Gaseous Viscosity Measured by the Interferometer U-Tube

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PHYSICS: CARL BAR US

VoI. 9, 1923

GASEOUS VISCOSITY MEASURED BY THE INTERFEROMETER U-TUBE* By CARL BARus DZPARTMENT OF PHYSICS, BROWN UNIVERSITY

Communicated, January 17, 1923

Apparatus. Observations.-If in the figure, U, U' are the two shanks of the U-tube, closed by glass plates, it is merely necessary (in case of air) to attach the capillary tube of length L and radius R, by aid of a short piece, r, of pure rubber hose, while U' is open to the atmosphere. Pushing r inward (or outward) sufficiently, U is put under a slight pressure excess, P-p, if p = Bpg is the atmospheric pressure and B the height of the barometer. As this pressure excess is recorded by the fringe displace-

120

i

k

Ir

-100

80 A

60

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Nl.

40 20

I

9, Z

0

,

I

I

1 0 12 14- 1. *8 8- E0in the of time. the latter vanishes With the ment s, lapse exponentially the arit to record fall of across is thus s, given tube, merely necessary a of an ocular with scale micrometer, stopwatch. bitrary equidistant parts The graphs show three independent series of this kind, loges and t being compared. The relation is obviously linear, remembering that U, as an air thermometer, is sensitive to much less than .001° C. In the winter season and a heated room, no closer agreement would be warrantable. The rates for the three cases were 103d(log s)/dt = -18.8, -17.9, - 18.5 the mean rate therefore, -.0184.

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PHYSICS: CARL BAR US

72

PsRoc. N. A. S.

Equation.-Because the pressures P and p, at the two ends of the capillary tube differ by less than .01 cm. of mercury, 0. E. Meyer'st transpiration equation =r p2 - p2 R 4( 16 piVI/t L

(where pi I/ = Rm1r refers to the pressure, volume, mass, and absolute temperature of the gas transpiring) will be greatly simplified. For since Milt comes out of the volume V = aH (area, normal depth) and mass m of gas at U, R(milt)r = PdV/dt + VdP/dt If h is the head due to the compression, dV = a dh/2; and P + p = 2Bpg,

P-p= hpg; so that

p1v1/t =-(aP/2 + Vpg)dh/dt If the coefficient of slip modified to

q = 11/e is neglected, equation (1) is now easily

2P hpg ?r R4 16 L (aP/2 + Vpg)dh/dt and this further (since d(log h)/dt = d(log s)/dt) to

=

r R4 Bpg 8 LV (B/2H + 1) d(loge s)/dt

In the apparatus

103R = 27.7 cm., L = 11.7 cm., V = 70 cm.3, H = 1 cm.; B = 75.4 cm. 1 + B/2H = 38.7 so that - 1io~ X 2-65 754 X 13-6 X 981 - .000180. 8 11 7 X 70 38 7 X .0184 A closer approach than this in the winter time would be impracticable for the reasons stated, for which reason R was only measured microscopically. Any other gas at U would be open to similar treatment; or the method might be reversed and a pressure deficiency installed relatively to an outer

reservoir. 1 Advance note from a Report to the Carnegie Institution of Washington, D. C. Meyer, 0. E., Pogg. Ann., Leipzig, 127, 269, 1866.

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