
ImpGal/h Imperial gallon per hour
ImpGal/h
Imperial gallon per hour
ImpGal/d Imperial gallon per day
ImpGal/d
Imperial gallon per day
bbl/s
barrel per second
bbl/s
barrel per second
bbl/min
barrel per minute
1 bbl = 42 US gallons
bbl/min
barrel per minute
bbl/h
barrel per hour
bbl/h
barrel per hour
bbl/d
barrel per day
bbl/d
barrel per day
W/m2
watt per square meter
W/m2
watt per square meter
mW/m2
milliwatt per square meter
mW/m2
milliwatt per square meter
µW/m2
microwatt per square meter
µW/m2
microwatt per square meter
pW/m2
picowatt per square meter
pW/m2
picowatt per square meter
Pa-s/m3
pascal second per cubic meter
Pa-s/m3
pascal second per cubic meter
N-s/m
newton second per meter
N-s/m
newton second per meter
Pa-s/m
pascal second per meter
Pa-s/m
pascal second per meter
B
bel
dB
decibel
1 dB = 10-1B
mol
mole
SI
kmol
kilomole
B
bel
dB
decibel
mol
mole
kmol
kilomole
mmol
millimole
mmol
millimole
µmol
micromole
µmol
micromole
kg/mol
kilogram per mole
kg/mol
kilogram per mole
g/mol
gram per mole
g/mol
gram per mole
m3/mol
cubic meter per mole
m3/mol
cubic meter per mole
dm3/mol
cubic decimeter per mole
dm3/mol
cubic decimeter per mole
cm3/mol
cubic centimeter per mole
cm3/mol
cubic centimeter per mole
L/mol
liters per mole
L/mol
liters per mole
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
J/mol kJ/mol
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
joule per mole
J/mol
joule per mole
kilojoule per mole
kJ/mol
kilojoule per mole
J/(mol-K) joule per mole kelvin
J/(mol-K)
joule per mole kelvin
mol/m3
mole per cubic meter
mol/m3
mole per cubic meter
mol/dm3
mole per cubic decimeter
mol/dm3
mole per cubic decimeter
mol/L
mole per liter
mol/L
mole per liter
mol/kg
mole per kilogram
mol/kg
mole per kilogram
mmol/kg
millimole per kilogram
mmol/kg
millimle per kilogram
Bq
becquerel
Bq
becquerel megabecquerel
1 Bq = 1-s-1
MBq
megabecquerel
MBq
kBq
kilobequerel
kBq
kilobequerel
Bq/kg
becquerel per kilogram
Bq/kg
becquerel per kilogram
kBq/kg
kilobecquerel per kilogram
kBq/kg
kilobecquerel per kilogram
MBq/kg
megabecquerel per kilogram
MBq/kg
megabecquerel per kilogram
Gy
gray
Gy
gray
mGy
milligray
rad
rad
Sv
sievert
mSv
millisievert
rem
rem
C/kg
1 Gy = 1 J/kg
mGy
milligray
1 rad = 10-2 Gy
rad
rad
1 Sv = 1 J/kg
Sv
sievert
mSv
millisievert
rem
rem
coulomb per kilogram
C/kg
coulomb per kilogram
mC/kg
millicoulomb per kilogram
mC/kg
millicoulomb per kilogram
R
röntgen
R
röntgen
m3/C
cubic meter per coulomb
m3/C
cubic meter per coulomb
V/K
volt per kelvin
V/K
volt per kelvin
mV/K
millivolt per kelvin
mV/K
millivolt per kelvin
pH
pH
ppm
parts per million
1 rem = 10-2 Sv
1 R = 2.58 x 10-4 C/kg
acidity or alkalinity of pH solution, negative base 10 log of Hydrogen ion activity, acid range 0-7, alkaline range 7-14
Copyright Fieldbus Foundation. Reprinted with permission.
ppm
pH
parts per million
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
ppb
parts per billion
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
ppb
parts per billion
ppt
parts per thousand
ppt
parts per thousand
degBrix
degrees Brix
% sugar by wt.
degBrix
degrees Brix
degBall
degrees Balling
% sugar by wt.
degBall
degrees Balling
proof/vol
proof per volume
proof/vol
proof per volume
proof/ mass
proof per mass
proof/mass
proof per mass
lb/ImpGal
pound per Imperial gallon
lb/ImpGal
pound per Imperial gallon
kcal/s
kilocalorie per second
kcal/s
kilocalorie per second
kcal/min
kilocalorie per minute
kcal/min
kilocalorie per minute
kcal/h
kilocalorie per hour
kcal/h
kilocalorie per hour
kcal/d
kilocalorie per day
kcal/d
kilocalorie per day
Mcal/s
megacalorie per second
Mcal/s
megacalorie per second
Mcal/min
megacalorie per minute
Mcal/min
megacalorie per minute
Mcal/d
megacalorie per day
Mcal/d
megacalorie per day
kJ/s
kilojoules per second
kJ/s
kilojoules per second
kJ/min
kilojoules per minute
kJ/min
kilojoules per minute
kJ/h
kilojoules per hour
kJ/h
kilojoules per hour
kJ/d
kilojoules per day
kJ/d
kilojoules per day
MJ/s
megajoules per second
MJ/s
megajoules per second
MJ/min
megajoules per minute
MJ/min
megajoules per minute
MJ/d
megajoules per day
MJ/d
megajoules per day
Btu/s
British thermal units per second
Btu/s
British thermal units per second
Btu/min
British thermal units per minute
Btu/min
British thermal units per minute
Btu/day
British thermal units per day
Btu/day
British thermal units per day
µgal/s
micro US gallon per second
µgal/s
micro US gallon per second
mgal/s
milli US gallon per second
mgal/s
milli US gallon per second
kgal/s
kilo US gallon per second
kgal/s
kilo US gallon per second
Mgal/s
mega US gallon per second
Mgal/s
mega US gallon per second
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
µgal/min
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
micro US gallon per minute
µgal/min
micro US gallon per minute
mgal/min
milli US gallon per minute
mgal/min
milli US gallon per minute
kgal/min
kilo US gallon per minute
kgal/min
kilo US gallon per minute
Mgal/min
mega US gallon per minute
Mgal/min
mega US gallon per minute
µgal/h
micro US gallon per hour
µgal/h
micro US gallon per hour
mgal/h
milli US gallon per hour
mgal/h
milli US gallon per hour
kgal/h
kilo US gallon per hour
kgal/h
kilo US gallon per hour
Mgal/h
mega US gallon per hour
Mgal/h
mega US gallon per hour
µgal/d
micro US gallon per day
µgal/d
micro US gallon per day
mgal/d
milli US gallon per day
mgal/d
milli US gallon per day
kgal/d
kilo US gallon per day
kgal/d
kilo US gallon per day
µImpGal/s
micro Imperial gallon per second
µImpGal/s
micro Imperial gallon per second
mImpGal/s milli Imperial gallon per second
mImpGal/s
milli Imperial gallon per second
kImpGal/s
kImpGal/s
kilo Imperial gallon per second
MImpGal/s mega Imperial gallon per second
MImpGal/s
mega Imperial gallon per second
µImpGal/ min
micro Imperial gallon per minute
µImpGal/min
micro Imperial gallon per minute
mImpGal/ min
milli Imperial gallon per minute
mImpGal/min milli Imperial gallon per minute
kImpGal/ min
kilo Imperial gallon per minute
kImpGal/min
MImpGal/ min
mega Imperial gallon per minute
MImpGal/min mega Imperial gallon per minute
µImpGal/h
micro Imperial gallon per hour
µImpGal/h
micro Imperial gallon per hour
mImpGal/h milli Imperial gallon per hour
mImpGal/h
milli Imperial gallon per hour
kImpGal/h
kImpGal/h
kilo Imperial gallon per hour
MImpGal/h
mega Imperial gallon per hour
kilo Imperial gallon per second
kilo Imperial gallon per hour
MImpGal/h mega Imperial gallon per hour Copyright Fieldbus Foundation. Reprinted with permission.
kilo Imperial gallon per minute
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
µImpGal/d
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
micro Imperial gallon per day
µImpGal/d
micro Imperial gallon per day
mImpGal/d
milli Imperial gallon per day
mImpGal/d
milli Imperial gallon per day
kImpGal/d
kilo Imperial gallon per day
kImpGal/d
kilo Imperial gallon per day
MImpGal/d
mega Imperial gallon per day
MImpgal/d
mega Imperial gallon per day
µbbl/s
microbarrel per second
µbbl/s
microbarrel per second
mbbl/s
millibarrel per second
mbbl/s
millibarrel per second
kbbl/s
kilobarrel per second
kbbl/s
kilobarrel per second
Mbbl/s
megabarrel per second
Mbbls
megabarrel per second
µbbl/min
microbarrel per minute
µbbl/min
microbarrel per minute
mbbl/min
millibarrel per minute
mbbl/s
millibarrel per minute
kbbl/min
kilobarrel per minute
kbbl/min
kilobarrel per minute
Mbbl/min
megabarrel per minute
Mbbl/min
megabarrel per minute
µbbl/h
microbarrel per hour
µbbl/h
microbarrel per hour
mbbl/h
millibarrel per hour
mbbl/h
millibarrel per hour
kbbl/h
kilobarrel per hour
kbbl/h
kilobarrel per hour
Mbbl/h
megabarrel per hour
Mbbl/h
megabarrel per hour
µbbl/d
microbarrel per day
µbbl/d
microbarrel per day
mbbl/d
millibarrel per day
mbbl/d
millibarrel per day
kbbl/d
kilobarrel per day
kbbl/d
kilobarrel per day
Mbbl/d
megabarrel per day
Mbbl/d
megabarrel per day
µm3/s
cubic micrometer per second
µm3/s
cubic micrometer per second
mm3/s
cubic millimeter per second
mm3/s
cubic millimeter per second
km3/s
cubic kilometer per second
km3/s
cubic kilometer per second
Mm3/s
cubic megameter per second
Mm3/s
cubic megameter per second
µm3/min
cubic micrometer per minute
µm3/min
cubic micrometer per minute
mm3/min
cubic millimeter per minute
mm3/min
cubic millimeter per minute
km3/min
cubic kilometer per minute
km3/min
cubic kilometer per minute
Mm3/min
cubic megameter per minute
Mm3/min
cubic megameter per minute
µm3/h
cubic micrometer per hour
µm3/h
cubic micrometer per hour
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
mm3/h
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
cubic millimeter per hour
cubic millimeter per hour
mm3/h
km3/h
cubic kilometer per hour
km3/h
cubic kilometer per hour
Mm3/h
cubic megameter per hour
Mm3/h
cubic megameter per hour
µm3/d
cubic micrometer per day
µm3/d
cubic micrometer per day
mm3/d
cubic millimeter per day
mm3/d
cubic millimeter per day
km3/d
cubic kilometer per day
km3/d
cubic kilometer per day
Mm3/d
cubic megameter per day
Mm3/d
cubic megameter per day
cm3/s
cubic centimeter per second
cm3/s
cubic centimeter per second
cm3/min cubic centimeter per minute
cm3/min
cubic centimeter per minute
cm3/h
cubic centimeter per hour
cm3/h
cubic centimeter per hour
cm3/d
cubic centimeter per day
cm3/d
cubic centimeter per day
kcal/kg
kilocalorie per kilogram
kcal/kg
kilocalorie per kilogram
Btu/lb
British thermal unit per pound
Btu/lb
British thermal unit per pound
kL
kiloliter
kL
kiloliter
kL/min
kiloliter per minute
kL/min
kiloliter per minute
kL/h
kiloliter per hour
kL/h
kiloliter per hour
kL/d
kiloliter per day
kL/d
kiloliter per day
Nm3
Normal cubic meter (0°C, 1atm)
Nm3
Normal cubic meter (0°C, 1atm)
Nm3/s
Normal cubic meter per second (0°C, 1atm)
Nm3/s
Normal cubic meter per second (0°C, 1atm)
Nm3/m
Normal cubic meter per minute (0°C, 1atm)
Nm3/m
Normal cubic meter per minute (0°C, 1atm)
Nm3/h
Normal cubic meter per hour (0°C, 1atm)
Nm3/h
Normal cubic meter per hour (0°C, 1atm)
Nm3/d
Normal cubic meter per day (0°C, 1atm)
Nm3/d
Normal cubic meter per day (0°C, 1atm)
Sm3
Standard cubic meter (20°C, 1atm)
Sm3
Standard cubic meter (20°C, 1atm)
Sm3/s
Standard cubic meter per second (20°C, 1atm)
Sm3/s
Standard cubic meter per second (20°C, 1atm)
Sm3/m
Standard cubic meter per minute (20°C, 1atm)
Sm3/m
Standard cubic meter per minute (20°C, 1atm)
Sm3/h
Standard cubic meter per hour (20°C, 1atm)
Sm3/h
Standard cubic meter per hour (20°C, 1atm)
Sm3/d
Standard cubic meter per day (20°C, 1atm)
Sm3/d
Standard cubic meter per day (20°C, 1atm)
NL
Normal liter (0°C, 1atm)
NL
Normal liter (0°C, 1atm)
NL/s
Normal liter per second (0°C, 1atm)
NL/s
Normal liter per second (0°C, 1atm)
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
NL/m
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
Normal liter per minute (0°C, 1atm)
NL/m
Normal liter per minute (0°C, 1atm)
NL/h
Normal liter per hour (0°C, 1atm)
NL/h
Normal liter per hour (0°C, 1atm)
NL/d
Normal liter per day (0°C, 1atm)
NL/d
Normal liter per day (0°C, 1atm)
SL
Standard liter (20°C, 1atm)
SL
Standard liter (20°C, 1atm)
SL/s
Standard liter per second (20°C, 1atm)
SL/s
Standard liter per second (20°C, 1atm)
SL/m
Standard liter per minute (20°C, 1atm)
SL/m
Standard liter per minute (20°C, 1atm)
SL/h
Standard liter per hour (20°C, 1atm)
SL/h
Standard liter per hour (20°C, 1atm)
SL/d
Standard liter per day (20°C, 1atm)
SL/d
Standard liter per day (20°C, 1atm)
Paa
pascal absolute
Paa
pascal absolute
Pag
pascal gauge
Pag
pascal gauge
GPaa
gigapascal absolute
GPaa
gigapascal absolute
GPag
gigapascal gauge
GPag
gigapascal gauge
MPaa
megapascal absolute
MPaa
megapascal absolute
MPag
megapascal gauge
MPag
megapascal gauge
kPaa
kilopascal absolute
kPaa
kilopascal absolute
kPag
kilopascal gauge
kPag
kilopascal gauge
mPaa
millipascal absolute
mPaa
millipascal absolute
mPag
millipascal gauge
mPag
millipascal gauge
µPaa
micropascal absolute
µPaa
micropascal absolute
µPag
micropascal gauge
µPag
micropascal gauge
hPaa
hectopascal absolute
hPaa
hectopascal absolute
hPag
hectopascal gauge
hPag
hectopascal gauge
g/cm2a
gram per square centimeter absolute
g/cm2a
gram per square centimeter absolute
g/cm2g
gram per square centimeter gauge
g/cm2g
gram per square centimeter gauge
kg/cm2a
kilogram per square centimeter absolute
kg/cm2a
kilogram per square centimeter absolute
kg/cm2g kilogram per square centimeter gauge
kg/cm2g
kilogram per square centimeter gauge
inH2Oa
inches of water absolute
inH2Oa
inches of water absolute
inH2Og
inches of water gauge
inH2Og
inches of water gauge
inH2Oa (4°C)
inches of water absolute at 4°C
inH2Oa(4°C)
inches of water absolute at 4°C
Copyright Fieldbus Foundation. Reprinted with permission.
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Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
inH2Og (4°C)
Equivalence
Standard Dictionary
Standard Dictionary Help String Unit
inches of water gauge at 4°C
inH2Og(4°C)
inches of water gauge at 4°C
inH2Oa (68°F)
inches of water absolute at 68°F
inH2Oa(68°F) inches of water absolute at 68°F
inH2Og (68°F)
inches of water gauge at 68°F
inH2Og(68°F) inches of water gauge at 68°F
mmH2Oa millimeters of water absolute
mmH2Oa
millimeters of water absolute
mmH2Og millimeters of water gauge
mmH2Og
millimeters of water gauge
mmH2Oa millimeters of water (4°C) absolute at 4°C
mmH2Oa (4°C)
millimeters of water absolute at 4°C
mmH2Og millimeters of water gauge (4°C) at 4°C
mmH2Og (4°C)
millimeters of water gauge at 4°C
mmH2Oa millimeters of water (68°F) absolute at 68°F
mmH2Oa (68°F)
millimeters of water absolute at 68°F
mmH2Og millimeters of water gauge (68°F) at 68°F
mmH2Og (68°F)
millimeters of water gauge at 68°F
ftH2Oa
feet of water absolute
ftH2Oa
feet of water absolute
ftH2Og
feet of water gauge
ftH2Og
feet of water gauge
ftH2Oa (4°C)
feet of water absolute at 4°C
ftH2Oa(4°C)
feet of water absolute at 4°C
ftH2Og (4°C)
feet of water gauge at 4°C
ftH2Og(4°C)
feet of water gauge at 4°C
ftH2Oa (68°F)
feet of water absolute at 68°F
ftH2Oa(68°F)
feet of water absolute at 68°F
ftH2Og (68°F)
feet of water gauge at 68°F
ftH2Og(68°F) feet of water gauge at 68°F
inHga
inches of mercury absolute
inHga
inches of mercury absolute
inHgg
inches of mercury gauge
inHgg
inches of mercury gauge
inHga (0°C)
inches of mercury absolute at 0°C
inHga(0°C)
inches of mercury absolute at 0°C
inHgg (0°C)
inches of mercury gauge at 0°C
inHgg(0°C)
inches of mercury gauge at 0°C
mmHga
millimeters of mercury absolute
mmHga
millimeters of mercury absolute
mmHgg
millimeters of mercury gauge
mmHgg
millimeters of mercury gauge
mmHga (0°C)
millimeters of mercury absolute at 0°C
mmHga (0°C)
millimeters of mercury absolute at 0°C
mmHgg (0°C)
millimeters of mercury gauge at 0°C
mmHgg (0°C)
millimeters of mercury gauge at 0°C
mv/pH
millivolts per pH
mv/pH
millivolts per pH
µS/cm
microsiemens per centimeter
µS/cm
microsiemens per centimeter
Mohm-cm
megaOhm-centimeter
Mohm-cm megaOhm-centimeter Copyright Fieldbus Foundation. Reprinted with permission.
