Water Watching

Water Watching

Edmund W. Jupp intellect

Water Watching

Edmund W. Jupp

intellectTM Bristol, UK Portland OR, USA

First Published in Paperback in UK in 2002 by Intellect Books, PO Box 862, Bristol BS99 1DE, UK First Published in USA in 2000 by Intellect Books, ISBS, 5804 N.E. Hassalo St, Portland, Oregon 97213-3644, USA Copyright © 2000 Intellect Ltd All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without written permission.

Consulting Editor: Masoud Yazdani Production and Cover Design: Peter Singh Production Assistant Vishal Panjwani

A catalogue record for this book is available from the British Library ISBN 1-84150-805-5

Printed and bound in Great Britain by Cromwell Press, Wiltshire

Contents Preface

iv

Some Basics

1

Still Water

8

Slow Motion

20

Fast Flow

29

Wave Motion

40

Glossary

47

iii

Preface A water-watcher is someone, of any age or nationality, who likes looking at water, in any of its forms.

A stretch of river Exe Water watchers enjoy this pleasurable pastime, whatever their educational background; but more knowledge of what to look for will, it is hoped, lead to even more satisfaction. The intention is to encourage interest in looking at water or watery fluids, which are all around us. You don't need any equipment, licences or permits, nor any special qualifications, other than some curiosity, a sense of wonder. The treatment won't be too technical, but hopes to show you how some natural laws control the behaviour and appearance of water. Some knowledge of this can make water so much more fascinating, wherever you see it. This isn't a book for the specialist. It will skim lightly over the more technical treatment and try to be not too pernicketty about the finer points. The discipline of fluids is a vast subject in all its branches, and a deep understanding of it does call for years of study. Here the treatment will breeze through the more difficult aspects, avoiding a rigorous attitude, without being too economical with the truth. Where a little algebra is used you don't have to absorb it; it will be minimal and not essential. The intention is to provide everyone with more enjoyment from just looking at water, and knowing a little of why it looks as it does. There is plenty of it about, (sometimes too much!) and it is easy to find some to look at whenever you have a little time to spare. You can find this magic fluid everywhere, (very nearly). Even in the arid desert areas of the world there is usually some water, perhaps in the air, or underground, deep within the earth. Sometimes that water below the surface can be found only by dowsers, and is of little direct interest to the water-watcher, who needs to see the liquid to find enjoyment, sometimes perhaps to feel and hear it. iv

Water Watching Although there are many who have a kindly and tolerant disdain for the claims of dowsers, some people say there is solid evidence of this mysterious bit of rural magic. It is said that more people have the gift of dowsing than you might think, and it is by no means confined to looking for water in the countryside. If you would like to try your hand at this ancient procedure, then the glossary may help you to see what happens when you follow the ancient methods. There is a great variety of surface water to be seen, waterfalls, streams, rivers, puddles, and lakes; there is rain, snow, hail, frost and dew, as well.

Snow scene You find it in the house, in the kitchen and wasbasin, and in the bath. You come across it on the roads, beside the the shore, tumbling down hills, squirting out of taps and hoses. It doesn't have to pure, either, to be of interest. On the whole polluted water, thin soup, tea, beer and thin gravy behave in pretty much the same way as pure water. Raindrops running down the window-pane may look different from the wet patch on a soaked towel; and the smooth ice on a frozen pond may reflect colours not seen in a flurry of snow; but basically it is all the same stuff. As you move around, or even sit indoors, there should be many occasions for doing some water-watching. I do hope this book will help you to get more pleasure from those opportunities. It might do more than that, of course. It could stimulate a desire for a deeper understanding of the magic behind it all. There is an enormous literature, extending back for many years, with enough information to satisfy the most enthusiastic reader. You will come across many famous names in such reading, and the surprisingly down-to-earth methods of these people are fascinating. Many of them did some wonderful work long before computers were available, patiently watching, measuring and gathering facts to build up the equations we still use today. There are many "coefficients" in the equations. These indicate how hard it has been to produce simple practical guidance for engineers and physicists dealing with problems v

Water Watching in hydrostatics and hydrodynamics. These coefficients need not concern the beginner; They were produced by practical engineers for the use of people dealing with everyday problems in their work with water. By their use many otherwise complicated equations were simplified and made easy to use and apply to common problems. So in special cases, and paying due attention to their limitations, short formulae were part of the mathematical "tool-kit" of practising engineers everywhere. Using them, an experienced engineer can give you a rough idea of the amount of water running along a channel, say, or the pressure to produce a particular flow in a pipe, from a few scribbles on the back of the traditional envelope, or even in his head. Before the invention of the pocket calculator, the slide rule was the chief tool of an engineer, and simple formulae were needed. At one time you could get special sliderules that were designed to solve hydraulics problems. With these you could work out quickly the size of pipe you would need in a layout, or the depth of water at some point in a stream, and so on. Now that computers and pocket calculators are so numerous and ready to hand life is simpler in many ways for those who deal with water.

Slide rules Well, as a beginner at water-watching you don't have to concern yourself with all the technicalities. For the time being, in what follows, you can skip any bits that seem too technical or mathematical, and enjoy your water-watching. Of course, you may start to see how fascinating it all is, and If you get hooked you may want to go further into the technical side of the subject. In that case you will need some mathematics and physics to understand all that has been written about water. There are plenty of books on the subject, and new ones seem to come out all the time. The total amount of water on our planet doesn't change. It just goes round and round, in its passage sustaining life in all its forms. Water-watchers can look at it during the different stages of its cyclic tour. So, besides enabling every living thing to exist, water provides free intriguing entertainment, to charm us with its magic. We can all take advantage of it.

vi

Some Basics Water is a restless substance, forever on the move. Even the water in a tumbler, at first glance quite still, is moving. Apart from the currents due to some parts being warmer than others, causing the warmer parts to move up while the cooler layers go down, there is what is known as the Brownian motion, tiny movements of particles as the molecules bump around. Water can exist as a solid, a liquid or a vapour,

Cloudscape above sea and all three forms appear often, sometimes changing from one to another as we watch. Most of it is constantly being cycled on the planet, bringing life to the creatures and

Water cycle plants that inhabit the earth. From the great oceans and the smallest puddles it passes into the air by evaporation, sails across the skies as cloud, and falls again to earth as rain, hail, snow or sleet. It then flows towards lower parts of the earth's surface till it 1

Water Watching reaches the sea, ready to start the process again. Much of it passes through plants and animals on its way, so that sap can flow up the trees, and blood can be pumped through the veins of animals. Some of it is locked into blocks of snow and ice;

Iceberg but even then it isn't really absolutely still. Little temperature variations can set off movements of great change. In the far polar regions there are enormous quantities of "solid" water, ice, and its changes are very important to all of us. A few degrees rise in temperature can result in severe flooding, as the sea level rises; a fall in temperature, and more water gets locked into the ice, so that there isn't so much running around. The polar ice can be thought of as a kind of water storage system. The volume of any mass of water depends upon its state, i.e., whether it is a solid, liquid or vapour, as well as the temperature and pressure. You can see this by melting an ice cube, to measure the change of volume, and then boiling the water to see what an enormous amount of space is occupied by the steam. For the most part it is colourless, but readily takes on hues in any of its forms. It can be flavoured with little difficulty, and perfumed too; but we shall not be concerned with qualities like taste, or odour. The properties that interest the water-watcher are those that can be seen, or whose effects are apparent, such as density, viscosity, and surface tension. We shall look at these in some detail. •

Mass and weight

To keep things simple we shall not use any of the many available units of measurement, like metres, feet, gallons, Pascals, and so on. Thus, we shall say that the density of this fascinating fluid is 1, i.e., one volume of water has unit mass . The weight of this unit volume, i.e. the force acting on it to draw it towards the earth, is g times the mass, where g is the acceleration due to gravity. If you are unfamiliar with these terms "mass" and "weight", and if the introduction of acceleration here seems odd, as it might, you can look in the glossary, where it is explained more fully. 2

Water Watching •

Viscosity

The viscosity of water is its treacle-like nature, its resistance to change of shape, or its reluctance to pour. Of course, it is not as viscous as treacle, and in many cases its viscosity can be ignored; but when it is moving its viscosity can be important to an understanding of its behaviour. The viscosity is usually written as the Greek letter , pronounced "mew". (There are actually two kinds of viscosity, so you may not always meet , but v, pronounced "new". The value of v depends on the density. For now we shall use only.) •

Surface tension

At the free surface of water there seems to be something like a skin, or layer of film, seen by its ability to support small creatures or light powder. This is called "surface tension",and is due to the molecules pulling one another together at the surface. This force is not very large, but is important in the formation of drops, bubbles, and froth, or lather.

Formation of drop •

Head

If we were to fill a vertical tube with water, the pressure at the bottom would depend upon the height of the upper end above the lower. We call this the "head", h, which is a convenient way of referring to pressure. Whenever water is under pressure we can measure it by its "head", or the height of a vertical tube full of water which would give us the same pressure. •

Water curves

We now turn our attention away from water itself to think about something that might not at first seem to have much to do with the subject. It will come into our discussion 3

Water Watching later, though, so we do need some understanding of this. I refer to some of the beautiful curves we come across in nature. If we take a little piece of wood, round at the bottom and tapering to a point at the top, we have a cone; and the cone is a very interesting shape, almost magical from some points of view. For a start, think of cutting it across horizontally, and removing the top, which is itself a cone. The cut section is a circle, that familiar shape which we seem to meet everywhere. It is the shape of a pipe section, or the earth seen from space, or most coins. It is indeed a popular shape.

A conic Cutting the cone across at a slight angle shows us another curve, the ellipse, a sort of squashed circle. It is like a circle having two different diameters, called the major and minor diameters. Strangely, it is the shape of the path followed by some heavenly bodies. You may like to think of a circle as a special case of the ellipse, where the major and minor diameters are equal. Both the circle and the ellipse are lovely curves, but there is more to come. Cutting the cone across at a steeper angle reveals another ellipse; and if we tilt the cut so as to be parallel with the side we have an open-ended curve called a "parabola", perhaps the commonest curve in nature. The path taken by a jet of water coming out of a tap, its "trajectory", depends upon the pressure in the pipe, which in turn is governed by the height of the reservoir above the tap, or by the head produced by a pump. It traces out a parabola as it falls. Another lovely curve that arises from cutting the cone is the hyperbola, and we shall have more to say about that one later. •

Pressure

One of the things that sometimes puzzle the beginner at water-watching is the enormous side pressure that water can exert, for example that on the wet face of a dam. Anywhere in a fluid the pressure is the same in all directions. So at the free surface, i.e. at the top, the pressure is that of the air. As we go deeper there is more water pressing down from above, so at each level the upward pressure has to be enough to balance this downward amount. As it presses with the same value in all directions, the sideways pressure must be greater, the deeper we go. 4

Water Watching

A ship's propeller may tend to turn the ships to one side. The force F2 on the lower blade of a 2-bladed propeller is greater when the force F1 on the upper blade, as it is lower in the water. When a diver goes down below the surface the pressure all round the body increases as the depth of dive increases. This is why the pressure of the air breathed has to be so great, and this in turn forces gas into the blood stream. On rising quickly there may not be enough time for the gas to get clear, and bubbles of gas in the blood can produce the painful and potentially fatal condition known as "the bends". For water-watchers a point of interest is the spurting of water from a point below the surface level, such as that from a dam, or a tap.

Jet from pipe The deeper the outlet below the surface the greater the pressure, and if the fluid comes out other than straight down, it traces out a pleasing parabolic curve as it falls freely, as mentioned above. Where the outlet is a distance h below the free surface then h will determine how far out the jet goes before striking the ground or lower water-level.

5

Water Watching

Jets of different strengths The pressure exerted on a retaining wall by water alone or in the soil behind the wall is normally reduced by drainage outlets that you can see in the face of the wall.

Drainage holes in stone wall If such provision is not made then the wall may collapse as the water pressure builds up behind it. High walls are most vulnerable, as the head of water depends upon the height of the wall, zero at the top, and increasing towards the bottom, where the pressure is greatest. Very high walls are often built with a "batter", that is a backwards slope, to help to resist the overturning effect of soil and water pressure.

Retaining wall with batter 6

Water Watching •

Mechanics of water

Broadly speaking, those who study the mechanics of water divide the subject into two sections, hydrostatics for water that isn't moving, and hydrodynamics for moving water. As water-watchers see both kinds we shall look at these aspects in some detail. Both sections are vast, and we cannot hope to cover everything. Whenever you come across some particularly interesting facet, and wish to go into it deeply there is plenty of opportunity. Diligent and enthusiastic probing by engineers and physicists has built up an enormous literature over the years. It has always been, and still is, a fruitful field for researchers. In this century the computer has helped our enquiries into the behaviour of liquids, and this is adding a great deal to the interest of water-watching. Researchers now have to hand facilities that were never dreamed of only a few years ago. When we look at still water, we shall examine buoyancy, the upthrust on immersed bodies like boats, people, and underwater structures. In this connection we shall use the letter w to represent the weight of unit volume of water. (In the literature the reader will often see this given as g, where the Greek letter (pronounced "roe") stands for the mass of unit volume of the water, and g is the gravitational acceleration. This need not be of much concern to the water-watcher, but it is mentioned here so that those who dig into the subject more deeply will not feel lost.) For moving water we shall use the letter v for the velocity. In studying water that is in motion we shall often encounter squares and square roots, because when water moves with a velocity v we find ourselves involved in simple equations containing v. However, we shall use only the smallest number of equations and formulae in our treatment. •

Conclusion

In the chapters that follow, the broad divisions of subject matter are not intended to be rigid. The chapter headings seemed to be convenient ones, to lead from thoughts about calm, stationary water to the more rumbustious behaviour of water on the move. However, the boundary between "fast" and "slow" is a little smudged; waves occur in all kinds of water, and we shall introduce some basic material here and there. We hope that by now you should have enough basic knowledge to follow the remaining chapters. The order in which you read them is not important, and you may like to dip in here and there, using the glossary as and when you feel the need.