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209
Fieldbus Foundation Standard Unit Codes Table (cont.) Display
Description
ml/min
Equivalence
Standard Dictionary Unit
Standard Dictionary Help String
milliliters per minute
ml/min
milliliters per minute
Barg
bar gauge
Barg
bar gauge
mBarg
millibar gauge
mBarg
millibar gauge
ft/s2
feet per second per second
ft/s2
feet per second per second
G’s
G’s
G’s
G’s
microns
microns
1 millionth of a meter
microns
microns
mils
mils
1 thousandth of an inch
mils
mils
lb/in
pounds per inch
lb/in
pounds per inch
Bara
Bar absolute
Bara
Bar absolute
MSCFD
thousand standard cubic feet per day
MSCFD
thousand standard cubic feet per day
MMSCFD million standard cubic feet per day
MMSCFD
million standard cubic feet per day
MLB/H
thousand pounds per hour
MLB/H
thousands pounds per hour
nA/ppm
nanoamperes per part per million
nA/ppm
nanoamperes per part per million
mS/m
millisiemens per meter
mS/m
millisiemens per meter
µS/m
microsiemens per meter
µS/m
microsiemens per meter
kOhm-cm
kiloOhm-centimeter
kOhm-cm
kiloOhm-centimeter
%/°C
percent per degrees Centigrade
%/°C
percent per degrees Centigrade
pH/°C
pH per degrees Centigrade
pH/°C
pH per degrees Centigrade
/cm
reciprocal centimeter
/cm
reciprocal centimeter
Copyright Fieldbus Foundation. Reprinted with permission.
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7
Safety
Hazardous Classes and Zones - Standard Definitions . . . . . . . . . . 213 Class, Division and Zone Definitions . . . . . . . . . . . . . . . . . . . . . . . . 213 Area (location) Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 North American methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Table Showing Area Classification . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Table Showing Apparatus Grouping . . . . . . . . . . . . . . . . . . . . . . . . 219 Table Summarizing NEC Class I, II, III Hazardous Locations . . . . . 220 Safety Integrity Level Verification. . . . . . . . . . . . . . . . . . . . . . . . . . . 221 • Equation Calculations Extracted from ISA-TR84.00.02-2002 Part 2, Safety Instrumentation Functions (SIF) – Safety Integrity Level (SIL) Evaluation Techniques Part 2: Determining the SIL of a SIF via Simplified Equations.
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Hazardous Classes and Zones - Standard Definitions A standard titled ANSI/ISA-12.01.01-1999, Definitions and Information Pertaining to Electrical Apparatus in I Hazardous (Classified) Locations, defines terminology to help those involved with the design, manufacture, installation, and maintenance of apparatus used in hazardous (classified) locations. It is also intended to promote uniformity. The standard uses definitions and explanations as published by several accepted standards organizations. For hazardous location apparatus, atmospheric conditions are generally considered to be: (a) an ambient temperature range of -20°C (-4°F) to 40°C (104°F); (b) an oxygen concentration of not greater than 21% by volume; (c) a pressure of 86 kPa (12.5 psia) to 108 kPa (15.7 psia); and (d) a relative humidity of 5% to 95%. Class, Division and Zone Definitions Class I location: a location in which flammable gases or vapors are or may be present in the air in quantities sufficient to produce explosive or ignitable mixtures. Class I, Division 1 location: a location (1) in which ignitable concentrations of flammable gases or vapors can exist under normal operating conditions; (2) in which ignitable concentrations of such gases or vapors may exist frequently because of repair or maintenance operations or because of leakage; or (3) in which breakdown or faulty operation of equipment or processes might release ignitable concentrations of flammable gases or vapors and might also cause simultaneous failure of electrical equipment that could act as a source of ignition. Class I, Division 2 location: a location (1) in which volatile flammable liquids or flammable gases are handled, processed, or used, but in which the liquids, vapors, or gases will normally be confined within closed containers or closed systems from which they can escape only in case of accidental rupture or breakdown of such containers or systems, or in case of abnormal operation of equipment; or (2) in which ignitable concentrations of gases or vapors are normally prevented by positive mechanical ventilation and might become hazardous through failure or abnormal operation of the ventilating equipment; or (3) that is adjacent to a Class I, Division 1 location and to which ignitable concentrations of gases or vapors might occasionally be communicated unless such communication is prevented by adequate positive-pressure ventilation from a source of clean air and effective safeguards against ventilation failure are provided.
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Class II location: a location that is hazardous because of the presence of combustible dust. Class II, Division 1 location: a location (1) in which combustible dust is in the air under normal operating conditions in quantities sufficient to produce explosive or ignitable mixtures; or (2) in which mechanical failure or abnormal operation of machinery or equipment might cause such explosive or ignitable mixtures to be produced and might also provide a source of ignition through simultaneous failure of electrical equipment, operation of protection devices, or from other causes; or (3) in which combustible dusts of an electrically conductive nature may be present in hazardous quantities. Class II, Division 2 location: a location in which combustible dust is not normally in the air in quantities sufficient to produce explosive or ignitable mixtures and dust accumulations are normally insufficient to interfere with the normal operation of electrical equipment or other apparatus, but combustible dust may be in suspension in the air as a result of infrequent malfunctioning of handling or processing equipment and where combustible dust accumulations on, in, or in the vicinity of the electrical equipment may be sufficient to interfere with the safe dissipation of heat from electrical equipment or may be ignitable by abnormal operation or failure of electrical equipment. Class III location: a location that is hazardous because of the presence of easily ignitable fibers or flyings but in which such fibers or flyings are not likely to be in suspension in the air in quantities sufficient to produce ignitable mixtures. Class III, Division 1 location: a location in which easily ignitable fibers or materials producing combustible flyings are handled, manufactured, or used. Class III, Division 2 location: a location in which easily ignitable fibers are stored or handled (except in the process of manufacture). Zone 0 (IEC): an area in which an explosive gas atmosphere is present continuously or for long periods. Zone 0, Class I (NEC): a Class I, Zone 0 location is a location (1) in which ignitable concentrations of flammable gases or vapors are present continuously; or (2) in which ignitable concentrations of flammable gases or vapors are present for long periods of time.
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Chapter 7/Safety 215
Zone 1 (IEC): an area in which an explosive gas atmosphere is likely to occur in normal operation. Zone 1, Class I (NEC): a Class I, Zone 1 location is a location (1) in which ignitable concentrations of flammable gases or vapors are likely to exist under normal operating conditions; or (2) in which ignitable concentrations of flammable gases or vapors may exist frequently because of repair or maintenance operations or because of leakage; or (3) in which equipment is operated or processes are carried on, of such a nature that equipment breakdown or faulty operations could result in the release of ignitable concentrations of flammable gases or vapors and also cause simultaneous failure of electrical equipment in a mode to cause the electrical equipment to become a source of ignition; or (4) that is adjacent to a Class I, Zone 0 location from which ignitable concentrations of vapors could be communicated, unless communication is prevented by adequate positive-pressure ventilation from a source of clean air and effective safeguards against ventilation failure are provided. Zone 2 (IEC): an area in which an explosive gas atmosphere is not likely to occur in normal operation and, if it does occur, is likely to do so only infrequently and will exist for a short period only. Zone 2, Class I (NEC): a Class I, Zone 2 location is a location (1) in which ignitable concentrations of flammable gases or vapors are not likely to occur in normal operation, and if they do occur, will exist only for a short period; or (2) in which volatile flammable liquids, flammable gases, or flammable vapors are handled, processed, or used, but in which the liquids, gases, or vapors normally are confined within closed containers or closed systems from which they can escape only as a result of accidental rupture or breakdown of the containers or system, or as the result of the abnormal operation of the equipment with which the liquids or gases are handled, processed, or used; or (3) in which ignitable concentrations of flammable gases or vapors normally are prevented by positive mechanical ventilation, but which may become hazardous as the result of failure or abnormal operation of the ventilation equipment; or (4) that is adjacent to a Class I, Zone 1 location from which ignitable concentrations of flammable gases or vapors could be communicated, unless such communication is prevented by adequate positive-pressure ventilation from a source of clean air, and effective safeguards against ventilation failure are provided. Zone 20 (IEC): an area in which combustible dust, as a cloud, is present continuously or frequently, during normal operation, in sufficient
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quantity to be capable of producing an explosible concentration of combustible dust in mixture with air and/or where layers of dust of uncontrollable and excessive thickness can be formed. This can be the case inside dust containment where dust can form explosible mixtures frequently or for long periods of time. This occurs typically inside equipment. Zone 21 (IEC): an area not classified as Zone 20 in which combustible dust, as a cloud, is likely to occur during normal operation, in sufficient quantity to be capable of producing an explosible concentration of combustible dust in mixture with air. This zone can include, among others, areas in the immediate vicinity of powder filling or emptying points and areas where dust layers occur and are likely in normal operation to give rise to an explosible concentration of combustible dust in mixture with air. Zone 22 (IEC): an area not classified as Zone 21 in which combustible dust, as a cloud, can occur infrequently, and persist only for a short period, or in which accumulations or layers of combustible dust can give rise to an explosive concentration of combustible dust in mixture with air. This zone can include, among others, areas in the vicinity of equipment containing dust, and in which dust can escape from leaks and form deposits (e.g., milling rooms in which dust can escape from the mills and then settle). Area (location) classification Area classification schemes should specify the kind of flammable material that may be present and the probability that it will be present in ignitable concentrations. Area classification schemes and systems of material classification have been developed to provide a succinct description of the hazard so that appropriate safeguards may be selected. The type of protection technique selected and the level of protection it must provide depend upon the potential hazard caused by using electrical apparatus in a location in which a combustible, flammable, or ignitable substance may be present. North American methods In the United States, the area classification definitions are stated in Articles 500 and 505 of the National Electrical Code, (NEC) NFPA 70. In Canada, similar definitions are given in the Canadian Electrical Code (CEC), Part 1, Section 18 and Annex J18 (CSA C22.1). Area classification definitions used in the United States and Canada include the following:
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a) CLASS – the generic form of the flammable materials in the atmosphere, which may include gas or vapor, dusts, or easily ignitable fibers or flyings; b) DIVISION (or ZONE) – an indication of the probability of the presence of the flammable material in ignitable concentration; and c) GROUP – the exact nature of the flammable material. Groups (NEC Article 500 / CEC Annex J18) The United States and Canadian Electrical Codes recognize seven groups: Groups A, B, C, D, E, F, and G. Groups A, B, C, and D apply to Class I locations; Groups E, F, and G apply to Class II Locations. In NEC these groups are defined as: Group A - Acetylene Group B - Flammable gas, flammable liquid-produced vapor, or combustible liquid-produced vapor mixed with air that may burn or explode, having either a maximum experimental safe gap (MESG) less than or equal to 0.45 mm or a minimum igniting current ratio (MIC RATIO) less than 0.4. A typical Class I, Group B material is hydrogen. Group C - Flammable gas, flammable liquid-produced vapor, or combustible liquid-produced vapor mixed with air that may burn or explode, having either MESG values greater than 0.45 mm and less than or equal to 0.75 mm or a MIC RATIO greater than or equal to 0.4 and less than or equal to 0.80. A typical Class I, Group C material is ethylene. Group D - Flammable gas, flammable liquid-produced vapor, or combustible liquid-produced vapor mixed with air that may burn or explode, having a MESG greater than 0.75 mm or a MIC RATIO greater than 0.80, or gases or vapors of equivalent hazard. A typical Class I, Group D material is propane. Group E - Atmospheres containing combustible metal dusts, including aluminum, magnesium, and their commercial alloys, or other combustible dusts whose particle size, abrasiveness, and conductivity present similar hazards in the use of electrical equipment. Group F - Atmospheres containing combustible carbonaceous dusts that have more than 8% total entrapped volatiles or that have been
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sensitized by other materials so that they present an explosion hazard. Coal, carbon black, charcoal, and coke dusts are examples of carbonaceous dusts. Group G - Atmospheres containing other combustible dusts, including flour, grain, wood flour, plastic, and chemicals. Groups (NEC Article 505/CSA C22.1 Section 18/IEC 60079-12/ per EN 60079-12) are defined as: Group IIC - Flammable gas, flammable liquid-produced vapor, or combustible liquid-produced vapor mixed with air that may burn or explode, having either MESG less than or equal to 0.5 mm or MIC RATIO less than 0.45, or gases or vapors of equivalent hazard. NOTE: This group is similar to a combination of Groups A & B, described previously, although the MESG and MIC RATIO numbers are slightly different. Typical gases include acetylene, carbon disulfide, hydrogen, and gases or vapors of equivalent hazard. Group IIB - Flammable gas, flammable liquid-produced vapor, or combustible liquid-produced vapor mixed with air that may burn or explode, having either MESG values greater than 0.5 mm and less than or equal to 0.9 mm or MIC RATIO greater than or equal to 0.45 and less than or equal to 0.80, or gases or vapors of equivalent hazard. NOTE: This group is similar to Group C, described previously, although the MESG and MIC RATIO numbers are slightly different. Typical gases include ethylene and gases or vapors of equivalent hazard. Group IIA - Flammable gas, flammable liquid-produced vapor, or combustible liquid-produced vapor mixed with air that may burn or explode, having MESG greater than 0.9 mm or MIC RATIO greater than 0.80, or gases or vapors of equivalent hazard. NOTE: This group is similar to Group D, described previously, although the MESG number is slightly different. Typical gases include propane and gases or vapors of equivalent hazard.
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Chapter 7/Safety 219
Area Classification Flammable Material Present Continuously
Flammable Material Present Intermittently
Flammable Material Present Abnormally
IEC/CENELEC
Zone 0 (Zone 20 – dust)
Zone 1 (Zone 21 – dust)
Zone 2 (Zone 22 – dust)
U.S. NEC® 505
Zone 0
Zone 1
Zone 2
U.S. NEC® 500
Division 1
Division 2
IEC classification per IEC 60079-10 CENELEC classification per EN 60079-10 U.S. classification per ANSI/NFPA 70 National Electric Codes (NECs) Article 500 or Article 505 Table courtesy of FM Approvals, an FM Global enterprise. Reprinted with permission.
Apparatus Grouping Typical Gas/Dust/Fiber
U.S. (NEC® 505) IEC CENELEC
U.S. (NEC® 500)
Acetylene
Group IIC
Class I/Group A
Hydrogen
(Group IIB + H2)
Class I/Group B
Ethylene
Group IIB
Class I/Group C
Propane
Group IIA
Class I/Group D
Methane
Group I*
Mining*
Metal Dust
None
Class II/Group E
Coal Dust
None
Class II/Group F
Grain Dust
None
Class II/Group G
Fibers
None
Class III
*Not within scope of NEC®. Under jurisdiction of Mine Safety and Health Administration (MSHA). Table courtesy of FM Approvals, an FM Global enterprise. Reprinted with permission.
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Table Summarizing NEC Class I, II, III Hazardous Locations CLASSES
GROUPS
DIVISIONS 1
I. Gases, A: Acetylene vapors, and liquids B: Hydrogen, etc. (Art. 501)
Normally explosive and hazardous
C: Ether, etc.
2 Not normally present in an explosive concentration (but may accidentally exist)
D: Hydrocarbons, fuels, solvents, etc. II. Dusts (Art. 502)
E: Metal dusts Ignitable (conductive,* and explo- quantities of dust sive) normally are or may be in susF: Carbon dusts (some pension, or conare conductive,* and all ductive dust may are explosive) be present G: Flour, starch, grain, combustible plastic or chemical dust (explosive)
III. Fibers and flyings (Art. 503)
Textiles, woodworking, etc. (easily ignitable, but not likely to be explosive)
Handled or used in manufacturing
Dust not normally suspended in an ignitable concentration (but may accidentally exist). Dust layers are present.