7

Still Water Much of the water seen in lakes, and in estuaries at the turn of the tide when it is still, can have a mirror-like surface if there is no wind.

Canal near Frimley Left to itself, water fills the available space, and the currents that are always present may not be apparent. Under these conditions the reflections in the surface determine the colours seen, and when the air is very still the water-side scenery is faithfully reflected in the surface. It is delicately poised, however, and a slight disturbance can produce ripples that destroy the images.

Ripples on the Exe Except in the purest of waters, particles of other materials are found in suspension. While the water is moving, this material is carried along, the amount thus transported depending upon the velocity of the flow and the density of the material. As the rate of flow decreases and falls below the "transport velocity" of the particles they drop down and rest on the bottom. The denser particles are deposited first, and then, as the water slows up more and more so the lighter particles fall. So below the surface a layer of silt is laid down, of finest particles where flow is slowest. Generally speaking, then, the bottom is sandy where velocity is low, and pebbly in regions of high speed. This is why, usually, narrow stretches of a stream have stony bottoms and broad reaches tend to run over muddy or sandy beds. 8

Water Watching The suspended particles of course affect the clarity. As soon as water moves it can pick up some particles, and these can obscure the bottom. The surface may still present a mirror-like appearance, though, and may even seem to be still, with the shoreline and sky perfectly reflected. Sunsets can offer double the beauty when seen beyond still water. The reflection offers the bonus of an inverted sky. Sometimes the surface of a sheet of water may not be uniform, some areas being smoother than others, and hence reflecting a different colour. This is specially true in lakes, estuaries and wide rivers.

Patchy surface The cause of this is the variation of surface movement. Part of the surface water may be flowing at a different rate from the rest, so that the relative speed of air and water is different. •

Surface movements

Air flowing over water with a relative velocity greater than a certain critical value induces ripples, wavelets whose height depends upon this relative speed. If there is a channel where the water moves at the same speed as the wind, no ripples are produced, and the surface remains flat. In other areas the glassy appearance is broken. So there are occasions when, by looking at the surface, you can tell where the channel lies, and the position of surface currents. Sailors of small boats are well aware of this, as they seek currents favourable to the direction they wish to take. Floating material, flotsam, may consist of weed, waste, odd scraps of wood, scum and so on, and this will often be found arranged in long lines. These lines mark the boundaries between adjacent streams in the surface layers. The bodies of water may be thought of as rubbing against one another, so that the flotsam is trapped between the two moving patches. By studying these lines the water-watcher can sometimes trace surface movements not otherwise apparent.

9

Water Watching Besides these surface movements there are horizontal layers moving in different directions below the surface. This can be dangerous for those unfamiliar with undercurrents when, with surface flow going out, a rising tide runs up under the surface. Relative movements like these can produce eddies or whirlpools too, and these will be considered when looking at moving water. •

Buoyancy

When we look at still water we find it convenient to examine buoyancy, the upthrust on immersed bodies like boats, people, and underwater structures. In this connection we shall use the letter w to represent the weight of unit volume of water. (In the literature the reader will often see this given as g. This is referred to elsewhere.) Buoyancy is the result of water being pushed up out of the way by immersed objects. It then tries to get back to its original position, so pushing against all submerged surfaces. In particular this is the supporting force under boats, buoys and everything that floats.

Boat When something is immersed in water it displaces an amount of liquid equal to its own volume V. If unit volume of water weighs, say, w, then the weight of water displaced by a body of volume V is Vw. For example, a block of material measuring 3 x 4 x 5 displaces a volume of 60; and if we say that unit volume of water weighs 1, the weight displaced is 60 x 1 = 60. This weight of water is pushed up above its normal level as the block enters, and cannot return while the block is there. So in trying to return it pushes up under the block. This is the force of buoyancy. •

Stability

If you take a small rectangular block of wood and put it in a bucket of water you will see that it lies "flat"; that is, it floats with its largest face upwards. This is a stable attitude. If you turn it so that the smallest face is upwards it is unstable, and will resume its former position. Stability is important for buoys and boats and is controlled by the shape and how the weight is distributed. For any floating body to be stable it has to be of the right shape below the water. When the body is tilted the immersed shape may change, and the line of upthrust may move horizontally. If this thrust moves to the wrong side of the downthrust due to the weight of the body instability results. 10

Water Watching Floating bodies of all kinds seek the most "comfortable" attitude, that is the one in which any tilting produces a restorative turning effect. The water-watcher will often see boats riding at moorings or at anchor; and when there is a wind or swell the vessels start to rock, at different frequencies for different boats. It is convenient to think of the three axes of rotation, one vertical, one fore-and-aft, and one athwartships, about which the vessel can rotate.

The corresponding movements are those of yaw, pitch and roll. The frequency of movement about each depends upon the shape of the immersed part, and the disposition of the weight. It can be of interest, then, to observe the movements of boats anchored or moored in restless water. Generally speaking the rate of roll is different from that of pitch, and the movements of small vessels quicker than those of large ones. •

Buoys

Buoys can be seen in rivers, estuaries, and lakes. Their shapes and colours are significant. The purpose of a buoy is to indicate some place on the bed of the water. For example, navigation buoys are large and prominent, and indicate the limits of channels, positions of wrecks, and other underwater obstructions. They help surface vessels keep to deep water and avoid the shallows. The principal navigation buoys are the red flat-topped ones and the black or green conical ones. They are placed so that a vessel coming up from seaward with the flood has the red flat-topped ones on its left or port side, and the conical ones on its right or starboard side. So when you see a pair of navigation buoys you can tell which way the flood tide runs.

11

Water Watching For the most part the horizontal cross-section of buoys is circular; but currents are sometimes so strong that the load on the mooring chains is severe, and trials have been made with buoys that at water-level present less drag or resistance, having a boatshaped section. Sometimes, where the water is sufficiently shallow, perches or withies are stuck in the bed to mark a channel. The withies are slender branches, but the perches are more substantial. They may have topmarks, triangular or pointed on the starboard side of the channel going with the flood, and T-shaped on the port side.

Starboard hand perch at Exmouth If you watch the movements of boats in shallow waters you will see them following the course shown by the buoys, perches and withies. If a boat goes outside the channel so marked you may assume that it is of shallow draught, that is the depth of boat below the water is comparatively modest. Boats may be positioned either by anchors, which are for temporary positioning, or by making fast to mooring buoys. These buoys can be recognised by the large mooring ring on the top or side. They are often barrel shaped, and black, floating on their sides. Alongside a pier or jetty a vessel may be moored to a bollard.

Mooring bollard 12

Water Watching Private moorings are usually indicated by small plastic buoys whose colour has no significance other than identification. They are attractive, bobbing about in a colourful display when the mooring is vacant. Fishermen use various kinds of buoys to mark the position of lobster pots, for example. Often they use "Dan buoys", which carry a little flag sticking up above the general level of the water. These are more easily seen from a distance. Small yachts often carry such buoys for man-overboard action. Tossed overboard they indicate the position where the person entered the water. Generally speaking, floating objects which don't change position relative to the sea bed are buoys.

Buoy Anything else is driftwood, or flotsam. There is plenty of flotsam about, some of it dangerous to high-speed vessels. Another peril for propellor-driven vessels is plastic material. It can wrap round the propellor shaft and stop further progress. Any waterwatcher who spots such stuff can do everyone a good turn by removing it. The gyroscopic properties of a spinning body can provide a kind of false buoyancy to something that might otherwise sink, like a flat pebble. Given sufficient spin about a vertical axis a flat stone will skim across the surface of still water, or even a mildly disturbed surface, as every schoolboy knows, till it loses its spin, when it sinks at once. This is not true buoyancy, but hydrodynamic lift produced by the motion of the pebble. •

Tidal movements

Tidal movements will be looked at later; but it might be helpful here to point out that if you have access to docks, in tidal waters, you will see how the height of the water varies, and judge the movements, by the weed growth on the sides of the dock.

13

Water Watching

Weed lines showing tidal range on wall Again, on the shores of tidal waters you may often see lines of weed left by the receding water. When tides are "cutting", that is, decreasing in range, there may be several such lines, marking the heights of successive tides.

Weed lines on slip When the tides start to "make", i.e. increase in range, these lines are usually washed away by successive movements of high water. Hence a look at the shoreline at low water may help you to learn whether the tides are making or cutting, and perhaps tell you how high the water can rise. •

Clouds

Although, strictly speaking, clouds do not represent still water, it will be convenient to mention them here. In the eternal cycle of the earth's water the clouds represent an important stage. They are a form of water, like a fog or mist, and constantly change shape and position. We most often see them from underneath, that is the shadow side. When we climb above them, on a mountain or in an aircraft and see the upper side they are no longer dark and gloomy, but gloriously brilliant, reflecting the sunlight or moonlight. Clouds represent a kind of heavenly storage system for water in tiny 14

Water Watching droplets. They are at the top of the cycle and their water falls to the ground, eventually to run down to the puddles ponds and oceans before being picked up again to continue the everlasting cyclic journey. Clouds form a particularly attractive form of water for the water-watcher. Apparently limitless in their variety, they have been classified, and are of much interest to meteorologists. The broad divisions are into classes according to their apparent density, ranging from the light tracery of the alto-stratus to the heavy darkness of the nimbus, and sometimes many kinds are present in the sky at the same time.

Cloudscape Watching their majestic progress across the sky is instructive. On a warm day, laying comfortably on one's back in long grass, or in a deckchair, the clouds present a heavenly spectacle; and this grand celestial show is not only restful, but free! If you take a film of the movements at slow speed, so that it can be speeded up when shown, the wild contortions of the masses can be awe-inspiring. The direction of movement of the clouds indicates the position of the pressure variations in the atmosphere. North of the equator the regions of low pressure are always on the left as one goes with the wind. These regions move round the world generally from west to east. Low pressure is usually associated with less pleasant weather. Knowing all this might help with your personal weather forecasting. Locally, you are likely to be more accurate in your predictions than the expert meteorologist, for you will be dealing with a smaller area, and accustomed to what happens locally. "When the wind is in the east, `tis good for neither man nor beast", "When yonder tower is clear and bright `twill rain afore the night". Old sayings in a particular locality often have a basis in observation over long periods. •

Snow and ice

Perhaps the least mobile forms of water are snow and ice at constant temperature. Snow, which seems so uniform on the surface, looks very different under the microscope, displaying a beauty of form which is striking. 15

Water Watching Ice, too, can show inclusions of considerable interest, especially when air has been trapped during its formation. It can shine with some wonderful colours, especially in large glaciers. Ice has a preservative function which is shown by the discovery of ancient men and animals deep-frozen many thousands of years ago. These have greatly increased our knowledge of those earlier times. So the dedicated water-watcher may find it of interest to journey to places where such antiquities have been discovered and preserved. In some places where ice can be readily obtained, and where for some time it remains frozen even in warmer air, like some places in Canada, ice sculpture is popular. Some people are expert at producing impressive figures from large blocks of ice, using simple chisels and mallets. Like sandcastles they don't have a long life, but while they last they are fascinating. •

Surface tension

At one time the earth was generally considered to be flat. To a certain extent, that was, and is, true. The curvature is so small that, over a restricted area, the deviation from flatness is not obvious. The surface of the water in a lake is curved, following the shape of the earth; but it is not apparent when we see it from the shoreline. Again, the water in a tumbler appears to be flat, except near the edges. (There it curves up to the glass, if partly full, or down to the rim if overfull, due to the surface tension.) Surface tension gives water the appearance of being covered by a thin elastic film or skin. In a fine tube, the pull of this film makes the water climb above the normal level. The finer the tube, the higher it climbs, since the ratio of the pull along the line of contact to the downward pull of the water is greater. Similarly, between two vertical surfaces, close together, the water level is higher than outside those surfaces. A simple demonstration is the one where two vertical pieces of glass are held together by a rubber band, with one pair of vertical edges touching and the other held apart by a matchstick. If this arrangement is now placed into water, the liquid level between the plates is seen to be much higher at the ends where the plates are touching. This is a particularly interesting demonstration because the water level between the plates forms a curve known as a rectangular hyperbola, which is a beautiful curve, related to the cone. The water surface follows this curve because of the nature of the equation for the hyperbola; between the glass plates the narrower the space, the greater is the height h of the water. Just as in the hyperbola we have the product of x and y constant, so if h is the height of water, and d the distance apart of the plates, the product hd is constant. The smaller the value of d the higher that of h. If you are interested you can easily draw a hyperbola, to compare the result with what you see with the pair of glass plates. There is more information in the glossary. Another effect of surface tension may be seen when a glass is gently overfilled. The level can be raised well above the level of the glass rim if care is taken when adding the 16

Water Watching water. It is important to realise that there isn't really a skin on the surface. It is only the effect of the intermolecular attractions.