Stored or handled in storage (exclusive of manufacturing)
*NOTE: Electrically conductive dusts are dusts with a resistivity less than 105 ohm-centimeter.
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Safety Integrity Level Verification [Note: The following is extracted from ISA-TR84.00.02-2002 – Part 2, Safety Instrumented Functions (SIF) – Safety Integrity Level (SIL) Evaluation Techniques Part 2: Determining the SIL of a SIF via Simplified Equations. For those determining the SIL of a SIF via Fault Tree Analysis, it is highly recommended they refer to ISA-TR84.00.02-2002 – Part 3. Readers are also advised an updated ISA Technical Report (TR) is planned on this subject, but was not available at the time of this ISA Handbook’s publication.] Assumptions Used in the Calculations The following assumptions were used in Part 2 for Simplified Equation calculations: • The SIF being evaluated will be designed, installed, and maintained in accordance with ANSI/ISA-84.01-1996. • Component failure and repair rates are assumed to be constant over the life of the SIF. • Once a component has failed in one of the possible failure modes it cannot fail again in one of the remaining failure modes. It can only fail again after it has first been repaired. This assumption has been made to simplify the modeling effort. • The equations assume similar failure rates for redundant components. • The sensor failure rate includes everything from the sensor to the input module of the logic solver including the process effects (e.g., plugged impulse line to transmitter). • The logic solver failure rate includes the input modules, logic solver, output modules and power supplies. These failure rates typically are supplied by the logic solver vendor. Note: ISA-TR84.00.02-2002 – Part 5 illustrates a suggested method to use in developing failure rate data for the logic solver. • The final element failure rate includes everything from the output module of the logic solver to the final element including the process effects. • The failure rates shown in the formulas for redundant architectures are for a single ‘leg’ or ‘slice’ of a system (e.g., if 2oo3 transmitters, the failure rate used is for a single transmitter, not three (3) times the single transmitter value.)
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• The Test Interval (TI) is assumed to be much shorter than the Mean Time To Failure (MTTF). • Testing and repair of components in the system are assumed to be perfect. • All SIF components have been properly specified based on the process application. For example, final elements (valves) have been selected to fail in the safe direction depending on their specific application. • All equations used in the calculations based on this part are based on Reference 3, Reliability, Maintainability and Risk, by David J. Smith, 4th Edition, 1993, Butterworth-Heinemann, ISBN 82-515-0188-1. • All power supply failures are assumed to be due to the de-energized state. • It is assumed that when a dangerous detected failure occurs, the SIS will take the process to a safe state or plant personnel will take necessary action to ensure the process is safe (operator response is assumed to be before a demand occurs, i.e., instantaneous, and PFD of operator response is assumed to be 0). Note: If the action depends on plant personnel to provide safety, the user is cautioned to account for the probability of failure of personnel to perform the required function in a timely manner. • The target PFDavg and MTTFspurious is defined for each SIF implemented in the SIS. • The Beta model is used to treat possible common cause failures. Note: A detailed explanation of the Beta model is given in Annex A of Part 1. • The equations developed in this part assume a graceful degradation path, i.e., 2oo4 system is assumed to degrade as 4-3-2-0. • ISA-TR84.00.02-2002 - Part 2 assumes that the User is familiar with the SIF verification techniques and has a general understanding of the principles behind data collection, failure modes, and effects and analysis, and common cause and diagnostic coverage assessment.
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Calculation Procedures Evaluation of a SIS or a portion of a SIS involves estimating both the PFDavg and the anticipated mean time to spurious trip or Mean Time to Failure - Spurious (MTTFspurious) of a single SIF. Both factors may be important in the final system selection and design.
The following steps are carried out in this evaluation: 1. Identify the hazardous event for which the SIS is providing a layer of protection and the specific individual components that protect against the event. 2. Identify the Safety Integrity Level (SIL) of each SIF required for each hazardous event. 3. List the components that have an impact on each SIF. This will typically be those sensors and final elements identified in the process hazard analysis (PHA) process. The associated SIFs are assigned a SIL by the PHA team. 4. Using the SIS architecture being considered, calculate the PFDavg for each SIF by combining the contributions from the sensors, logic solver, final elements, power supply, and any other components that impact that SIF. 5. Determine if the PFDavg meets the Safety Requirements Specification for each SIF. 6. If required, modify SIS (hardware configuration, test interval, hardware selection, etc.) and recalculate to meet the requirements specified in the Safety Requirements Specifications (See ANSI/ISA-84.01-1996, Clause 5 and Clause 6.2.2) for each SIF. 7. If SIS reliability impacts the consequence of concern, determine the expected Spurious Trip Rate (STR) for system components and combine to obtain MTTFspurious for the SIS. 8. If the calculated MTTFspurious is unacceptable, modify configuration (add redundancy, use components with better reliability, etc.) and re-calculate to meet requirements in the Safety Requirements Specifications. This will require re-calculation of the PFDavg value for each SIF as well. 9. When the PFDavg and MTTFspurious values meet or exceed those specified in the Safety Requirements Specifications, the calculation procedure is complete.
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5.1 PFDavg Calculations The PFDavg is determined by calculating the PFD for all the components in each SIF which provide protection against a process hazardous event and combining these individual values to obtain the SIF PFD value. This is expressed by the following: (Eq. No. 1) PFDSIS = ∑ PFDSi + ∑ PFD Ai + ∑ PFDLi + ∑ PFDPSi
where PFDA is the final element PFDavg for a specific SIF PFDS is the sensor PFDavg for a specific SIF PFDL is the logic solver PFDavg PFDPS is the power supply PFDavg , and PFDSIS is the PFDavg for the specific SIF in the SIS. i represents the number of each type of components that is a part of the specific SIF Each element of the calculation is discussed in the following sections: 5.1.1 Determining the PFDavg for sensors: The procedure for determining the PFDavg for sensors is as follows: 1. Identify each sensor that detects the out-of-limits condition that could lead to the event the SIF is protecting against. Only those sensors that prevent or mitigate the designated event are included in PFD calculations. 2. List the MTTFDU for each sensor. 3. Calculate the PFD for each sensor configuration using the MTTFDU and the equations in 5.1.5 with appropriate consideration for redundancy. 4. Sum the PFD values for the sensors to obtain the PFDS component for the SIF being evaluated. This step is only required if multiple sensor inputs are required in the SIF being evaluated.
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Combined sensor PFDavg component for SIF : PFDS = ∑ PFDSi
(values for individual sets of sensors)
5.1.2. Determining the PFDavg for Final Elements The procedure for determining the PFDavg for final elements is as follows: 1. Identify each final element that protects against the out-of-limits condition that could lead to the event the SIS is protecting against. Only those final elements that prevent or mitigate the designated event are included in PFD calculations. 2. List the MTTFDU for each final element. 3. Calculate the PFDavg for each final element configuration using the MTTFDU and the equations in 5.1.5 with appropriate consideration for redundancy. 4. Sum the PFD values for the final elements to obtain the PFDA component for the SIF being evaluated. This step is only required if multiple final elements are required in the SIF being evaluated. Combined final element PFDavg component for SIF : PFD A = ∑ PFD Ai
(values for individual sets of final elements)
5.1.3 Determining the PFD for the logic solver Note: A common logic solver may provide the logic for several SIFs. The procedure for determining the PFDavg for the logic solver is as follows: 1. Identify the type of logic solver hardware used. 2. Select the MTTFDU for the logic solver (typically obtained from logic solver manufacturer). Note: Since the PFDavg for the logic solver is a non-linear function, the user should request the MTTFDU for a number of functional test intervals of interest and use the one that matches the system requirements.
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3. Calculate the PFDavg for the logic solver portion of SIF using equations in 5.1.5 with appropriate consideration for redundancy. (Note that this step is only required when the manufacturer does not supply the PFDavg for the fully integrated logic solver system.) 4. If the user must determine the PFD for a PES logic solver, refer to Part 5 of ISA-TR84.00.02-2002 for an approach that can be used. 5.1.4 Determining PFDavg for power supply If the SIS is designed for de-energize to trip, the power supply does not impact the SIF PFDavg because a power supply failure will result in action taking the process to a safe state. If the SIS is energize to trip, the power supply PFDavg is determined by the following: 1. List the MTTFDU for each power supply to the SIS. 2. Calculate the PFDavg for the power supplies using the appropriate redundancy and the equations in 5.1.5. 5.1.5 System equations The following equations cover the typical configurations used in SIS configurations. To see the derivation of the equations listed, refer to Reference 3 or ISA-TR84.0.02 – Part 5. Converting MTTF to failure rate, λ : (Eq. No. 2) λDU =
1 MTTF DU
Equations for typical configurations: 1oo1 Note: “1oo1” (above) is ISA Standards speak for “one out of one,” meaning only one device so identified is responsible for taking action. “1oo2” (see Eq. No. 4A) means there are two devices making the decision, and they both must be in a “go” mode before an output can be achieved. The electrical equivalent of 1oo2 is two switches wired in series and connected to a load.
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(Eq. No. 3) TI TI PFDavg = λDU x + λD Fx 2 2
where λDU is the undetected dangerous failure rate D λ F is the dangerous systematic failure rate, and TI is the time interval between manual functional tests of the component. Note: The equations in ISA-TR84.00.02-2002 - Part 1 model the systematic failure as an error that occurred during the specification, design, implementation, commissioning, or maintenance that resulted in the SIF component being susceptible to a random failure. Some systematic failures do not manifest themselves randomly, but exist at time 0 and remain failed throughout the mission time of the SIF. For example, if the valve actuator is specified improperly, leading to the inability to close the valve under the process pressure that occurs during the hazardous event, then the average value as shown in the above equation is not applicable. In this event, the systematic failure would be modeled using lxTI. When modeling systematic failures, the reader must determine which model is more appropriate for the type of failure being assessed. 1oo2 (Eq. No. 4A) PFDavg = (1 − β) × λDU
(
)
2
×
TI TI TI 2 DU × λDD × MTTR × TI + β × λDU × + λD + (1 − β) × λ F × 2 2 3
For simplification, 1 – β is generally assumed to be one, which yields conservative results. Consequently, the equation reduces to: (Eq. No. 4B) PFDavg = λDU
( )
2
×
TI TI 2 DU TI × λDD × MTTR × TI + β × λDU × + λD + λ F × 3 2 2
where MTTR is the mean time to repair λDD is dangerous detected failure rate, and β is fraction of failures that impact more than one channel of a redundant system (common cause).
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The second term represents multiple failures during repair. This factor is typically negligible for short repair times (typically less than 8 hours). The third term is the common cause term. The fourth term is the systematic error term. 1oo3 (Eq. No. 5) PFDavg = λDU
( )
3
×
TI 3 DU 2 DU TI D TI 2 DD × + λF × + (λ ) × λ × MTTR × TI + β × λ 4 2 2
The second term accounts for multiple failures during repair. This factor is typically negligible for short repair times. The third term is the common cause term and the fourth term is the systematic error term. 2oo2 (Eq. No. 6) TI PFDavg = λDU × TI + β × λDU × TI + λD F × 2
The second term is the common cause term and the third term is the systematic error term. 2oo3 (Eq. No. 7)
( )
PFDavg = λDU
2
TI TI × (TI )2 + 3λDU × λDD × MTTR × TI + β × λDU × + λD F × 2 2
The second term in the equation represents multiple failures during repair. This factor is typically negligible for short repair times. The third term is the common cause term. The fourth term is the systematic error term. 2oo4 (Eq. No. 8)
( )
PFDavg = λDU
3
TI TI × (TI )3 + 4(λDU )2 × λDD × MTTR × (TI )2 + β × λDU × + λD F × 2 2
The second term in the equation represents multiple failures during repair. This factor is typically negligible for short repair times. The third term is the common cause term. The fourth term is the systematic error term. For equipment configurations other than those indicated above, see ISA-TR84.00.02-2002 - Part 5.
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The terms in the equations representing common cause (Beta factor term) and systematic failures are typically not included in calculations performed in the process industries. These factors are usually accounted for during the design by using components based on plant experience. Common cause includes environmental factors, e.g., temperature, humidity, vibration, external events such as lightning strikes, etc. Systematic failures include calibration errors, design errors, programming errors, etc. If there is concern related to these factors, refer to ISATR84.00.02-2002 - Part 1 for a discussion of their impact on the PFDavg calculations. If systematic errors (functional failures) are to be included in the calculations, separate values for each sub-system, if available, may be used in the previous equations. An alternate approach is to use a single value for functional failure for the entire SIF and add this term as shown in Equation 1a in 5.1.6. Note: Systematic failures are rarely modeled for SIF Verification calculations due to the difficulty in assessing the failure modes and effects and the lack of failure rate data for various types of systematic failure. However, these failures are extremely important and can result in significant impact to the SIF performance. For this reason, ANSI/ISA-84.011996, IEC 61508, and IEC 61511 provide a lifecycle process that incorporates design and installation concepts, validation and testing criteria, and management of change. This lifecycle process is intended to support the reduction in the systematic failures. SIL Verification is therefore predominantly concerned with assessing the SIS performance related to random failures. The simplified equations without the terms for multiple failures during repair, common cause and systematic errors reduce to the following for use in the procedures outlined in 5.1.1 through 5.1.4. 1oo1 (Eq. No. 3a) PFDavg = λDU ×
TI 2
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1oo2 (Eq. No. 4a)
PFDavg
( )
DU λ =
2
× TI 2
3
1oo3 (Eq. No. 5a)
PFDavg
Page 230
( )
DU λ =
3
× TI 3
4
2oo2 (Eq. No. 6a) PFDavg = λDU × TI
2oo3 (Eq. No. 7a) PFDavg = (λDU )2 × TI 2 2oo4 (Eq. No. 8a) PFDavg = (λDU )3 × (TI )3
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5.1.6 Combining components’ PFDs to obtain SIF PFDavg Once the sensor, final element, logic solver, and power supply (if applicable) portions are evaluated, the overall PFDavg for the SIF being evaluated is obtained by summing the individual components. The result is the PFDavg for the SIF for the event being protected against. (Eq. No. 1a) TI PFDSIS = ∑ PFDSi + ∑ PFD Ai + ∑ PFDLi + PFDPSi + λD F × 2
Note: The last term in the equation, the systematic failure term, is only used when systematic error has not been accounted for in individual component PFD and the user desires to include an overall value for the entire SIF.
5.1.7 PFD improvement techniques Where adjustments are required to decrease PFDavg, additional redundancy may be used on components, the functional test interval may be decreased, the SIS configuration may be changed, or components with lower failure rates may be considered. spurious
5.2 Mean time to failure spurious (MTTF
) calculations
A safe failure of a component may cause a spurious trip of the system. Mean time to a safe failure is referred to as Mean Time to Failure Spurious (MTTFspurious) that is the estimated time between safe failures of a component or system. If trips of the SIS caused by failures of system components are a concern, the anticipated spurious trip rate may be calculated to determine if additional steps are justified to improve SIS reliability. The procedures for making these calculations are presented in the sections that follow. In ISA-TR84.00.02-2002, the term Spurious Trip Rate (STR) refers to the rate at which a nuisance or spurious trip might occur in the SIS. Note: All components that can cause a SIS trip even though not directly related to a specific hazardous event must be considered in this evaluation.
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5.2.1 Determining the STR for sensors The procedure for determining the spurious trip rate caused by sensors is as follows: 1. Identify each sensor that is an initiator in the SIS. 2. List the MTTFspurious for each sensor. 3. List the MTTR for each sensor. 4. Calculate the spurious trip rate for each sensor using the equations in 5.2.5 with appropriate consideration for redundancy. 5. Sum the individual trip rates to determine the SIS trip rate based on sensors. Combined sensor, STRS = ∑ STRSi figurations)
(values for individual sensor con-
5.2.2 Determining the STR for final elements The procedure for determining the spurious trip rate for final elements used in the SIS is as follows: 1. Identify each final element controlled or driven by the SIS. 2. List the MTTFspurious for each final element. 3. List the MTTR for each final element. 4. Calculate the spurious trip rate for each final element using the equations in 5.2.5 with appropriate consideration for redundancy. 5. Sum the individual trip rates to determine the SIS trip rate based on final elements. Combined final element, STRA = ∑ STRAi element configurations)
(values for individual final
5.2.3 Determining the STR for logic solver(s) The procedure for determining the spurious trip rate for logic solver(s) is as follows: 1. Identify each logic solver in the SIS. 2. List the MTTFspurious for each logic solver (typically obtained from manufacturer).