Overfilled glass A simple device often used to find the level of water is a vertical piece of wire plunged into the surface with the bottom bent round through 180 and the end sharply pointed. This "hook gauge" is then finely adjusted till the point just breaks the surface. Any change of level is at once apparent. This simple instrument is often used upstream of a weir or other arrangement to find the water level at a particular point. You can easily make one, and you will see that the point seems to push up the "skin" arising from surface tension, enabling you to judge to a nicety the level of the water. •

Tide-line

If you look out over the mud or sand in an estuary or on the coast at low tide it may appear flat, apart from the channels left by the ebbing water. This is far from the case, however. It is only that the slope is so gentle. When the tide returns it covers the sand or mud gradually, as it climbs up the gradient of the shore. It can be an interesting exercise for a water-watcher to walk out at low water if the sand is firm, and insert vertical sticks at equal distances apart in a straight line stretching out towards the incoming water. Timing the intervals between the tide-line reaching each stick gives some indication of variations in the steepness of slope of the ground. However, the water-level doesn't rise by equal amounts in equal intervals of time, so assuming a steady rise does introduce some error. If a floating barrier is placed across water where wind-driven ripples approach a beach, it will be found that a calmer surface appears on the leeward side of the barrier. Where electrical power is generated by what are referred to as "nodding ducks" the energy of the waves is extracted by the devices, and shoreward the surface may be impressively stilled. So still water can be produced from rough water by suitable floating barriers. 17

Water Watching •

Dewponds

Air can hold water as a vapour, and the maximum amount depends upon the temperature. This moisture content, the humidity, is of interest to the water-watcher since a lowering of temperature causes an increase in the humidity. When the air is saturated with vapour any further fall in temperature brings it to the "dew point", when the water is deposited as a liquid. Dew occurs principally, though not invariably, at night, when radiation from the earth chills the air in contact with the ground and the water is deposited as droplets. At one time, on the South Downs in Sussex for example, large flocks of sheep grazed the short grass on the chalk hills. Providing water for the sheep led to the development of special ponds. There were no rivers up there, and these ponds drew their water from rain and from the condensation of mist and dew. Indeed, they were called "dewponds". A dew-pond was formed by a shallow depression in the ground lined with an impermeable clay and insulated from the ground with straw. At night they presented a comparatively cold aspect to the air, so that any moisture in the air would condense and add to the contents of the pond. They were shallow, and with gently sloping edges, to provide easy access for the sheep. Dewponds required little maintenance beyond occasional cleaning, and made a valuable contribution to the prosperity of the region. Although no longer common, there has been some attempt to restore dew ponds as a link with the past, so you may have an opportunity of seeing one. They are easily recognised, for they are circular, shallow, and gently shelving at the rim. They are usually situated near the crests of hills. Some of them date back a very long time. In winter thermal radiation from the earth may be so intense as to take the temperature below freezing point, when frost or ice may result. The ground temperature may then be lower than that of the air generally. This surface cooling can give rise to vertical movement in otherwise still water as the dense cold layers sink. When ice forms it floats, because ice is less dense than water at this temperature. Goldfish know where to go when it gets cold. •

Flotsam

Before leaving the subject of still water there is one further aspect of interest. This concerns the way in which floating bodies tend to congregate, and to seek the boundary. Even in a cup of tea, the bubbles tend to move to the sides. In lakes and ponds, in conditions of flat calm, floating debris collects in masses which tend to make their way to the shore. If you drop into a cup of water some floating particles you will see them coalesce on the surface. When water moves, and is unsteady, dispersion takes place, and flotsam no longer congregates in the same way. 18

Water Watching Out at sea, sometimes, water may have still-water characteristics even when there is a long swell, in wind-free conditions, and masses of flotsam may then build up; but heavy weather soon breaks up such masses. It concluding this chapter it may be helpful to point out that in the form of vapour, or steam, water is invisible. It can be seen only when it condenses. Perhaps the best proof of this is to look carefully at the steam coming out from the spout of a kettle. You will notice that near the spout there is nothing to be seen. It is only after the vapour has spurted out some distance from the end of the spout, where it condenses into water droplets, that it can be seen.

19

Slow Motion When water moves slowly surface tension and viscosity can play an important part in the motion. At higher rates of flow the importance of gravity increases, and may overcome the effects of other forces. Slow flow, or viscous movement, is basically different in appearance from more rapid flow. Movement takes place when there is a difference of head between two points in a body of water that is not restricted. When you hold a bowl of water perfectly still the surface is flat and horizontal. Tilting the bowl would raise one part of the surface above another if the water were not free to move. Being free, the liquid moves to restore the position of the surface relative to the horizon. Slowness is a relative term, of course, and the flow is obviously slow when you look at seepage or small drips; but in this chapter we shall regard motion as slow whenever the liquid appears to move uniformly without disturbance, when the major influence is surface tension and/or viscosity. Water then seems to move sluggishly, without any eddies or waves, something like syrup or thick custard. You can see this kind of action in small or large bodies of water. Even when the overall speed is considerable the surface can sometimes appear flat and calm as it sweeps along, and behaves as if it were a solid mass. You can sometimes see movement like this in surface flow approaching a waterfall, when it may have a glassy appearance, even though it may then be moving rapidly.

Still water above a waterfall •

Surface tension

When the discharge of water from a tap is cut down enough it no longer forms a jet, but issues in small drops; and when the flow rate is very small indeed these form slowly. Careful examination will show that the shape of the lower part is a beautiful curve.

20

Water Watching The drop grows in size like a slowly inflated balloon, until it becomes too heavy, and falls, yielding place to the next drop. It seems to behave as if it were inside a skin which is elastic and gives with the increasing volume of the drop until it can no longer cope with the strain. This behaviour is controlled by surface tension, and different fluids have different values of surface tension. It is measured by the force on unit length of a line drawn in the fluid. The value can be changed by adding small quantities of certain other substances. Surface tension produces the meniscus at the water surface in a small-bore tube. Because of this small creatures are able to walk on water, too. When liquids move very slowly the surface tension is important, but has little effect in rough conditions. Where water touches a porous material and when there is a difference of head, or pressure, between the two sides of the material it moves slowly through the tiny pores. This movement is called "seepage", and is of importance in filtration, for the size of the interstices determines the size of particles retained by the filter. The passages within the material are tortuous, according to the shape of the particles. Under a microscope the tiny pieces of sand or soil appear as rough-surfaced solids. The liquid tends to fill the small irregularly-shaped pockets, sometimes trapping air. Differences of head then drive the fluid through the tiny passages. Because of the phenomenon called "capillarity" seepage can take place upwards and sideways, as well as downwards. For this to occur the spaces between the particles must be small. As each tiny passage fills with water, the tighter the packing of the particles the higher will the water travel. Capillary movement arises from surface tension, so the seepage depends upon the surface tension of the liquid and the size of the passages within the porous material. •

Tide

Away from the poles, large scale tidal movements sweep round the earth at very high speeds, fastest at the equator; but we shall treat this as a slow movement as a matter of convenience here, for it is not the water itself that moves horizontally at this great speed, but the tidal "hump". The movements cause tidal streams which can vary in rate from slow to very rapid. If it were everywhere at rest, water would surround the earth like a kind of liquid orange peel very nearly, with the mountains and high ground poking up through it here and there; and it would be of even depth if it were not affected by the pull of other heavenly bodies. Well, it is not at rest, and it is affected by other bodies. So the water doesn't lie evenly around the earth. At its simplest you can think of the gravitational pull of the moon drawing up a heap of water; and, because the earth is also under its influence the earth is drawn away from the water on the other side, opposite the moon. So you can envisage the water forming two smooth lumps, one on each side, travelling round as the moon moves relative to 21

Water Watching the earth. The sun has an effect, too, for although it is farther away it is much more massive than the moon. However, the sun is only sometimes in line with the moon and the earth, so its effect is to modify the simple effect produced by the moon alone. When the sun is in line with the moon the pull of both together produces very high tides, the "spring tides"; when they are at right-angles, the total effective pull is reduced, producing what are known as "neap tides". So the tidal rise at any place varies continually, each successive high water being greater when the tides are "making" and less when they are "cutting". The predictions of times and heights of high water are important for mariners, and those who are concerned with risks of flooding, the operation of machinery dependent upon tides, and many others besides. From careful study of the movements of the sun and moon the heights and times can be forecast with accuracy. In every maritime country this work is undertaken every year for the year ahead. So tables showing tidal predictions are published annually. They are sold at boat chandlers, and angling shops. The water-watcher who is near tidal waters will find these tables of extra interest. If they are not available the times of spring and neap tides can be estimated fairly accurately by noting the phases of the moon. After some experience, it becomes almost a habit to note the look of the moon, new, full, or growing or waning. From this you can tell if the tides are making or cutting, and how many days it will be before there is a spring or neap tide. The times of high water at any particular place, especially in an estuary, can be only approximate, as they are affected by recent heavy rainfall, and by strong winds. The heights, too, depend upon recent rainfall, and upon the barometric pressure. The implied precision of times and heights in tide tables takes no account of local weather conditions. So these tables must be used with some caution, and with due attention to recent and prevailing weather conditions. •

Tidal movements

The tidal movements that travel round the earth give rise to changes in water-level everywhere. At any particular place the level rises and falls with a somewhat complicated harmonic motion. Basically, the fundamental movement is sinusoidal, that is the height varies as a sine curve;

22

Water Watching

A sin curve but this simple pattern is distorted by other components. So if at some chosen spot you plot the height of the water, every hour say, during a few days, the resulting curve is likely to look smooth but rather irregular. A very rough guide to the height is the "twelfths rule". This states that when the tidal level is rising it does so in the ration 1, 2, 3, 3, 2, 1. These represent twelfths of the range. Again, when ebbing, the level falls in that same ration of 1, 2, 3, 3, 2, 1.

If then we divide the rise by twelve, it will change by only 1 twelfth of the total rise in the first hour, then two in the next hour, three in the next, and so on. You see from this that, starting and finishing slowly, it moves most rapidly in the middle part of the rise or fall. Although not precise this rough rule approximates closely enough to the sine curve to suit the cases where exact levels are not required.

23

Water Watching Where there are large differences in water levels, locks are sometimes built. These break up the channel & insulate stretches of water from tidal effect.

Locks As the tidal hump passes the mouth of an estuary the rising level causes a tidal stream to flow into the river mouth, and this water then passes up the river as the flood stream. After the wave has passed the mouth, this current slackens, stops, and reverses as the ebb. All of this is a wonderful regular occurrence, and you may enjoy watching it happen when you have time to spare. Although, for convenience, we have considered tides as slow motion, the tidal ebb and flow are not always slow events. As the water moves along confined channels it speeds up, and in some places the rush is so great that a wall of water rushes along to provide spectacular sights. The Severn Bore is a well-known example. The shape of an estuary decides to some extent the behaviour of tidal variations in level. In broad deltas the water appears to creep across the ground with slow changes of height, because of the great width. In narrow fissures the water can roar in and out. The rate of flow of the tidal water depends upon the steepness of the shore. In some places, the shore shelves so gradually that a small increase in depth results in a large advance of the tide line. This can be a source of considerable danger to bathers and others who may be unaware of the speed with which the water-line can advance. Coastal inlets vary greatly in size and shape. If the inlet is idealised it can be considered as a closed container. You can easily verify that the "slosh rate", or the time for a wave to travel along from one end and be reflected from the other end, in a bath or bowl 24

Water Watching depends upon the depth, as well as the length of the container. Coastal inlets are usually very complicated in shape, but the general principle applies. So when a tidal rise takes place at the opening to a short inlet the water travels to the other end of the inlet comparatively quickly and is then reflected, if the inlet ends abruptly. If the inlet ends in a shelving shore or tributaries, the wave may not be reflected but instead will be dissipated. For a long inlet the rise in level created by the passing tidal change may take a long time to reach the upper or inner end of the inlet. By the time the ebb has started at the mouth the reflected wave may not have reached there. So the height changes can be a complex matter. In tidal water the changes in direction of the stream depend, too, upon the position of the main channel, and the contours of the shoreline. In general you can tell why the direction of flow is in one direction rather than another by carefully studying these points. When there are boats afloat in tidal waters you might feel that it would be easy to judge the direction of flow on the surface by looking at the way the bows are pointing. This can be misleading, though. Winds can affect the way boats lie to their moorings. When wind is the predominant factor the boats are said to be "windrode", their bows pointing into the wind. When there is little wind, they are "tiderode", and they point into the stream.

Wind-rode and tide-rode boats in estuary However, this is not always a safe guide, since the underwater shape of a boat will affect the amount of influence of the water; and the shape of the vessel above the waterline will settle how much the wind will control the boat's attitude when at rest. So when you are looking at boats moored or at anchor in tidal waters you may see that they do not all point in the same direction. Boats of shallow draught are pretty sure to be windrode, whereas those drawing more water feel the tidal pull. You may be able to judge the draught of a boat simply by noticing how she lies. However, the currents and counter-currents must be noted, too. The direction of the tidal stream in the vicinity of a buoy is often obvious from the appearance of the water surface round the buoy. There is a tendency for the water to 25

Water Watching pile up on the upstream side, and to form eddies downstream, just as though the buoy were being driven through stationary water. At the top of the tide, or at low water, the buoy is steady, and the water lies round it at rest. When you see a buoy sitting quietly then, in tidal water, you know that the tide is on the turn, and ready to start a run for about half a dozen hours. As the tidal current starts it will at first flow smoothly and quietly past the buoy, and the shoreline. The surface is glassy, in the absence of wind, and the water moves like treacle. Not till the speed reaches a certain value does the surface tend to break up. Ripples and eddies appear, and the features of fast flow are seen. •

Syphon

A siphon can be thought of as an arrangement for producing flow "uphill". In its simplest form it consists of a pipe dipping into fluid in a reservoir or tank, and leading to some point above the surface before turning downwards and discharging below that level. It is probably best known for its effectiveness in removing petrol from a tank, or draining a garden pond. A siphon will not work unless the pipe is completely filled with the fluid. The elevation of the upper part of the pipe is limited by the barometric pressure.