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Note: Since the MTTFspurious for the logic solver is a non-linear function, the user should request the MTTFspurious as a function of MTTR. The user should specify the range of MTTR that is acceptable. 3. List the MTTR for each logic solver. 4. Calculate the spurious trip rate for each logic solver using the equations in 5.2.5 with appropriate consideration for redundancy. Note: This step is only required for a PES logic solver when the manufacturer does not supply the spurious trip rate value for the fully integrated logic solver system. 5. Sum the individual trip rates to determine the SIS spurious trip rate based on logic solver. Combined logic solver - STRL = ∑ STRLi solver configurations)
(values for individual logic
5.2.4 Determining the STR for power supplies Note: The power supplies referred to here are those power sources external to the SIS. These typically are UPS, diesel generators, or alternate power sources. The power supplies internal to the logic solver must also be considered if their failure rate is not taken into account in the logic solver failure rate itself. Unless otherwise noted, the internal power supplies are assumed to be included in the logic solver failure rate for the calculations which follow. The procedure for determining the spurious trip rate for power supplies is as follows: 1. Identify each power supply that impacts the SIS. 2. List the MTTFspurious for each power supply. 3. List the MTTR for each power supply. 4. Calculate the spurious trip rate for the power supply using the equations in 5.2.5 with appropriate consideration for redundancy. Combined power supply - STRPS = ∑ STRPSi (values for multiple individual power supplies)
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5.2.5 System equations for evaluating MTTFspurious The following equations cover the typical configurations used in SIS configurations. To see the derivation of the equations listed, refer to ISA-TR84.00.02-2002 - Part 5. The MTTFspurious for the individual SIS elements is converted to failure rate by, (Eq. No. 9) λS =
1 MTTF
spurious
1oo1 (Eq. No. 10) STR = λS + λDD + λSF
Where λS is the safe or spurious failure rate for the component, λDD is the dangerous detected failure rate for the component, and S λF is the safe systematic failure rate for the component. The second term in the equation is the dangerous detected failure rate term and the third term is the systematic error rate term. The dangerous detected failure term is included in the spurious trip calculation when the detected dangerous failure puts that channel (of a redundant system) or system (if it is nonredundant) in a safe (de-energized) state. This can be done either automatically or by human intervention. If dangerous detected failure does not place the channel or system into a safe state, this term is not included in Equations 10 through 15. 1oo2 (Eq. No. 11)
(
)
(
)
STR = 2 × λS + λDD + β × λS + λDD + λSF
The second term is the common cause term and the third term is the systematic error rate term.
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1oo3 (Eq. No. 12)
(
)
(
)
STR = 3 × λS + λDD + β × λS + λDD + λSF
The second term is the common cause term and the third term is the systematic error rate term. 2oo2 (Eq. No. 13)
(
)
STR = 2 × λS (λS + λDD ) × MTTR + β × λS + λDD + λSF
The second term is the common cause term and the third term is the systematic error rate term. This equation, as well as Equations 14 and 15, assumes that safe failures can be detected on-line. If safe failures can only be detected through testing or inspection, the testing (or inspection) interval TI should be substituted for MTTR. 2oo3 (Eq. No. 14)
(
)
STR = 6 × (λS ) × (λS + λDD ) × MTTR + β × λS + λDD + λSF
The second term is the common cause term, and the third term is the systematic error rate term. 2oo4 (Eq. No. 15)
(
)
STR = 12 × (λS + λDD )3 × MTTR 2 + β × λS + λDD + λSF
The second term is the common cause term, and the third term is the systematic error rate term. Note: The above equations apply to elements with the same failure rates. If elements with different failure rates are used, appropriate adjustments must be made (See ISA-TR84.00.02-2002, Part 5 for method). SIS in the process industry typically must be taken out of service to make repairs when failures are detected unless redundancy of components is provided. Accounting for additional failures while repairs are
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being made is typically not considered due to the relatively short repair time. Common cause and systematic error are handled as described in 5.1.5. Therefore, the equations above can be reduced to the following: 1oo1 (Eq. No. 10a) STR = λS
1oo2 (Eq. No. 11a) STR = 2 × λS
1oo3 (Eq. No. 12a) STR = 3 × λS
2oo2 (Eq. No. 13a)
( )
STR = 2 × λS
2
× MTTR
2oo3 (Eq. No. 14a)
( )
STR = 6 × λS
2
× MTTR
2oo4 (Eq. No. 15a)
( )
STR = 12 × λS
3
× MTTR 2
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5.2.6 Combining spurious trip rates for components to obtain SIS MTTFspurious Once the sensor, final element, logic solver, and power supply portions are evaluated, the overall MTTFspurious for the SIS being evaluated is obtained as follows: (Eq. No. 16) STRSIS = ∑ STRSi + ∑ STRAi + ∑ STRLi + ∑ STRPSi + λSF
Note: The last term in the equation, the systematic failure term, is only used when systematic error has not been accounted for in individual component STR and the user desires to include an overall value for the entire system. (Eq. No. 17) MTTF spurious =
1 STRSIS
The result is the MTTFspurious for the SIS.
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8
Environmental Measurement U.S. Environmental Protection Agency (EPA) . . . . . . . . . . . . . . . . . 241 National Ambient Air Quality Standards (NAAQS) . . . . . . . . . . . . 241 Air Quality Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Airborne Contaminants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 • Liquids, Vapors, Aerosols, Sea Salt Mist • Table Classifying Chemically Active Contaminants: Liquid Aerosols • Solid Contaminants • Table Classifying Airborne Particulates • Gas Contaminants • Table Classifying Reactive Environments & Terminology
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U.S. Environmental Protection Agency The U.S. Environmental Protection Agency is perhaps the single best source of information regarding environmental rules, regulations and topics. EPA’s mission is to protect human health and the environment. Readers seeking EPA-related information are encouraged to go to EPA’s web site: http://www.epa.gov All topics covered by EPA are listed alphabetically – with links to locate detailed information – at: http://www.epa.gov/ebtpages/alphabet.html U.S. National Ambient Air Quality Standards The U.S. Clean Air Act, last amended in 1990, requires the U.S. Environmental Protection Agency (EPA) to set National Ambient Air Quality Standards (NAAQS) for pollutants considered harmful to public health and the environment. The Clean Air Act established two types of national air quality standards. Primary standards set limits to protect public health, including the health of “sensitive” populations such as asthmatics, children, and the elderly. Secondary standards set limits to protect public welfare, including protection against decreased visibility, damage to animals, crops, vegetation, and buildings. The EPA Office of Air Quality Planning and Standards (OAQPS) established National Ambient Air Quality Standards for seven principal pollutants, called “criteria” pollutants. They are listed in the following table. Units of measure for the standards are parts per million (ppm) by volume, milligrams per cubic meter of air (mg/m3), and micrograms per cubic meter of air (µg/m3).
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National Ambient Air Quality Standards Pollutant
Primary Standards
Averaging Times
Secondary Standards
Carbon Monoxide
9 ppm (10 mg/m3)
8-hour1
None
35 ppm (40 mg/m3)
1-hour1
None
Lead
1.5 µg/m3
Quarterly Average
Same as Primary
Nitrogen Dioxide
0.053 ppm (100 µg/m3)
Annual Same as Primary (Arithmetic Mean)
Particulate Matter (PM10)
50 µg/m3
Annual2 (Arith. Mean)
150 ug/m3
24-hour1
15.0 µg/m3
Annual3 (Arith. Mean)
65 µg/m3
24-hour4
0.08 ppm
8-hour5
Same as Primary
0.12 ppm
1-hour6
Same as Primary
0.03 ppm
Annual (Arith. Mean)
———
0.14 ppm
24-hour1
———
Particulate Matter (PM2.5)
Ozone
Sulfur Oxides
———
3-hour1
Same as Primary
Same as Primary
0.5 ppm (1300 µg/m3)
1 Not to be exceeded more than once per year. 2 To attain this standard, the expected annual arithmetic mean PM concentration at each monitor 10 within an area must not exceed 50 µg/m3. 3 To attain this standard, the 3-year average of the annual arithmetic mean PM 2.5 concentrations from 3
single or multiple community-oriented monitors must not exceed 15.0 ug/m .
4 To attain this standard, the 3-year average of the 98th percentile of 24-hour concentrations at each population-oriented monitor within an area must not exceed 65 µg/m3. 5 To attain this standard, the 3-year average of the fourth-highest daily maximum 8-hour average ozone
concentrations measured at each monitor within an area over each year must not exceed 0.08 ppm. 6 (a) The standard is attained when the expected number of days per calendar year with maximum
hourly average concentrations above 0.12 ppm is <= 1. (b) The 1-hour NAAQS will no longer apply to an area one year after the effective date of the designation of that area for the 8-hour ozone NAAQS. The effective designation date for most areas is June 15, 2004. (40 CFR 50.9; see Federal Register of April 30, 2004 [69 FR 23996].
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Air Quality Index The Air Quality Index (AQI) is an index for reporting daily air quality. It tells how clean or polluted the air is, and what associated health effects might be a concern. The AQI focuses on why health effects might be experienced within a few hours or days after breathing polluted air. EPA calculates the AQI for five major air pollutants regulated by the Clean Air Act: ground-level ozone, particle pollution (also known as particulate matter), carbon monoxide, sulfur dioxide, and nitrogen dioxide. An AQI value of 100 generally corresponds to the national air quality standard for the pollutant, which is the level EPA has set to protect public health. AQI values below 100 are generally thought of as satisfactory. When AQI values are above 100, air quality is considered to be unhealthy — at first for certain sensitive groups of people, then for everyone as AQI values get higher. To make it easier to understand, the AQI is divided into six categories: Air Quality Index (AQI) Values
Levels of Health Concern
Colors
When the AQI is in this range:
...air quality conditions are:
...as symbolized by this color:
0 to 50
Good
Green
51 to 100
Moderate
Yellow
101 to 150
Unhealthy for Sensitive Groups
Orange
151 to 200
Unhealthy
Red
201 to 300
Very Unhealthy
Purple
301 to 500
Hazardous
Maroon
Each category corresponds to a different level of health concern. The six levels of health concern and what they mean are: • “Good” The AQI value for your community is between 0 and 50. Air quality is considered satisfactory, and air pollution poses little or no risk. • “Moderate” The AQI for your community is between 51 and 100. Air quality is acceptable; however, for some pollutants there may be a moderate health concern for a very small number of people. For example, people who are unusually sensitive to ozone may experience respiratory symptoms.
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• “Unhealthy for Sensitive Groups” When AQI values are between 101 and 150, members of sensitive groups may experience health effects. This means they are likely to be affected at lower levels than the general public. For example, people with lung disease are at greater risk from exposure to ozone, while people with either lung disease or heart disease are at greater risk from exposure to particle pollution. The general public is not likely to be affected when the AQI is in this range. • “Unhealthy” Everyone may begin to experience health effects when AQI values are between 151 and 200. Members of sensitive groups may experience more serious health effects. • “Very Unhealthy” AQI values between 201 and 300 trigger a health alert, meaning everyone may experience more serious health effects. • “Hazardous” AQI values over 300 trigger health warnings of emergency conditions. The entire population is more likely to be affected.
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Airborne Contaminants An ISA standard, ISA-71.04-1985, Environmental Conditions for Process Measurement and Control Systems: Airborne Contaminants, classifies airborne contaminants that may affect process measurement and control instruments. The standard establishes airborne contaminant classes for fixed (non-mobile) installations during normal operation (non-emergency conditions) or during transportation and storage. The classification consists of a class contaminant letter followed by a severity identification numeral.
Airborne Contaminants — Liquids, Vapors, Aerosols, Sea Salt Mist Liquids — This refers to liquids that will corrode unprotected equipment and are typically transported to the equipment by condensation, rain, splashing liquids, or cleaning fluids sprayed from hoses. The majority of these are not classified, but should be specified to the manufacturers of equipment by special classification LX. Vapors — Solvents sometimes occur as vapors which may condense and form puddles that become corrosive to instruments and controls. Aerosols — Aerosols are liquids carried in gas or air in the form of small droplets generating mists. Aerosols can vary in composition and are a major source of chemical contamination to equipment. Sea Salt Mist — Class LC1: Inland more than 0.5 km from shore; Class LC2: Inland less than 0.5 km from shore; Class LC3: Offshore installations (oil rigs, etc.)
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Classification of Chemically Active Contaminants: Liquid Aerosols (Measured in µg/kg except as specified) Severity Level 1
Severity Level 2
Severity Level 3
Severity Level X (special)
Contaminant
Class
Value
Value
Value
Value
Vapors*
LA
< 1.0
< 5.0
< 20.0
≥ 20.0
Oils
LB
< 5.0
< 50.0
< 100.0
≥ 100.0
Sea salt mist
LC
More than 0.5 km inland
Within 0.5 km inland
Offshore installation
T.B.S.
Special T.B.S.
LX
T.B.S.
T.B.S.
T.B.S.
T.B.S.
*For example, trichloroethylene (CHClCCl2) NOTES: 1.0 µg/kg = 1.0 part per billion (p/109) T.B.S. = To Be Specified < is defined as “less than” > is defined as “more than” ≥ is defined as “greater than or equal to”
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Airborne Contaminants — Solids Dust is a universal contaminant and is a cause of environmentally induced equipment failures. Failure modes may be mechanical, chemical, electrical, thermal, or magnetic. To maximize equipment reliability and life, every effort should be made to minimize exposure to airborne particulates. The sensitivity of control equipment to different types of particulates varies widely. In the table below, solid particulates are classified by size. The environment should be described in terms of concentration severity level for each class, Classes SA through SD. Classification of Airborne Particulates Severity Level (concentration measured in µg/m3 Particle Size
Class
1
2
3
X
> 1 mm
SA
< 1000
< 5000
< 10,000
≥ 10,000
100 µm to 1000 µm
SB
< 500
< 3000
< 5000
≥ 5000
1 µm to 100 µm
SC
< 70
< 200
< 350
≥ 350
< 1 µm
SD
< 70
< 200
< 350
≥ 350
Notes: µm = micrometer = 0.001 millimeter µg/m3 = micrograms per cubic meter
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Airborne Contaminants — Gases Two methods have been used for environmental characterization. One is a direct measure of selected gaseous air pollutants. The other, which can be termed “reactivity monitoring,” provides a quantitative measure of the overall corrosion potential of an environment. High values will confirm that a severe environment exists. The reverse, however, is not necessarily true. Industrial environments may contain a complex mixture of contaminants that interact to greatly accelerate (or retard) the corrosive action of individual gas species. To avoid these practical difficulties, the nature of industrial environments is defined in terms of the rate at which they react with copper. Copper has been selected as the coupon material because data exists which correlates copper film formation with reactive (corrosive) environments. Four levels of corrosion severity are established in Table 3. Concentration levels of some gases that contribute to these reactivity rates are also cited: Severity level G1: Mild — An environment sufficiently well-controlled such that corrosion is not a factor in determining equipment reliability. Severity level G2: Moderate — An environment in which the effects of corrosion are measurable and may be a factor in determining equipment reliability. Severity level G3: Harsh — An environment in which there is a high probability that corrosive attack will occur. These harsh levels should prompt further evaluation resulting in environmental controls or specially designed and packaged equipment. Severity level GX: Severe — An environment in which only specially designed and packaged equipment would be expected to survive. Specifications for equipment in this class are a matter of negotiation between user and supplier.
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Classification of Reactive Environments & Terminology Severity Level
G1 Mild
G2 Moderate
G3 Harsh
G4 Severe
Copper Reactivity Level (in angstroms)*
< 300
< 1000
< 2000
≥ 2000
The gas concentration levels shown below are provided for reference purposes. They are believed to approximate the Copper Reactivity Levels stated above, providing the relative humidity is less than 50%. For a given gas concentration, the Severity Level (and Copper Reactivity Level) can be expected to be increased by one level for each 10% increase in relative humidity above 50% or for a relative humidity rate of change greater than 6% per hour. Contaminant
Gas
Group A
H2S
<3
< 10
< 50
≥ 50
SO2, SO3
<10
< 100
< 300
≥ 300
Cl2
<1
<2
< 10
≥ 10
NOx
< 50
< 125
< 1250
≥ 1250
HF
<1
<2
< 10
≥ 10
NH3
< 500
O3
<2
Reactive Species†,‡
Group B§
Concentration
< 10,000 < 25,000 < 25
< 100
25,000 100
* Measured in angstroms after one month’s exposure. † mm3/m3 (cubic millimeters per cubic meter) parts per billion average for test period for the gases in Groups A and B. ‡ The Group A contaminants often occur together and the reactivity levels include the synergistic effects of these contaminants. § The synergistic effects of Group B contaminants are not known at this time.
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Humidity Measurement
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Principles of Humidity and Moisture Measurement. . . . . . . . . . . . 254 Percent Relative Humidity Equation . . . . . . . . . . . . . . . . . . . . . . . . 254 Dalton’s Law of Partial Pressures . . . . . . . . . . . . . . . . . . . . . . . . . . 255 Humidity and Moisture Conversion Table . . . . . . . . . . . . . . . . . . . 256 Psychrometric Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
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253
Introduction Popular devices for humidity measurement include the hygrometer, a device which measures only relative humidity; thermohygrometer, a device which measures both temperature and humidity; psychometer, which measures humidity and dew point through water evaporation rate interpretation; and dew point meter, which measures the temperature at which moisture will form in the sampled environment. In process control, moisture and temperature often need to be measured in combination.
Thermohygrometers are available in wall mount, dial meter type units that do not require electrical power and digital models. Battery operated digital units are popular. Dial meter type thermohygrometers generally use a “cellulose” sponge type sensor for humidity and a spring or glass bulb thermometer for temperature. As moisture increases, the sponge expands and the lever mechanism moves the indicating needle. Accuracies are typically in the +/- 3% range, and response time is slow. Electronic thermohygrometers generally use either a capacitance or resistance sensor. As the humidity rises, the circuit resistance or capacitance changes a digital display reading. When portability is needed, a psychometer is often used. It typically has two thermometers-a normal “dry” bulb thermometer, plus another called the “wet” bulb, featuring a wick moistened with water. As air passes over the two thermometers, two temperatures (wet and dry bulb) are generated. Using a table, the humidity can be calculated.
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Principles of Humidity and Moisture Measurement Measurement Factor
Measurement Description
Units of Measure
Wet Bulb Thermometer
The temperature of a wetted thermometer in a stream of air.
°F or °C
Percent Relative Humidity
The ratio of actual vapor pressure to saturation vapor pressure.
0-100%
Dew Point
The temperature that air must be cooled °F or °C to achieve saturation.
Volume or Mass
Parts per million by volume or weight.
Percent Relative Humidity RH =
wvpa × 100 wvps
where RH = percent relative humidity wvpa = absolute water vapor pressure wvps = saturated water vapor pressure
ppmv or ppmw
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Chapter 9/Humidity
255
Dalton’s Law of Partial Pressures John Dalton’s law: The Total Pressure of a gas mixture is the sum of the pressures of each gas component.
P = Pn + Po + Par + . . . 2
2
“Partial Pressure” is defined as the pressure of a single gas in the mixture as if that gas alone occupied the container. Main Gas Components in Air Gas
% Volume
% Weight
Nitrogen N2
78.03
75.47
Oxygen O2
20.99
23.20
Argon Ar
0.93
1.28
Carbon Dioxide CO2
0.03
0.04
All others: H2, He, Ne, Kr etc.
0.02
0.01
Water in its gaseous state (vapor) is an additional gas component of air, and also appears in Dalton’s law as:
P = Pn + PO + PAr + PCO …… + e = Pda + e 2
2
2
where e = partial pressure of (water) vapor [mbar] Pda = partial pressure of dry air
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ISA Handbook of Measurement Equations and Tables
Humidity and Moisture Conversion Table To Convert from
To
Multiply by:
Atmosphere
Millibar
1013.25
Atmosphere
mm Mercury
760.0
cm Mercury
Millibar
13.3322
cm Mercury
mm water
135.951
cm water
Millibar
0.980665
cm water
mm Mercury
0.735559
cm3
in3
0.06102374
cm3
m3
0.000001
cm3
mm3
1000
cm3
gallon
0.00026417
cm3
Milliliter
1
cm3-Atmosphere
Joule
0.101325
ft3
cm3
28316.847
ft3
in3
1728
ft3
gallon
7.480519
ft3
liter
28.316847
ft3-Atmosphere
liter-Atmosphere
28.316847
in3
cm3
16.387064
in3
ft3
0.0005787
in3
gallon
0.0043290
in3
liter
0.016387064
mm3
in3
0.0000610237
°C-temp. interval
°F
1.8
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Chapter 9/Humidity
Humidity and Moisture Conversion Table (cont.) To Convert from
To
Multiply by:
°C-temp. interval
Kelvin
1.0
°F-temp. interval
°C or Kelvin
0.555556
ft water
Atmosphere
0.0294998
ft water
Bar
0.0298907
ft/°F
m/°C
0.54864
gallon
cm3
3785.412
gallon
ft3
0.13368
gallon
in3
231
gallon
liter
3.785412
in Mercury
Millibar
33.8639
in Mercury
Atmosphere
0.0334211
in water
Millibar
2.49089
in/°F
mm/°C
45.72
liter
ft3
0.03532467
liter
in3
61.02374
liter
gallon
0.26417205
liter-Atmosphere
ft3-Atmosphere
0.0353147
liter-bar
Joule
100
mm Mercury
Atmosphere
0.001315789
mm Mercury
Millibar
1.333224
mm water
Atmosphere
0.000096784
mm water
Millibar
0.098665
part per million
Milligram/Kilogram
1
part per million
Milliliter/m3
1
257
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ISA Handbook of Measurement Equations and Tables
Psychrometric Chart 90 .028
%
% 80
60
70
.016
W et
Bu lb
(F
)
40
%
.020
.012
60 % 20
50
.008
40 .004
40
50
60
70
80
90
100
110
Humidity Ratio = mass of water vapor (Lbv)/mass of dry air (Lba)
.024 80
120
Dry Bulb Temperature (F)
For applications such as air conditioning, the psychrometric chart is a good analysis tool to assess the thermal comfort conditions throughout the year. Atmospheric factors such as air temperature and moisture in the air are key to thermal comfort. The psychrometric chart represents the state of a given atmosphere by a point which gives dry-bulb, wetbulb, relative humidity, specific volume and saturation temperature. Relative humidity (RH) is an expression of the moisture content of a given atmosphere as a percentage of the saturation humidity at the same temperature: Wet bulb temperature (WBT) is measured by a hygrometer (or psychrometer), which consists of two thermometers – one measuring the dry bulb temperature (DBT), the other having its bulb enclosed in a wet wick. “Web bulb depression” is a term meaning the difference in the temperatures between the wet wick thermometer and the DBT, as happens when the wet wick thermometer is cooled down by the evaporation on the wick. The amount of evaporation is a direct indication of the moisture carrying capacity of the atmospheric air at that temperature. When the air is saturated, there is no evaporation, and DBT and WBT readings are identical. The “status point” is determined at the intersection of the vertical DBT line and the WBT slope on the psychrometric chart.
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10
Electrical Measurement
Principles of Electrical Measurement. . . . . . . . . . . . . . . . . . . . . . . . 261 Principles of Oscilloscopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 Electrical Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Voltage Ratios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 Resistance Ratio Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Electricity Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270 Inductance Measurement.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Geometric Mean Distances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 Values for Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 Mutual Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Self Inductance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285, 298
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Chapter 10/Electrical Measurement
261
Principles of Electrical Measurement Resistance Ω=
V (T ) AT
where Ω = resistance V = voltage AT = ampere turns T = turns Ampere Turns AT =
V (T ) Ω
Amperes A=
AT Ω
Rsh1 1/
9/
M Rm = 100
Rsh2
where A = amperes
Rsh3 10 mA Configuration
Direct Current The Universal (Arytron) Shunt
Rsh2
For 0 to 10 mA, use:
99/ Rsh3
0.009 (Rsh1 + Rsh2 + Rsh3 ) = 0.001 (Rm )
where Rsh1 = 0.111 ohm shunt Rsh2 = 1.11 ohm shunt Rsh3 = 11.1 ohm shunt Rm = 100 For 10.01 to 100 mA, use: 99 (Rsh2 + Rsh3 ) = 1 (Rm + Rsh1) For 100.01 mA to 1 amp, use: 999 (Rsh3 ) = 1 (Rm + Rsh1 + Rsh2 )
Rsh1
1/ M
Rm = 100
100 mA Configuration
999/
Rsh2
1/
Rsh1
Rsh3 M
Rm = 100
1 amp Configuration
The Universal (Arytron) Shunt
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ISA Handbook of Measurement Equations and Tables
Ohm’s Law for Direct Current
2
E2 R
E R
I R EI
P
I
PR
E
R
P I IR
P
Ohm’s Law for Alternating Current
P E
2
I R
E2 Z
E Z
P R
EI
P
I
E I
E2 P
Z
E
P
E2 P
I2
PZ
P E P Z IZ P I
I2
P = power in watts I = current in amperes E = electromotive force in volts R = resistance in ohms Two resistances in parallel combination: req =
R1 − R2 R1 + R2
Any number of resistances in parallel combination: 1 1 1 1 = + + req R1 R2 Rn
For calculating capacitance in series combinations, substitute C for R in the above equations.
1 1 XL = = 2π LC 2πCX c 2πL XL = 2π f L 1 Xc = 2π f C 1 XL L= = 2π f (2π f )2C 1 1 C= = 2π f X c (2π f )2L f =
Z = R 2 + X 2 = R 2 + (XL − X c )2 Z = R when XL = X c
where Z = impedance in ohms XL = inductive reactance in ohms Xc = capacitive reactance in ohms L = inductance henrys C = capacitance in farads f = frequency in cycles per second 2π f = 377 for 60 cps
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Chapter 10/Electrical Measurement
Determining Required Shunt Resistance Rsh
I R = m m Ish
where Rsh = shunt resistor Im = full-scale deflection current Rm = dc resistance of meter Ish = current to be shunted dc Voltmeters Determining the Total Resistance Required to Drop Full-scale Voltage at fsd Current
263
Series Voltmeters Determining the Value of a Multiple Resistor Rv =
V − Rm Im
where Rv = multiple resistor value V = full-scale voltage for desired range Im = full-scale deflection current Rm = meter resistance dc Bridges Balance for a Wheatstone Bridge
M Rt = r − Rm Im la
where Rt = required resistance drop Mr = desired meter range Im = full-scale deflection current Rm = dc resistance of meter Meter Sensitivity Ms =
1V = Ms ohms / V Im
where Ms = meter sensitivity V = volts Im = full-scale deflection current
Ra
Rb
lb
Null lx
Rx
Rs
ls
Current for Bridge Mathematics
Rx =
Ra Rs Rb
where Rx = unknown resistance Ra and Rb = ratio arms Rs = variable standard resistance when Ra = Rb bridge is balanced and Rx = Rs
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ISA Handbook of Measurement Equations and Tables
Principles of Oscilloscopes Alternating Current Waveforms Factors Used for Sinusoidal Wave Shape Given
Average
r.m.s
Peak
Peak to Peak
Average
1.0
1.11** 2.22**
1.57
3.14
r.m.s.
0.90* 0.45*
1.0
1.414
2.828
Peak
0.637
0.707
1.0
2.00
Peak to Peak
0.318
0.3541
0.500
1.0
*0.9 for full-wave rectification. *0.45 for half-wave rectification. **1.11 for full-wave rectification. **2.22 for half-wave rectification.
+1.0
Amplitude
+0.707 +0.636 avg. 0
0˚
90˚
180˚
270˚
avg.
-0.636 -0.707 -1.0
Period
Time
A Sinusoidal Wave Form
r.m.s
Peak
360˚ r.m.s
Peak
Peak to peak
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Chapter 10/Electrical Measurement
Electrical Power Determining the Gain or Loss of Power in Decibels dB = 10log
Po Pi
where Po = power out Pi = power in Conversion Tables, Power Ratios to Decibel (dB) Values
265
Conversion Tables, Power Ratios to Decibel (dB) Values (cont.) Power Ratio Loss
10 log Ratio - db +
Power Ratio Gain
0.3981
4.0
2.512
0.3162
5.0
3.162
0.2512
6.0
3.981
0.1995
7.0
5.012
0.1585
8.0
6.310
Power Ratio Loss
10 log Ratio - db +
Power Ratio Gain
0.1259
9.0
7.943
0.1000
10.0
10.00
1.000
0.0
1.000
0.0794
11.0
12.59
0.9772
0.1
1.023
0.0631
12.0
15.85
0.9550
0.2
1.047
0.0501
13.0
19.95
0.9333
0.3
1.072
0.0399
14.0
25.12
0.9120
0.4
1.096
0.0316
15.0
31.62
0.8913
0.5
1.122
0.0251
16.0
39.81
0.8710
0.6
1.148
0.0199
17.0
50.12
0.8511
0.7
1.175
0.0159
18.0
63.10
0.8318
0.8
1.202
0.01259
19.0
79.43
0.8128
0.9
1.230
0.0100
20.0
100.0
0.7943
1.0
1.259
0.0010
30.0
103
0.6310
2.0
1.585
10-4
40.0
104
0.5012
3.0
1.995
10-5
50.0
105
10-6
60.0
106
10-7
70.0
107
10-8
80.0
108
10-9
90.0
109
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ISA Handbook of Measurement Equations and Tables
Determining Voltage or Current Gain (dB) when Input and Output Are Not Equal
dB = 20log
V or I output R input V or I input R output
where V = voltage I = impedance R = resistance Determining Voltage or Current Loss (dB) when Input and Output Are Not Equal
dB = 20log
V or I input R output V or I output R input
Voltage/Current Ratio Tables Voltage/ Current Ratio Gain
Decibels Voltage/ Current Ratio Loss
Voltage/Current Ratio Tables (cont.) Voltage/ Current Ratio Gain
Decibels Voltage/ Current Ratio Loss
1.585
4.0
0.6310
1.788
5.0
0.5623
1.995
6.0
0.5012
2.239
7.0
0.4467
2.512
8.0
0.3981
3.162
10.0
0.3162
3.548
11.0
0.2818
3.981
12.0
0.2515
4.467
13.0
0.2293
5.012
14.0
0.1995
5.632
15.0
0.1778
6.310
16.0
0.1585
1.000
0.0
1.000
7.079
17.0
0.1413
1.012
0.1
0.9886
7.943
18.0
0.1259
1.023
0.2
0.9772
8.913
19.0
0.1122
1.035
0.3
0.9661
10.00
20.0
0.1000
1.047
0.4
0.9550
31.62
30.0
0.0316
1.059
0.5
0.9441
102
40.0
10-2
1.072
0.6
0.9333
316.23
50.0
0.000316
1.084
0.7
0.9226
103
60.0
10-3
1.096
0.8
0.9120
3.16 x 103
70.0
3.162 x 10-4
1.109
0.9
0.9016
104
80.0
10-4
1.122
1.0
0.8913
3.16 x 104
90.0
3.162 x 10-5
1.259
2.0
0.7943
105
100.0
10-5
1.413
3.0
0.7079
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Chapter 10/Electrical Measurement
Resistance Ratio Bridges
Measuring Capacitance
Measuring Inductance Lx =
Ra Ls Rb
Cx =
Ra Cs Rb
Rx =
Ra Rs Rb
and
and Rx =
267
Ra Rs Rb
where Cx = reactive component Rx = resistive component
where Lx = reactive component Rx = resistive component
unknown inductor (resistance + inductance)
Lx
Ra
Rx detector Rs Rb
Rs = standard resistor
Ls
Ls = standard inductor
Resistance Ratio Bridge to Measure Inductance
Cx Ra
unknown capacitance (reactive and resistive component) Rx
detector Rs
Rb Cs
Rs = standard resistor Cs = standard capacitor
Resistance Ratio Bridge to Measure Capacitance
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ISA Handbook of Measurement Equations and Tables
Measuring Capacitance, Wien Bridge
R1 = 2 R2 Cx
R1
Cx =
Rx
R2 Rs − Cs R1 Rx
detector Rs R2
Cs
Wien Bridge
Measuring Capacitance, Schering Bridge Cx
R C x = Cs b Rs
Cs
and
Rx
detector
C Rx = Rs b Cs
Rb Rs
Cb
Measuring Inductance, Maxwell Bridge
Schering Bridge
Lx = RbRaCs Cs
and
Ra
R Rx = b Ra Rs
Rs detector Lx Rb Rx Maxwell Bridge
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Chapter 10/Electrical Measurement
Measuring Inductance, Hay Bridge Q Ratio Greater than 10
r.m.s. Values of Voltage and Current
Lx = RbRaCs
E=
Em
I=
Im
and Rx =
RbRaCs 1 1+ Qx
2
and
Rb Ra Rs
Measuring Inductance, Hay Bridge Q Ratio Less than 10 Lx =
269
2
Cs
2
Ra
Rs detector
and Rx =
1 RbRa (1) + Rs Qx
Lx
Rb Rx
where Q = reactive/resistive ratio
Hay Bridge
Measuring Inductance, Owens Bridge Lx = RbRsCa
Rs Ca
and Rx =
Cs
Ca Ra Cs
detector
Lx La
Measuring Wattage
Rx
Average Power in a Cycle P = E I cos φ
where P = power E = sinusoidal voltage I = current φ = phase angle that current lags behind voltage
Owens Bridge
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ISA Handbook of Measurement Equations and Tables
Conversion Tables for Electricity To Convert from
To
Multiply by:
Amp/hr
Coulomb
3600
Btu
Calorie
251.996
Btu
ft-lb force
778.169
Btu
Horsepower-hr
0.000393015
Btu
Kilocalorie
0.251996
Btu
Kg-meter force
107.586
Btu
Kw-hr
0.000293071
Btu/hr
Btu/min
0.01666667
Btu/hr
Btu/sec
0.000277778
Btu/hr
Calorie/sec
0.0699988
Btu/hr
Horsepower
0.000393015
Btu/hr
Watt
0.293071
Btu/min
Calorie/sec
4.19993
Btu/min
Horsepower
0.0235809
Btu/min
Watt
17.5843
Btu/min-ft2
Watt/m2
189.273
Btu/lb
Calorie/gm
0.555556
Btu/lb
Watt-hr/Kg
0.64611
Btu/sec
Horsepower
1.41485
Btu/sec
Kw
1.055056
Btu/sec-ft2
Kw-m2
11.3565
Btu/ft2
Watt-hr/m2
3.15459
Calorie
Btu
0.00396832
Calorie
ft-lb force
3.08803
Calorie
Horsepower-hr
0.00000155961
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Chapter 10/Electrical Measurement
271
Conversion Tables for Electricity (cont.) To Convert from
To
Multiply by:
Calorie
Kg-force-m
0.426935
Calorie
Kw-hr
0.000001163
Calorie
Watt-hr
0.001163
Calorie/°C
Btu/°F
0.0022046
Calorie/gm
Btu/lb
1.8
Calorie/min
Watt
0.06978
Calorie/sec
Watt
4.1868
Calorie/sec-cm2
Kw/m2
41.868
Chu (°C heat unit)