When the barometer is high the atmospheric pressure is high, and will support a longer column of water. The discharge from some reservoirs is sometimes effected by a siphon. The usual lavatory cistern uses a small one, and you may sometimes come across them in use for large reservoirs. The siphon allows the water to rise to a certain level which corresponds with the lip inside the siphon. When the water begins to run over this lip it starts the siphoning action. Full discharge then occurs till the level in the reservoir falls 26

Water Watching below that of the siphon entry. This allows air to enter and break the siphon. This arrangement is an example of slow movement of water leading to rapid discharge. •

Dimensionless numbers

In the literature you may come across references to the "Reynolds number." This is one of the "dimensionless numbers" so important to those who deal with water movement. It is a number which depends upon the rate of flow, the viscosity, and some length measurement. The interest here is in the fact that whether or not flow is "slow" or "fast" in the sense we have used is set by the value of the Reynolds number. Viscous flow occurs at low values, and turbulent flow at high numbers. We shall not pursue this academic aspect here, but for the reader who would like to know more about Reynolds and his work there are many books and papers dealing with the subject. You can find references to the Reynolds number in books on physics or engineering. The rate of flow depends upon the head producing the flow. Those who deal with such matters use a simple equation to express this relationship. Calling the velocity v and the head h, they write v=kh where k is some constant. This means that, in a pipe, if we apply twice the head we double the rate of flow, and halving the head reduces the speed by 50%; but this applies only to slow flows. As the flow speeds up a different law applies. •

Water cycle

As water moves round its cycle from ocean to cloud, rain and back to ocean it invigorates plant and animal life. Part of its journey is rapid, but much of it is slow. As it percolates through the soil and travels up the stems of plants and the trunks of trees it carries with it nutrients to stimulate the function of foliage, and the production of blossom and fruit. In a large tree the distance from root to leaf can be considerable. At the leaf the water passes into the air by transpiration, to continue its cycle. When the sap rises it has to flow through tubes of capillary size over large vertical distances. Though much of this is not visible to the water-watcher, the results are clear. The flow is technically slow, but it is easily seen that a drooping flower revives very quickly after it is well watered. Foliage generally responds quickly to rain showers. Within the bodies of animals flow can be faster, as it does not depend only upon capillarity. Animals have pumping equipment, (hearts), not present in plant life, to supply the necessary head. Reduction of bore in the vessels carrying blood demands a greater head from the pump, and can be the cause of distress or complete failure. Animal life depends upon the heart, as this pumps the necessary fluids to the brain, the 27

Water Watching organ controlling the bodily functions. The blood of an animal demands water to remain liquid, and without water animal life, like plant life, is not possible. Sometimes we can trace the course of underground water by the presence of green plants visible among other growth thirsting for water. In many parts of the world, where conditions fluctuate between drought and flood, plant life withers and flourishes accordingly, and this shows up strikingly where conditions are severe. •

Ice

The slowest water movements occur where it is solid, where blocks and sheets of ice are subject to great forces. Glaciers sometimes move with unhurried pace down to lower levels under the influence of gravity, sometimes accompanied by changes of shape. This is a special kind of fluid flow, like the creep in metals and other substances. The movement is often undetectable, except over a long period of time. To observe the movements it is often necessary to visit such places at intervals of several months, or even years. •

Thixotropic fluids

Before leaving the subject of slow flow it is worth noting that some liquids behave in strange ways, sometimes flowing easily like water, and sometimes being stodgy, like porridge. Such fluids are called "thixotropic", and are most often met in substances like paint. Apparently thick and sluggish, they react to vigorous stirring by liquefying. Left to stand, they revert to the more solid state.

28

Fast Flow The division of water motion between "slow" and "fast" is not meant to be rigid. It is just a useful way of splitting up our treatment of moving water into separate parts, and there is bound to be some overlap. In this chapter we consider water that is generally moving a little more briskly than that of the previous chapter. There will be one or two equations, but it doesn't matter very much if you skip those bits. •

Pipe flow

We start with some flow that you can't even see, the flow of water inside pipes. Although we can't see inside, unless we are using transparent glass or plastic tubing, what happens there controls the appearance at the outlet. At very low rates of flow when conditions are sluggish, the following comments will not apply, as the way the water behaves is controlled by the viscosity effects, and the water moves like thick soup. Here we shall be looking at faster moving water. If one end of a pipe is higher than the other, and the water is free to move, it will flow from the upper end to the lower with a discharge dependent upon a number of factors. Firstly, of course, the flow will be affected by the head h, or difference of height of the two ends. Then there is the diameter d, of the pipe, the frictional effects of the inside surface, and the shape of the entry and outlet ends. Pipes do not always flow full. If they are circular then at very low rates of flow the water creeps along the bottom, and the water can sometimes move so slowly that it is below the transport velocity for some of the solid material that may be present in the water. That is, solid particles don't move along with the water, but collect in the bottom of the pipe. Because of this, sewers are sometimes egg-shaped in section, with the narrow section at the bottom. This makes the water move more quickly when there isn't much of it. In some cases a narrow gutter may be formed at the bottom to give the same effect. The reduction in width encourages faster flow. This is not always apparent to the water-watcher, as the pipes are underground; but sometimes the discharge end of a pipe may be visible, or repairs may reveal the pipe, in which case the special shape may be seen. Holes dug by people from the water supply authority are always interesting to waterwatchers. When a pipe is not running full it is really like a channel, or flume. Channel flow has special features, which will be looked at later in the chapter. So we shall here think about pipes running full, the whole circumference being wetted.

29

Water Watching If you don't like equations you can skip the next few paragraphs, as we shall now use a few symbols and formulae. These are put in to help those with some mathematical skill, but omitting them won't affect the general understanding of the subject. Returning now to our pipe carrying water, the discharge Q is the mean or average velocity v times the cross-sectional area a of the pipe. So we have Q = va We speak of "mean velocity" because, across the section of the pipe the flow is faster near the middle than near the walls. The velocity depends upon the head h of course, for it is this that pushes the water along; but there is friction between the water and the walls of the pipe, and turbulence, too. The speed is reduced by this friction, which takes up some of the energy of the flow. (If you look over the side of a moving boat you may see surface bubbles clinging to the hull and layers of water further from the hull moving past at increasing rates.) The head causing the flow may be due to the difference of levels of the pipe ends, or it may be produced by a pump of some kind, and is referred to as a head h or a pressure p. The two are connected by the equation p = wh Here w is the weight of unit volume of water, which is itself equal to g. The mass density of water is represented by , and g is the gravitational acceleration. When looking at small rates of flow we saw that the velocity varied according to the head so that we had the equation v = kh For fast flow though, it is the square of the velocity that varies with the head. This affect is important when we look at the amount of power needed to drive water through a pipe. You can think of the energy of a body of water as is its ability to do work. For example, if we have a lavatory cistern full of water it has the capacity or potential to flush a lavatory bowl. Water in a mains system under pressure can send a jet out over the garden. The energy stored in a reservoir can move water along pipes in a distribution system, or drive a turbine to generate electricity. The water retained by a dam has enough potential energy to light a town, or to sweep away buildings and do other extensive damage.