Btu
1.8
Chu (°C heat unit)
Calorie
453.592
clo
°C-m2/watt
0.155
Coulomb
amp-sec
1.0
Decibel
Neper
0.115129255
Erg
Watt-hr
2.777778 x 10-11
Erg/cm2-sec
Watt/cm3
0.001
ft-lb force
Btu
0.00128507
ft-lb force
Calorie
0.323832
ft-lb force
Horsepower-hr
5.05051 x 10-7
ft-lb force
Watt-hr
0.000376616
ft-lb force/min
Horsepower
0.000030303
ft-lb force/min
Watt
0.022597
ft-lb force/sec
Horsepower
0.00181818
ft-lb force/sec
Watt
1.355818
Horsepower
Btu/hr
2544.43
Horsepower
Btu/min
42.4072
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ISA Handbook of Measurement Equations and Tables
Conversion Tables for Electricity (cont.) To Convert from
To
Multiply by:
Horsepower
Btu/sec
0.706787
Horsepower
ft-lb force/hr
1980000.0
Horsepower
ft-lb force/min
33000.0
Horsepower
ft-lb force/sec
550.0
Horsepower
Kilocalorie/hr
641.186
Horsepower
Kilocalorie/min
10.6864
Horsepower
Kilocalorie/sec
0.178107
Horsepower
Kg-force-m/sec
76.0402
Horsepower
Kw
0.74570
Horsepower/hr
Btu
2544.43
Horsepower/hr
ft-lb force
1980000.0
Horsepower/hr
Kilocalorie
641.186
Horsepower/hr
Kw-hr
0.74570
Kilocalorie/hr
Watt
1.163
Kilocalorie/hr-m2
Watt/m2
1.163
Kilocalorie/Kg
Btu/lb
1.8
Kilocalorie/min
ft-lb force/sec
51.4671
Kilocalorie/min
Horsepower
0.0935765
Kilocalorie/min
Watt
69.78
Kilocalorie/sec
Kw
4.1868
Kw
Btu/hr
3412.14
Kw
Btu/min
56.8690
Kw
Btu/sec
0.947817
Kw
ft-lb force/hr
2655220.0
Kw
ft-lb force/min
44253.7
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Chapter 10/Electrical Measurement
273
Conversion Tables for Electricity (cont.) To Convert from
To
Multiply by:
Kw
ft-lb force/sec
737.562
Kw
Horsepower
1.34102
Kw
Kilocalorie/hr
859.845
Kw
Kilocalorie/min
14.3308
Kw
Kilocalorie/sec
0.0238846
Kw
Kg force-m/hr
367098.0
Kw
Kg force-m/min
6118.3
Kw
Kg force-m/sec
101.972
Kw-hr
Btu
3412.14
Kw-hr
ft-lb force
2655220.0
Kw-hr
horsepower-hr
1.34102
Kw-hr
Kilocalorie
859.845
Kw-hr
Kg-force-m
367098.0
Kw-hr/lb
Btu/lb
3412.14
Kw-hr/lb
Kilocalorie/kg
1895.63
Kw-hr/Kg
Btu/lb
1547.72
Megajoule
Kw-hr
0.2777778
Neper
Decibel
8.68589
Ohm/ft
Ohm/m
3.28084
Ohm-cm
Ohm-m
0.01
Pond
Gram-force
1.0
Statohm
Ohm
8.987552 x 1011
Statvolt
Volt
299.7925
Volt/in
Volt/m
39.37008
Volt-sec
Weber
1.0
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Conversion Tables for Electricity (cont.) To Convert from
To
Multiply by:
Watt
Btu/hr
3.41214
Watt
Btu/min
0.056869
Watt
Calorie/min
14.3308
Watt
Calorie/sec
0.238846
Watt
Erg/sec
10000000.0
Watt
ft-lb-force/min
44.2537
Watt
ft-lb-force/sec
0.737562
Watt
Horsepower
0.00134102
Watt
Joule/sec
1.0
Watt
Kilocalorie/hr
0.859845
Watt
Kg-force-m/sec
0.101972
Watt/in2
Btu/hr-ft2
491.348
Watt/in2
Kilocalorie/hr-m2
1332.76
Watt/in2
Watt/m2
1550.003
Watt/m2
Kilocalorie/hr-m2
0.859845
Watt-hr
Btu
3.41214
Watt-hr
Calorie
859.845
Watt-hr
ft-lb force
2655.22
Watt-hr
Horsepower-hr
0.00134102
Watt-hr
Joule
3600.0
Watt-hr
Kg-force-m
367.098
Watt-sec
Erg
10000000.0
Watt-sec
Joule
1.0
Watt-sec
Newton-m
1.0
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275
Inductance Measurement The most direct method of calculating inductances is based on the definition of flux linkages per ampere. To calculate flux linkages, it is necessary to write the expression for the magnetic induction at any point of the field, and then to integrate this expression over the space occupied by the flux that is linked to the element in question. Biot-Savart Law of Magnetic Field Intensity d
dH =
i ds r2
sinθ
where dH = magnetic field density i = current ds = length of circuit element r = radius vector θ = angle between ds and the radius vector
θ
ds
Mutual Inductance of Two Conductors Values of loge in the equation: loge R = loge p + loge k (Longer sides of rectangles in same straight line.) γ=
c 1 B , = p ∆ c
See Tables on next page for values.
r
χ
c
c
B
B p
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Geometric Mean Distances In calculating the mutual inductance of two conductors whose cross sectional dimensions are small compared with their distance apart, we assume that the mutual inductance is the same as the mutual inductance of the filaments along their axes, and use the appropriate basic formula for filaments to calculate mutual inductance. For conductors whose cross section is too large to justify this assumption, it is necessary to average the mutual inductances of all the filaments of which the conductors consist. That is, the basic formula for the mutual inductance is to be integrated over the cross sections of the conductors. Values of logc k in equation:
Geometric Mean Distance of Equal Parallel Rectangles, Longer Sides of Rectangle in Same Straight Line γ
1 =0 ∆
.02
.04
.06
.08
1.0
0.05
-0.0002
-0.0002
-0.0002
-0.0001
-0.0001
+0.0000
0.10
-0.0008
-0.0008
-0.0007
-0.0005
-0.0003
+0.0000
0.15
-0.0019
-0.0018
-0.0016
-0.0012
-0.0006
+0.0000
0.20
-0.0034
-0.0032
-0.0028
-0.0021
-0.0012
+0.0000
0.25
-0.0053
-0.0051
-0.0044
-0.0034
-0.0019
+0.0000
0.30
-0.0076
-0.0073
-0.0064
-0.0048
-0.0027
+0.0001
0.35
-0.0105
-0.0100
-0.0087
-0.0066
-0.0036
+0.0002
0.40
-0.0138
-0.0132
-0.0115
-0.0086
-0.0047
+0.0002
0.45
-0.0176
-0.0169
-0.0146
-0.0110
-0.0059
+0.0003
0.50
-0.0220
-0.0210
-0.0182
-0.0136
-0.0073
+0.0005
0.55
-0.0269
-0.0257
-0.0222
-0.0164
-0.0087
+0.0007
0.60
-0.0325
-0.0310
-0.0267
-0.0196
-0.0103
+0.0010
0.65
-0.0388
-0.0369
-0.0316
-0.0231
-0.0120
+0.0014
0.70
-0.0458
-0.0435
-0.0370
-0.0269
-0.0137
+0.0019
0.75
-0.0536
-0.0509
-0.0431
-0.0310
-0.0156
+0.0023
0.80
-0.0625
-0.0591
-0.0470
-0.0354
-0.0176
+0.0031
0.85
-0.0725
-0.0683
-0.0569
-0.0401
-0.0195
+0.0037
0.90
-0.0839
-0.0786
-0.0648
-0.0451
-0.0216
+0.00046
0.95
-0.0973
-0.0903
-0.0734
-0.0504
-0.0236
+0.0056
1.00
-0.1137
-0.1037
-0.0828
-0.0561
-0.0258
+0.0065
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277
loge R = logc p + logc k c
(Longer sides of the rectangle perpendicular to lines joining their centers.) B=
c
B
B c ,∆ = p B
p
Geometric Mean Distances of Equal Parallel Rectangles (concluded) Geometric Mean Distance of Equal Parallel Rectangles, Longer Sides of the Rectangle Perpendicular to Centers B
∆=0
0.2
0.4
0.6
0.8
1.0
0.1
0.0008
0.0008
0.0007
0.0005
0.0003
0.0000
0.2
0.0033
0.0032
0.0028
0.0021
0.0012
0.0000
0.3
0.0074
0.0071
0.0062
0.0048
0.0027
0.0001
0.4
0.0129
0.0124
0.0109
0.0084
0.0050
0.0003
0.5
0.0199
0.0191
0.0169
0.0131
0.0077
0.0005
0.6
0.0281
0.0271
0.0240
0.0185
0.0111
0.0011
0.7
0.0374
0.0361
0.0320
0.0251
0.0155
0.0019
0.8
0.0477
0.0461
0.0411
0.0321
0.0200
0.0031
0.9
0.0589
0.0569
0.0506
0.0404
0.0254
0.0046
1.0
0.0708
0.0685
0.0614
0.0492
0.0313
0.0065
0.9
0.0847
0.0821
0.0738
0.0596
0.0382
0.8
0.1031
0.0999
0.0903
0.0745
0.0485
0.7
0.1277
0.1240
0.1125
0.0925
0.6
0.1618
0.1573
0.1436
0.1194
0.5
0.2107
0.2053
0.1886
0.4
0.2843
0.2776
0.2567
0.3
0.4024
0.3942
0.2
0.6132
0.6021
0.1
1.0787
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For accurate interpolation in the case of broad rectangles, near together (1/B small and D small), write: loge R = loge B + loge K'
Values for logeK' 1/B
∆=0
0.00
-1.5000
0.05
-1.3542
0.10
-1.2239
-1.2278
0.15
-1.1052
-1.1084
0.20
-0.9962
-0.9989
-1.0073
0.25
-0.8953
-0.8977
-0.9049
0.30
-0.8015
-0.8037
-0.8098
-0.8208
0.35
-0.7140
-0.7159
-0.7215
-0.7311
0.40
-0.6321
-0.6337
-0.6387
-0.6472
-0.6596
0.45
-0.5550
-0.5565
-0.5610
-0.5687
-0.5797
0.50
-0.4825
-0.4838
-0.4879
-0.4948
-0.5046
0.1
0.2
0.3
0.4
0.5
-0.5178
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279
Values of Constants for the Geometric Mean Distance of a Rectangle Sides of the rectangle are B and c. The geometric mean distance R is given by: loge R = loge (B + c) - 1.5 + loge e.
R = K (B + c), loge K = - 1.5 + loge e Values for Constants K, logee B/c or c/B
K
loge e
B/c or c/B
K
loge e
0.00
0.22313
0.0000
0.50
0.22360
0.00211
0.025
0.22333
0.00089
0.55
0.22358
0.00203
0.05
0.22346
0.00146
0.60
0.22357
0.00197
0.10
0.22360
0.00210
0.65
0.22356
0.00192
0.15
0.22366
0.00239
0.70
0.22355
0.00187
0.20
0.22369
0.00249
0.75
0.22354
0.00184
0.25
0.22369
0.00249
0.80
0.22353
0.00181
0.30
0.22368
0.00244
0.85
0.22353
0.00179
0.35
0.22366
0.00236
0.90
0.22353
0.00178
0.40
0.22364
0.00228
0.95
0.223525
0.00177
0.45
0.22362
0.00219
1.00
0.223525
0.00177
Geometric Mean Distance of a Line of Length (a) from Itself loge R = loge a −
3 2
or R = 0.22313a Circular Area of Radius (a) from Itself loge R = loge a −
1 4
or R = 0.7788a Ellipse with Semiaxes (a) and (b) loge R = loge
a +b 1 − 2 4
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Geometric Mean Distance of an Annulus from Itself p
1
loge R = logp1 − logeζ
p2
Geometric Mean Distance of a Point or Area from an Annulus loge R =
p12 loge p1 − p22 loge p2 p12 − p22
1 − 2
point A
area
Values for Geometric Mean Distance of an Annulus p2/p1
logeζ
d1
0.00
0.2500
-12
0.05
0.2488
-36
-24
0.10
0.2452
-57
-21
0.15
0.2395
-75
-18
0.20
0.2320
-92
-16
0.25
0.2228
-105
-14
0.30
0.2123
-116
-12
0.35
0.2007
-127
-10
0.40
0.1880
-135
-8
0.45
0.1745
-142
-7
0.50
0.1603
-144
-6
0.55
0.1456
-147
-5
0.60
0.1304
-152
-4
0.65
0.1148
-156
-3
0.70
0.0989
-159
-3
0.75
0.0827
-162
-2
0.80
0.0663
-163
-1
0.85
0.0499
-164
-1
0.90
0.0333
-165
-1
0.95
0.0167
-166
-1
1.00
0.0000
-167
d2
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Chapter 10/Electrical Measurement
Inductance of Parallel Elements of Equal Length Mutual Inductance of Two Equal Parallel Straight Filaments
ι or p
l l2 d2 d M = 0.002l loge + 1 + 2 − 1 + 2 + l d l d
M = 0.002lQ
Values for Q, d/l d/l
Q
d1
0.050
2.7382
-903
0.055
2.6479
-822
0.060
2.5657
-752
0.065
2.4905
-693
0.070
2.4212
-642
0.075
2.3570
-597
0.080
2.2973
-558
0.085
2.2415
-524
0.090
2.2189
-493
0.095
2.1398
-466
0.100
2.0932
-440
0.105
2.0492
-418
0.110
2.0074
-397
0.115
1.9677
-379
0.120
1.9298
-361
0.125
1.9837
-345
0.130
1.8592
-330
0.135
1.8262
-318
0.140
1.7944
-305
0.145
1.7639
-293
0.150
1.7346
-281
281
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Values for Q, d/l (cont.) d/l
Q
d1
0.155
1.7065
-271
0.160
1.6794
-262
0.165
1.6532
-253
0.170
1.6279
-244
0.175
1.6035
-236
0.180
1.5799
-228
0.185
1.5571
-222
0.190
1.5349
-215
0.195
1.5134
-208
0.200
1.4926
-398
0.210
1.4528
-376
0.220
1.4152
-355
0.230
1.3797
-337
0.240
1.3460
-321
0.250
1.3139
-305
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283
Values for Q, d/l (cont.) d/l
Q
d1
d/l
Q
d1
0.260
1.2834
-290
0.520
0.8016
-227
0.270
1.2544
-277
0.540
0.7789
-215
0.280
1.2267
-265
0.560
0.7574
-204
0.290
1.2002
-253
0.580
0.7370
-194
0.300
1.1749
-243
0.600
0.7176
-184
0.310
1.1506
-233
0.620
0.6992
-175
0.320
1.1273
-224
0.640
0.6817
-167
0.330
1.1049
-214
0.660
0.6650
-160
0.340
1.0835
-207
0.680
0.6490
-152
0.350
1.0627
-199
0.700
0.6338
-145
0.360
1.0429
-192
0.720
0.6193
-139
0.370
1.0238
-186
0.740
0.6054
-134
0.380
1.0052
-178
0.760
0.5920
-128
0.390
0.9874
-172
0.780
0.5792
-122
0.400
0.9702
-166
0.800
0.5670
-118
0.410
0.9536
-161
0.820
0.5552
-113
0.420
0.9375
-156
0.840
0.5439
-109
0.430
0.9219
-151
0.860
0.5330
-105
0.440
0.9068
-146
0.880
0.5225
-101
0.450
0.8922
-141
0.900
0.5124
-97
0.460
0.8781
-137
0.920
0.5027
-93
0.470
0.8644
-133
0.940
0.4934
-90
0.480
0.8511
-130
0.960
0.4843
-87
0.490
0.8381
-125
0.980
0.4756
-84
0.500
0.8256
-240
1.000
0.4672
-81
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Values for Q, l/d l/d
Q
d1
l/d
Q
d1
1.00
0.4672
-84
0.50
0.2451
-94
0.98
0.4588
-83
0.48
0.2357
-95
0.96
0.4505
-84
0.46
0.2262
-96
0.94
0.4421
-85
0.44
0.2166
-95
0.92
0.4336
-85
0.42
0.2071
-96
0.90
0.4251
-85
0.40
0.1975
-97
0.88
0.4166
-86
0.38
0.1878
-97
0.86
0.4080
-87
0.36
0.1781
-97
0.84
0.3993
-87
0.34
0.1684
-97
0.82
0.3906
-87
0.32
0.1587
-98
0.80
0.3819
-88
0.30
0.1489
-98
0.78
0.3731
-88
0.28
0.1391
-98
0.76
0.3643
-89
0.26
0.1293
-99
0.74
0.3554
-90
0.24
0.1194
-98
0.72
0.3464
-90
0.22
0.1096
-99
0.70
0.3374
-90
0.20
0.0977
-99
0.68
0.3284
-91
0.18
0.0898
-100
0.66
0.3193
-91
0.16
0.0798
-99
0.64
0.3102
-92
0.14
0.0699
-100
0.62
0.3011
-93
0.12
0.0599
-99
0.60
0.2918
-92
0.10
0.0500
-100
0.58
0.2826
-93
0.08
0.0400
-100
0.56
0.2733
-93
0.06
0.0300
-100
0.54
0.2640
-94
0.04
0.0200
-100
0.52
0.2546
-95
0.02
0.0100
-100
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Chapter 10/Electrical Measurement
Mutual Inductance of Two Equal Parallel Conductors d 1d 2l M = 0.002l loge − loge k − 1 + − 2 d l 4l 2
Self-Inductance of a Straight Conductor General Formula ζ 2l L = 0.002l loge − 1 + 1 r l
where r = geometric mean distance ζ1= arithmetic mean distance of the points of the cross section
285
For Elliptical Wire 2l L = 0.002l loge − 0.05685 α+β
where α = β semiaxes of the ellipse Inductance of Multiple Conductors Two Equal Parallel Wires, Separated by Distance (d) between Centers
2l 7 L = 0.002l loge − pd 8
For a Round Wire, Radius p 2l 3 L = 0.002l loge − p 4
For a Round Magnetic Wire 2l µ L = 0.002l loge − 1 + p 4 where µ = permeability
For Rectangular Wire, Sides B and C 2l 1 L = 0.002l loge + − loge e 2 B + C
where B and C = see table, Values of constants for Geometric Mean Distance for Rectangles
Three Equal Parallel Wires, at the Corners of an Equilateral Triangle of Side (d)
2l L = 0.002l loge − 1 2 1/ 3 ( rd )
where r = geometric mean distance of circular area of radius (p) Inductance of a Return Circuit of Parallel Conductors Equal Round Wires of Radius (p) d 1 d L = 0.004l loge + − p 4 l
Equal Permeable Round Wires d µ d L = 0.004l loge + − p 4 l
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Return Circuit of Two Tubular Conductors, One Inside the Other 2 P 2 2 P1 p p × lo L = 0.002l loge 1 + oge 1 − 1 + loge ζ1 + loge ζ3 2 p2 p3 p 1 − 2 p1
where loge ζ1 and loge ζ3 = values from table, geometric mean distance of an annulus Return Circuit of Polycore Cable 2 P 2 2 P1 p1 p1 1 a 1 + loge ρ + loge ξ + − 1 L = 0.002l loge + loge 2 a n n 4n p2 p 1− 2 p1
Mutual Inductance of Unequal Parallel Filaments General Formula α β γ ζ M = 0.001α sin h −1 − β sin h −1 − γ sin h −1 + ζ sin h −1 − α 2 + d 2 d d d d + β2 + d 2 + γ 2 + d 2 − ζ 2 + d 2
p1
where α=l+m−ζ β=l−ζ γ=m−ζ
p2
ι
a
p
p
ζ
m
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287
Mutual Inductance of Filaments Inclined at an Angle Equal Filaments Meeting at a Point R12 = 2l 2 (1 − cos ε)
ι
Mutual Inductance between Filaments l M = 0.004l cos ε tan h −1 l + R1
ε
R1
ι
or
M = 0.001 lS
Values of Factor S
Value of Factor S (cont.)
cos ε
S
d1
cos ε
S
d1
0.95
3.7830
-7236
-0.05
-0.0867
-867
0.90
3.0594
-4462
-0.10
-0.1707
-840
0.85
2.6132
-3316
-0.15
-0.2523
-815
0.80
2.2816
-2679
-0.20
-0.3316
-793
0.75
2.0137
-2274
-0.25
-0.4088
-772
-0.4840
-752
0.70
1.7863
-1991
-0.30
0.65
1.5872
-1780
-0.35
-0.5574
-734
0.60
1.4092
-1618
-0.40
-0.6290
-716
0.55
1.2474
-1488
-0.45
-0.6991
-701
0.50
1.0986
-1382
-0.50
-0.7677
-686
0.45
0.9604
-1294
-0.55
-0.8348
-671
0.40
0.8310
-1218
-0.60
-0.9006
-658
0.35
0.7092
-1154
-0.65
-0.9651
-645
-1.0284
-633
0.30
0.5938
-1097
-0.70
0.25
0.4841
-1048
-0.75
-1.0906
-622
0.20
0.3793
-1003
-0.80
-1.1517
-611
0.15
0.2789
-964
-0.85
-1.2118
-601
0.10
0.1825
-929
-0.90
-1.2709
-591
0.05
0.0896
-896
-0.95
-1.3290
-581
0.00
0.0000
-867
-1.00
-1.3862
-572
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Unequal Filaments Meeting at a Point
m1 l1 M = 0.002 cos ε l1 tan h −1 + m1 tan h − 1 l + R m 1 1 +R or M = 0.001 l1 S1
Values for S1, Unequal Filaments Meeting at a Point 0.8
0.6
0.4
0.2
0.95
m1 =1 l1 3.7830
3.3406
2.7622
2.0473
1.1776
0.90
2.0594
2.7095
2.2597
1.6957
0.9918
0.85
2.6132
2.3178
1.9422
1.4690
0.8688
0.80
2.2816
2.0256
1.7028
1.2950
0.7727
0.75
2.0137
1.7889
1.5073
1.1513
0.6917
0.70
1.7863
1.5876
1.3402
1.0272
0.6209
0.65
1.5872
1.4113
1.1931
0.9172
0.5572
0.60
1.4092
1.2534
1.0609
0.8177
0.4991
0.55
1.2474
1.1098
0.9404
0.7264
0.4452
0.50
1.0986
0.9776
0.8291
0.6417
0.3947
0.40
0.8310
0.7398
0.6283
0.4880
0.3020
0.30
0.5938
0.5288
0.4496
0.3501
0.2179
0.20
0.3793
0.3378
0.2876
0.2244
0.1404
0.10
0.1825
0.1626
0.1385
0.1083
0.0680
0.00
0.0000
0.0000
0.0000
0.0000
0.0000
-0.10
-0.1707
-0.1522
-0.1298
-0.1018
-0.0644
-0.20
-0.3316
-0.2956
-0.2523
-0.1982
-0.1257
-0.30
-0.4840
-0.4314
-0.3684
-0.2898
-0.1844
-0.40
-0.6290
-0.5608
-0.4791
-0.3772
-0.2406
-0.50
-0.7677
-0.6845
-0.5850
-0.4611
-0.2948
-0.60
-0.9006
-0.8031
-0.6865
-0.5416
-0.3470
-0.70
-1.0284
-0.9172
-0.7844
-0.6194
-0.3976
-0.80
-1.1517
-1.0272
-0.8788
-0.6944
-0.4467
cos ε
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Unequal Filaments in the Same Plane, Not Meeting
b
l 2m 2 (R22 − R32 − l 2 ) + α 2 (R42 − R32 − m 2 ) µ= 4l 2m 2 − α 4 m 2l 2 (R42 − R32 − m2 ) + α 2 (R22 − R32 − l 2 4l 2m 2 − α 4
R12 = (µ + l )2 + (v + m)2 − 2(µ + l )(v + m)cos ε R22 = (µ + l )2 + v 2 − 2v (µ + l )cos ε R32 = µ 2 + v 2 − 2µ v cos ε R42 = µ 2 + (v + m)2 − 2µ (v + m)cos ε
Equation for Mutual Inductance M m = (µ + l )tan h −1 R1 + R2 2 cos ε l m + (v + m)tan h −1 − µ tan h −1 R1 + R4 R3 + R 4 l − v tan h −1 R2 + R3
ι R2
R1
R3
∈ ν
C
m
α 2 = R42 − R32 + R22 − R12
µ
ν
a
where
v =
d p
α2 lm
R
4
m
B
ε
Equations Connecting the Two Systems 2 cos ε =
ι
A
p
289
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Mutual Inductance of Two Filaments Placed in Any Desired Position
M m = 2 (µ + l )tan h −1 R1 + R2 0.001 cos ε m l +2 (v + m)tan h −1 − µ tan h −1 R3 + R 4 R1 + R4 1 Ωd −2 v tan h −1 − R2 + R3 sin ε
where d 2 cos ε + (µ + l )(v + m)sin2 ω = tan−1 dR1 sin ε d 2 cos ε + (µ + l )v sin2 ε − tan−1 dR2 sin ε d 2 cos ε + µ v sin2 ε = tan−1 dR3 sin ε d 2 cos ε + µ(v + m)sin2 ε − tan−1 dR4 sin ε
ε
Circuits Composed of Combinations of Straight Wires Equation for the Inductance of a Triangle of Round Wire 2a 2b 2c c 2 + b2 − a2 L = 0.002 a loge + b loge + c loge − (b − c )sin h −1 V ρ ρ ρ 2 2 2 a 2 + b2 − c 2 −1 a + c − b − (a + b + c ) − (a + b)sin h−1 − (a + c )sin h V V µ + (a + b + c ) 4
where V 2 = 2(a 2b 2 + a 2c 2 + b 2c 2 ) − a 4 − b 4 − c 4
a,b,c = sides of the triangle
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291
Equation for the Inductance of a Rectangle of Round Wire 2a 2b a b L = 0.004 a loge + loge + 2 a 2 + b 2 − a sin h −1 − b sin h −1 ρ ρ b a µ − 2(a + b) + (a + b) 4
Regular Polygons of Round Wire Equilateral Triangle s µ L = 0.006s loge − 1.40546 + ρ 4 Square s µ L = 0.008s loge − 0.77401 + ρ 4 Pentagon s µ L = 0.010s loge − 0.40914 + ρ 4
Hexagon µ s L = 0.012s loge − 0.15152 + ρ 4
Octagon s µ L = 0.016s loge + 0.21198 + ρ 4
Equation for the Calculation of Inductance of Any Plane Figure 2l µ L = 0.002l loge − α + ρ 4
where l = perimeter of the figure
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Values for α (alpha) for Certain Plane Figures Isosceles Triangles
Rectangles
ε
α
β
α
5°
4.884
0.05
4.494
10°
4.152
0.10
3.905
20°
3.690
0.15
3.589
30°
3.424
0.20
3.404
40°
3.284
0.25
3.270
50°
3.217
0.30
3.172
60°
3.197
0.40
3.041
70°
3.214
0.50
2.962
80°
3.260
0.60
2.913
90°
3.331
0.70
2.882
100°
3.426
0.80
2.865
110°
3.546
0.90
2.856
120°
3.696
1.00
2.854
130°
3.875
140°
4.105
150°
4.399
160°
4.813
170°
7.514
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Regular Polygons N
α
3
3.197
4
2.854
5
2.712
6
2.636
7
2.591
8
2.561
9
2.542
10
2.529
11
2.519
12
2.513
13
2.506
14
2.500
15
2.495
16
2.492
17
2.489
18
2.486
19
2.484
20
2.482
21
2.481
22
2.480
23
2.478
24
2.477
∞
2.452
293
Mutual Inductance of Equal, Parallel, Coaxial Polygons of Wire s = length of the side of the polygon. d = distance between their planes. Squares 2a 4 s = π d d M=
4s ∫F 2π
Equilateral Triangles 2a 3 s = π d d
M=
3s ∫F 2π
Hexagons 2a 6 s = π d d
M=
6s ∫F 2π
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Values for (F) in Coaxial Equal Polygons, d/s d/s
Triangles F
Diff.
Squares F
Diff.
0.00
1.0000
0.05
0.7245
-2755
0.8642
-1358
0.9449
-551
0.10
0.6640
-605
0.8362
-280
0.9350
-99
0.15
0.6217
-423
0.8165
-197
0.9283
-67
0.20
0.5890
-327
0.8007
-158
0.9231
-52
0.25
0.5624
-266
0.7875
-132
0.9188
-43
0.30
0.5402
-222
0.7760
-115
0.9150
-38
0.35
0.5215
-187
0.7658
-102
0.9117
-33
0.40
0.5054
-161
0.7565
-93
0.9087
-30
0.45
0.4914
-140
0.7480
-85
0.9057
-30
0.50
0.4792
-122
0.7402
-78
0.9029
-28
0.55
0.4686
-106
0.7329
-73
0.9003
-26
0.60
0.4592
-94
0.7262
-67
0.8078
-25
0.65
0.4507
-85
0.7200
-62
0.8054
-24
0.70
0.4437
-70
0.7140
-60
0.8031
-23
0.75
0.4372
-65
0.7085
-55
0.8906
-25
0.80
0.4314
-58
0.7035
-50
0.8884
-22
0.85
0.4263
-51
0.6988
-47
0.8863
-21
0.90
0.4216
-47
0.6941
-47
0.8843
-20
0.95
0.4175
-41
0.6899
-42
0.8823
-20
1.00
0.4138
-37
0.6861
-38
0.8802
-21
1.000
Hexagon F
Diff.
1.000
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295
Values for (F) in Coaxial Equal Polygons, s/d s/d
Triangles F
Diff.
Squares F
Diff.
1.00
0.4138
0.90
0.4066
-72
0.6783
-78
0.8761
-41
0.80
0.3996
-70
0.6701
-82
0.8713
-48
0.70
0.3930
-66
0.6613
-88
0.8656
-57
0.60
0.3866
-64
0.6525
-88
0.8592
-64
0.50
0.3808
-58
0.6439
-86
0.8518
-74
0.40
0.3757
-51
0.6362
-77
0.8440
-78
0.30
0.3714
-43
0.6289
-73
0.8364
-76
0.20
0.3682
-32
0.6221
-68
0.8297
-67
0.10
0.3662
-20
0.6182
-39
0.8243
-54
0.00
0.3655
-7
0.6169
-13
0.8225
-18
0.6861
Hexagon F
Diff.
0.8802
Coaxial Triangles s d 11d 2 203d 4 M = 0.006s loge − 1.4055 + 2.209 − + .... d s 12s 2 864s 4 Coaxial Squares s d d2 d4 M = 0.008s loge − 0.7740 + − 0.0429 2 − 0.109 4 .... d s s s Coaxial Hexagons s d d2 d4 M = 0.012s loge − 0.15152 + 0.3954 + 0.1160 2 − 0.052 4 .... d s s s
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Inductance of Single-Layer Coils on Rectangular Winding Forms 2 aa 1b a a a 1b 1 a b L = 0.008 N 2 1 sin h −1 + sin h −1 1 − 1 − 12 sin h −1 2 b 2a1 b 2a b 2 b a1 a b 1 + 12 b 2 2 2 aa1 g 1a 1b 1g 1a1 −1 a −1 a1 π −1 + + − tan 1 + 2 1 2 sin h sin h − − 3aa1 2b a1 2b a 2 b 2b g2 b2 1 + 2 b 1b 2 a2 1a 2 1b 2 1a 2 1b 2 1b g 3a 3a13 a2 + − 1 + 2 1 − 2 − 1 − 12 1 − 12 + 3aa1 6aa1 b 2 3aa1 3aa1 2 2 b 2 b b b
where g 2 = a 2 + a12
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297
Coefficients, Short Rectangle Solenoid β1′ =
1 1 1 + π k
κ
β1’
β1
β2
β3
β5
β7
1.00
0.4622
0.6366
0.2122
-0.0046
0.0046
-0.0382
0.95
0.4574
0.6534
0.2234
-0.0046
0.0053
0.90
0.4512
0.6720
0.2358
-0.0046
0.0064
0.85
0.4448
0.6928
0.2496
-0.0042
0.0080
0.80
0.4364
0.7162
0.2653
-0.0031
0.0103
0.75
0.4260
0.7427
0.2829
-0.0010
0.0141
0.70
0.4132
0.7730
0.3032
0.0026
0.0198
0.65
0.3971
0.8080
0.3265
0.0085
0.0291
0.60
0.3767
0.8488
0.3537
0.0179
0.0432
0.55
0.3500
0.8970
0.3858
0.0331
0.0711
0.50
0.3151
0.9549
0.4244
0.0578
0.1183
-0.7855
0.40
0.1836
1.1141
0.5305
0.1679
0.3898
-2.4030
0.30
-0.0314
1.3359
0.7074
0.5433
2.0517
-7.850
0.20
-0.6409
1.9099
1.0610
2.3230
14.5070
15.51
0.10
-3.2309
3.5014
2.1220
22.5480
497.360
14282.0
-0.0525
-0.0838
-0.1564
-0.3372
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b = nb pb c = nc pc N = nbnc
For Closely Wound Coils: b = δnb c = δnc N=
bc δ
where pb = pc δ = diameter of the covered wire
c
Nomenclature a = mean radius of turns b = axial dimension of the cross-section c = radial dimension of the cross-section N = total number of turns nb = number of turns per layer nc = number of layers pb = distance between centers of adjacent turns in the layer pc = distance between centers of corresponding wires in consecutive layers
a
Self-Inductance of Circular Coils of Rectangular CrossSection
b
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11 VISCOSITY MEASUREMENT Principles of Viscosity & Definitions . . . . . . . . . . . . . . . . . . . . . . . . 301 Viscosity SI Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 Dynamic, Absolute, or Simple Viscosity . . . . . . . . . . . . . . . . . . . . . 302 Kinematic Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 Common Viscosity Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 Other Viscosity Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 Measuring Viscosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Hagen-Poiseuille’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Stoke’s Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Values of Viscometer Constants A and B . . . . . . . . . . . . . . . . . . . . 306 Viscosity Conversion Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Poise to lb-force sec/ft2 Conversion Table . . . . . . . . . . . . . . . . . . . . 308 lb-force sec/ft2 to Pa-sec Conversion Table . . . . . . . . . . . . . . . . . . . 309
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301
Principles of Viscosity & Definitions Viscosity is a quantity describing a fluid’s resistance to flow. Fluids resist the relative motion of immersed objects through them as well as to the motion of layers with differing velocities within them. Formally, viscosity (represented by the symbol η) is the ratio of the shearing stress (F/A) to the velocity gradient (∆vx/∆z or dvx/dz) in a fluid. F ∆v x η= ÷ A ∆z
or
F dv η= ÷ x A dz
The more usual form of this relationship is called “Newton’s equation.” It states the resulting shear of a fluid is directly proportional to the force applied and inversely proportional to its viscosity. Note the similarity to Newton’s second law of motion (F = ma). F ∆v x A = η ∆z ∆v F =m ∆t
or
dv F =η x A dz dv F =m dt
Viscosity SI Units According to NIST’s Guide for the International System of Units (SI), the proper SI units for expressing values of viscosity η (also called dynamic viscosity) and values of kinematic viscosity ν are, respectively, the Pascal second (Pa·s) and the meter squared per second (m2/s) (and their decimal multiples and submultiples as appropriate). The Pascal second [Pa·s] has no special name. And, although touted as an international system, the International System of Units (SI) has had very little international impact. The Pascal second is rarely used in scientific and technical publications today. The most common unit of viscosity is the dyne second per square centimeter (dyne · s/cm2), which is given the name poise (P) after the French physiologist Jean Louis Poiseuille (1799-1869). Ten poise equal one Pascal second (Pa·s) making the centipoise (cP) and millipascal second (mPa·s) identical.
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1 Pascal second = 10 poise = 1,000 millipascal second 1 centipoise = 1 millipascal second English/Metric Viscosity Units Quantity
English
Metric
Viscosity
Poise
Pa/sec
Kinematic Viscosity
Stroke
m2/sec
There are actually two quantities called viscosity. The quantity defined above usually is just called viscosity. However, it sometimes is also called dynamic viscosity, absolute viscosity, or simple viscosity to distinguish it from the other quantity. Dynamic, Absolute, or Simple Viscosity Va = At −
B t
where Va = dynamic, absolute, or simple viscosity A = a viscometer constant B = a viscometer constant t = time for a volume of fluid to pass through an aperture Kinematic Viscosity The other quantity, called kinematic viscosity (represented by the symbol ν), is the ratio of the viscosity of a fluid to its density. v =
η ρ
Kinematic viscosity is a measure of the resistive flow of a fluid under the influence of gravity. It is frequently measured by a “capillary viscometer” — basically a graduated can with a narrow tube at the bottom. When two fluids of equal volume are placed in identical capillary viscometers and allowed to flow under the influence of gravity, a viscous fluid takes longer than a less viscous fluid to flow through the tube.
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Chapter 11/Viscosity Measurement
Kv =
303
V D
where Kv = kinematic viscosity V = viscosity of fluid D = density of fluid The SI unit of kinematic viscosity is the square meter per second (m2/s), which also has no special name. This unit is so large it is rarely used. A more common unit of kinematic viscosity is the square centimeter per second (cm2/s), which has been given the name stoke [St] after the English scientist George Stoke. Since this unit is also large, the more commonly used unit is the square millimeter per second (mm2/s) or centistoke (cSt). According to NIST’s Guide for the International System of Units (SI), the CGS units commonly used to express values of these quantities, the poise (P) and the stokes (St), respectively [and their decimal submultiples the centipoise (cP) and the centistoke (cSt)], are not to be used. However, since CGS units are, in fact, the most widely used terms, they are included in this ISA Handbook. Common Viscosity Units 1 m2/s = 10,000 cm2/s (stoke) = 1,000,000 mm2/s (centistokes) 1 cm2/s = 1 stoke 1 mm2/s = 1 centistoke 1 Poise = 1 dyne sec/cm2 1 Poise = 0.1 Pa sec 1 Centipoise = 0.001 Pa/sec 1 Centipoise = 1 cm2/sec 1 cP = viscosity of water at 68°C 1 lb-force sec/ft2 = 1 slug/ft sec
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Other Viscosity Equations S V = s Sr
where V = viscosity of a fluid Ss = shear stress, force per area Sr = shear rate, velocity per layer thickness Ratio of Shear Stress to Shear Rate, Hagen-Poiseuille Law V =
πPd R 4 8QL
where V = viscosity Pd = pressure differential of liquid R = inside radius of tube Q = rate of liquid flow L = length of tube Apparent Viscosity (Consistency) C=
Ad Ws
where C = consistency, percent Ad = dry-weight of solid Ws = weight of solid plus liquid
x 100
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305
Measuring Viscosity Hagen-Poiseuille’s Law French physician and physiologist Jean Poiseuille, while developing an improved method for measuring blood pressure, formulated a mathematical expression for the flow rate for the laminar (nonturbulent) flow of fluids in circular tubes. Discovered independently by Gotthilf Hagen, a German hydraulic engineer, this relation is also known as the HagenPoiseuille equation, or Hagen-Poiseuille Law. For laminar, non-pulsatile fluid flow through a uniform straight pipe, the flow rate (volume per unit time) is: • directly proportional to the pressure difference between the ends of the tube, • inversely proportional to the length of the tube, • inversely proportional to the viscosity of the fluid, and • proportional to the fourth power of the radius of the tube.
φ=
π∆Pr 4 8 η
Stoke’s Law George Gabriel Stokes, an Irish-born mathematician who spent much of his life working with fluid properties, is most famous for his work describing the motion of a sphere through viscous fluids. This led to the development of Stokes’s Law – an equation that shows the force needed to move a small sphere through a continuous, quiescent fluid at a certain velocity. It is based primarily on the radius of the sphere and the viscosity of the fluid. He found what has become known as Stokes’ Law: The drag force on a sphere of radius (R) moving through a fluid of viscosity η at speed Vc is given by: F (drag) = 6πR ηVc
Where R = the radius of the sphere η = the viscosity Vc = the velocity through a continuous fluid The faster a sphere falls through a fluid, the lower the viscosity. The measurement involves dropping a sphere through a measured distance of fluid and measuring how long it takes to traverse the distance.
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Since you know distance and time, you also know velocity, which is distance/time. A formula for determining the viscosity in this manner is: viscosity = η =
2(∆p)ga2 9v
Where ∆p = difference in density between the sphere and the liquid g = acceleration of gravity a = radius of sphere v = velocity = d/t = (Distance sphere falls/time it takes to fall) Values of Viscometer Constants A and B Viscometer
Constant A
Constant B
Time of Efflux
Saybolt Universal
0.226 0.220
195 135
32-100 over 100
Saybolt Furol
2.24
184
25-40
Redwood #1
0.260 0.247
179 50
34-100 over 100
Redwood #2
2.46 2.45
100 -
32-90 over 90
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Viscosity Conversion Table To Convert from
To
Multiply by:
Centipoise
Pascal/sec
0.001
Centistroke
m2/sec
0.000001
cm3/sec
ft3/min
0.00211888
cm3/sec
liter/hr
3.6
ft3/hr
cm3/sec
7.865791
ft3/hr
liter/min
0.4719474
ft3/min
cm3/sec
471.9474
ft3/sec
cm3/hr
101.9406
ft3/sec
liter/min
1699.011
in3/min
cm3/sec
0.2731177
Dyne-sec/cm2
Poise
1.0
Geepound
Slug
1.0
Gram-force
Dyne
980.665
kilogram-force
Dyne
0.0000980665
liter/sec
ft3/hr
127.1328
liter/sec
ft3/min
2.11888
liter/sec
gallon/hr
951.0194
part per million
mg/kg
1.0
part per million
ml/cm3
1.0
Poise
Dyne-sec/cm2
1.0
Poise
gram/cm-sec
1.0
Poise
Pascal-sec
0.1
lb-force-sec/ft2
Pascal-sec
47.8803
lb-force-sec/in2
Pascal-sec
6894.76
Slug
kg
14.5939
307
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ISA Handbook of Measurement Equations and Tables
Conversion Table, Poise to lb-force sec/ft2 Poise
lb-force sec/ft2
Poise
lb-force sec/ft2
1
478.80
800
383,040
2
957.60
900
430,920
3
1436.40
1000
478,800
4
1915.20
2000
957,600
5
2394.00
3000
1,436,400
6
2872.80
4000
1,915,200
7
3351.60
5000
2,394,000
8
3830.40
6000
2,872,800
9
4309.20
7000
3,351,600
10
4788.00
8000
3,830,400
20
9576.00
9000
4,309,200
30
14,364.00
10,000
4,788,000
40
19,152.00
20,000
9,576,000
50
23,940.00
30,000
14,364,000
60
28,728.00
40,000
19,152,000
70
33,516.00
50,000
23,940,000
80
38,304.00
60,000
28,728,000
90
43,092.00
70,000
33,516,000
100
47,880.00
80,000
38,304,000
200
95,760.00
90,000
43,092,000
300
143,640.00
100,000
47,880,000
400
191,520.00
110,000
52,668,000
500
239,400.00
120,000
57,456,000
600
287,280.00
130,000
62,244,000
700
335,160.00
140,000
67,032,000
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Chapter 11/Viscosity Measurement
309
Conversion Table, lb-force sec/ft2 to Pa-sec lb-force sec/ft2
Pa/sec
lb-force sec/ft2
Pa/sec
100
4788.03
600,000
28,728,180
200
9576.06
700,000
33,516,210
300
14,364.09
800,000
38,304,240
400
19,152.12
900,000
43,092,270
500
23,940.15
1,000,000
47,880,300
600
28,728.18
2,000,000
95,760,600
700
33,516.21
3,000,000
143,640,900
800
38,304.24
4,000,000
191,521,200
900
43,092.27
5,000,000
239,401,500
1000
47,880.30
6,000,000
287,281,800
2000
95,760.60
7,000,000
335,162,100
3000
143,640.90
8,000,000
383,042,400
4000
191,521.20
9,000,000
430,922,700
5000
239,401.50
10,000,000
478,803,000
6000
287,281.80
20,000,000
957,606,000
7000
335,162.10
30,000,000
1,436,409,000
8000
383,042.40
40,000,000
1,915,212,000
9000
430,922.70
50,000,000
2,394,015,000
10,000
4,788,030.00
60,000,000
2,872,818,000
20,000
9,576,060.00
70,000,000
3,351,621,000
30,000
14,364,090.00
80,000,000
3,830,424,000
40,000
19,152,120.00
90,000,000
4,309,227,000
50,000
23,940,150.00
100,000,000
4,788,030,000
311 Index Term
Links
A Absolute pressure,
62
Air Quality Index,
243
Air quality standards - U.S.,
241
Airborne contaminants, ANSI/ISA-75.01.01-2002,
245-248 101
Approximate plant calculations ‘old timer’s’ tips,
116
Aqueous solutions - electrical conductivity,
98
Bernoulli’s equation,
84
B
Bridges - measuring inductance & capacitance,
267-269
C Communications - topologies,
183
Control valves - sizing,
101
D Dalton’s Law,
255
Density - Mercury & distilled water, Density of an imperfect gas, Dielectric constants,
45 59 172-176
Differential pressure,
63
pressure measurements,
46
pressure meters compensation for,
79
E Elbow meter,
84
Electrical conductivity - liquids,
99
Electrical measurement, dc bridges,
259 263
312 Index Term
Links
geometric mean distances,
276
principles of,
261
series voltmeters,
263
shunt resistance,
263
Electrical power - determining gain or loss, Electrical units - conversion table,
265 270-274
English & SI units,
61
English to metric conversions,
12
English to SI conversions,
10
English unit conversions,
15
Environmental measurement,
239
F Fieldbus Foundation - standard unit codes table,
189-209
Flow English & metric units,
62
inferential methods,
58
mass methods,
60
principles of,
57
velocity methods,
59
volume rate,
75
volumetric methods,
61
conversion table,
64
measurement,
55
nozzle,
83
Flow rate - hole in tank,
85
Flowmeter rate of heat loss,
95
temperature rise,
95
accuracy,
76
accuracy rotameters - effect of fluid properties on,
80
313 Index Term
Links
elements - head type,
80
performance - viscosity influence,
73
Flowmeters differential pressure,
80
magnetic,
59
target,
94
ultrasonic,
60
ultrasonic,
100
vortex shedding,
97
59
Fluid density,
63
Fluid pressure,
62
Fluids & gases physical properties, Flumes,
61 91-93
Fraction to inch to mm conversions, ft-lb to Joule conversions,
17 42
Fundamental constants & conversion factors, Fundamental physical constants,
62 20
G Gas compressibility factors,
70
Gas expansion factor,
77
Gases - critical values,
71
Gauge pressure,
62
Geometry measurements,
22
Glass tube meters - typical pressure ratings, Greek alphabet,
96 3
H Hagan-Poiseuille Law,
304
Head losses in pipes,
73
Head type flowmeter elements,
80
305
314 Index Term Humidity - psychrometric chart,
Links 258
Humidity & moisture conversion table, Humidity measurement,
256 251
253
Humidity measurement principals of,
254
I Inches to mm to fraction conversions, Incompressible fluids, Inductance measurement,
17 84 275-298
Industrial communications buses,
181
Industrial networking technologies, Inferential mass flow,
185 58
J Joule to ft-lb conversions,
43
K kg/mm2 to psi conversions,
38
ksi to Mpa conversions,
40
L lb-force sec/ft2 to Pa/sec conversion table,
309
Level bubblers,
164
conductance,
168
differential pressure,
164
displacers,
164
electrical measurement,
169
float switch,
168
floats,
164
head level measurement,
169
171
315 Index Term
Links
hydrostatic measurement in open tank,
170
hydrostatic pressure,
167
magnetostrictive,
167
nuclear,
166
radar,
166
RF ,
165
TDR,
167
ultransonic/sonic,
165
measurement,
161
measurement - principles of,
163
179
Linear volumetric meter signals compensation of,
77
Liquids - conductivity,
99
M Manometers - equations, Metals - total emmissivities,
44 159
mm to inches to fraction conversions, Mpa to ksi conversions, Mutual inductance,
17 41 285
O Ohm’s Laws, Open channel flow, Orifice plate, Oscilloscopes - principles of,
262 85 81 264
P Parshall flumes,
91
Pitot tube,
83
84
156
158
Planck’s radiation law, Plant calculations - ‘old timer’s tips’ to approximate, Platinum - resistance vs.
116
316 Index Term
Links
temperature,
149-153 2
Poise to lb-force sec/ft conversion table,
308
Pressure absolute & gauge examples,
33
fundamental constants & English conversions,
32
fundamental constants & metric conversions,
32
measurement types,
31
principles of,
31
some units & conversions,
34
units of,
32
Pressure measurement, 2
psi to kg/mm conversions, Pyrometers,
29 38 160
R Reactive environments classification of,
249
Reynolds numbers,
75
Rotameter signals - compensation of,
78
Rotameters - effect of fluid properties on , RTD material resistivity,
80 148
S Safety,
211
Groups,
217
Hazardous Classes & Zones,
213
Integrity Level Verification (SIL) (SIF), ISA-TR84.00.02.2002 - Part 2
221 221-237
317 Index Term Self inductance, SI to English conversions,
Links 285
298
10
SI units Classes,
4
definitions,
5
Sizing control valves, Specific heats - fluids & gases, Steam tables,
101 74 47
Stefan-Boltzmann law,
157
Stoke’s Law,
305
T Temperature heat transfer,
127
IPTS-68 vs. ITS-90 vs. EPT-76,
121
°C to °F conversion table,
134
°F to Kelvin conversions,
132
°F to °C conversions,
129
relation of scales,
125
Temperature conversion equations,
125
Temperature conversion table,
131
Temperature measurement,
119
Temperature measurement principles of,
121
Thermistor,
154
Thermocouples,
136
limits of error,
147
Type E voltage,
139
Type J voltage,
141
Type K voltage,
143
Type T voltage,
145
Thermometers
123
318 Index Term
Links
comparative characteristics of,
122
vapor pressure,
156
Tube flow rates - typical range,
96
Turbine meters,
60
U U.S. Environmental Protection Agency (EPA), Units of measurement, Universal gas constant - values,
241 1 70
V Venturi tube,
83
Viscosity common units,
303
conversion table,
307
dynamic, absolute, simple,
302
influence on flowmeter performance, principles of & definitions, Viscosity measurement,
73 301 299
W Water - weight at various temperatures,
177
Weir Cipolletti,
90
91
rectangular,
87
88
triangular,
86
triangular (V-notch) sharp crest, Wheatstone Bridge,
85 154
Wien’s radiation & displacement laws,
157
89