30

Water Watching

Water storage tower This potential energy depends upon the head h through which the water will fall when released. For every unit volume of water the available energy is wh, where w is its weight. So the potential energy is some constant times the head. P.E. = kh k being the appropriate constant, depending upon the system of units. On the other hand, water on the move has energy of motion, or "kinetic" energy. This kind can be appreciated when we see waves break against an obstruction, or a jet of water moving things. The kinetic energy depends upon the square of the velocity. Here again, with a suitable constant c we have K.E. = cv These two kinds of energy, potential and kinetic, can easily be changed from one to the other. The potential energy, PE of still water is converted into kinetic energy, K.E., as soon as it moves. So the water in a reservoir has potential energy which is converted to kinetic energy when the sluice is opened, or a dam fails. If we have a reservoir of water which is to be discharged to a lower level through a vertical distance h, then ideally its potential energy is converted into an equal amount of kinetic energy. So this kinetic energy and the potential energy have the same value. Expressed in symbols, we have CV = kh or, combining the constants, we could write v = ah putting a instead of k/c 31

Water Watching Although it looks simple, this is an important equation in the study of fluid flow. Since v is some constant times h then we can change round the equation to get:v = b÷h This tells us that the velocity of a jet of water, when caused by a head h, is some constant times the square root of h. Notice what happens as we change the head h. Doubling the available head increases the velocity by less than a half, (just over 40%). Again, if we have a head h to drive water through a pipe, and we wished to make it flow ten times as fast we should need to increase the head a hundredfold. Well, that is the end of our equations and formulae for now. The flow inside a pipe is really quite a complex affair as soon as it starts to move rapidly. You can imagine the water being held back by the layers near the pipe walls clinging to the pipe, while the inner core rushes along. The layers drag against one another, and this causes eddies and general turbulence. None of this is apparent to the water-watcher except at the outlet; but as it issues from the end of the pipe the water is disturbed, and it comes out in a jumbled kind of jet unless the end of the pipe is suitably shaped to calm it down. The drag of the pipe walls on the water uses some of the energy, turning it into heat, which then flows into the water and the pipe walls, so that there is a constant loss of energy, or head. This loss increases as the square of the velocity. The faster the flow the greater the loss of head. Double the speed and the head needed goes up four times. If the flow in a hose is reduced by pinching the end, the rate of flow is less, so the loss of head in the hose is not so high, the pressure at the end goes up, and the jet spurts forth with a higher velocity. So pinching the end of a hose enables one to throw the water further, a common experience among gardeners and small children. Water distribution systems start with a large pipe from the reservoir, and then the pipes are progressively smaller as the flow is divided further along the system. So the main pipe laid along a road, for example, has smaller pipes tapped into it to supply individual premises. Whenever water enters a pipe, or there is a change of diameter there is a loss of head. This loss is proportional to the square of the velocity. So the higher the velocity of flow the greater is the loss of head at each pipe change. In general the overall losses in a system can be written as a constant times the square of the velocity at some point. H = kv

32

Water Watching If water is being pumped at a particular rate then, and we wish to double the speed of delivery we have to apply four times the head. To make it flow three times as fast will demand nine times the head, and so on. Since pumping costs money, engineers design systems so as to require minimum head for the discharge demanded. Larger pipes cost more, but smaller pipes demand more pressure. A cunning balance has to be struck between the advantages of each. So water distribution systems use many different sizes of pipes.

Ball valve controlling level in cistern Some cisterns are fitted with a device to control the level within. Usually float operated, they close a valve as the level rises, shutting off completely when the water reaches the right level. Sometimes, when the opening is nearly fully shut vibrations can arise as the valve bounces, causing "singing" or "booming". One cure for this is to fit some form of damping to the float mechanism. Sometimes turning down the stopcock a little will reduce the rate of flow and so stop the vibration. •

Discharge trajectory

The discharge from the outlet end of a pipe follows that beautiful curve, the parabola, most clearly seen when the jet is at some angle to the vertical. The reason for this form is that the water is drawn downwards by gravity, so that the distance fallen at any time t is proportional to t. At the same time the horizontal distance travelled is proportional to t only. In the curve known as a parabola, distances along one axis are equal to the squares of distances along the other axis, so water jets have to follow parabolic paths. Waterfalls, too, show this kind of curve. If you are unfamiliar with the curve you can draw a parabola in several different ways. Perhaps the easiest is to draw up some values, x, say, and their corresponding squares, x, and plot one against the other. If a stroboscopic light is available it can sometimes show how the jet from the end of a pipe breaks up into droplets as it moves farther from the outlet. (The same effect can be 33

Water Watching seen when viewing the jet through the blades of a spinning fan.) The jet may hold its cross-sectional shape longer if the outlet is shaped so as to produce converging flow. •

Channel flow

Turning now to flow in rivers, streams, brooks, burns, canals, flumes, leets, gutters, and channels in general, the flow under ideal conditions is fairly straightforward; but you don't meet such conditions very often. So the behaviour of open water which we see may not follow very closely our theoretical ideas. Here we shall treat the flow as ideal, and the water-watcher will then have some understanding as to why the flow appears as it does, and not exactly as we might expect from simple theory. Firstly, the quantity passing along a channel is bound to be the same at all sections if there are no leaks. So along narrow stretches the flow has to increase in speed, whilst it slows up at fuller sections. Fish pools are sometimes regions of low velocity because of the increased depth there; and where banks close in the flow speeds up. A stroll along the banks of a small stream will show you this. The surface speed is not necessarily the same as the speed at greater depths, of course, and if the stream carries leaves and other pieces of floating and submerged items, this is obvious. Floating material can give a good idea of surface movements. It shows up the eddies, and changes of speed in the general flow. Where there is none, a few twigs cast into the water at suitable points can be helpful. •

Hydraulic jump

There is one speed, called the "critical" velocity, for channels, which decides the sort of flow you will see. This occurs when the depth of water is the "critical depth". When the depth is less than this the flow is fast; but when the water is deeper the speed is much lower. So at lower values than the critical velocity the water flows more or less calmly and deep; and at higher speeds the water is shallower. Changes in the bed may cause the flow to change suddenly from one sort of behaviour to the other as the depth alters. The "hydraulic jump" is a feature which takes place when fast-flowing water changes to a velocity less than the critical. The water then jumps up to its new depth. This can be seen in brooks where the flow meets some obstruction such as a large underwater stone, or in channels where a jump has been deliberately introduced to use up some of the energy of the flow. The water jumps to its new depth, and stays there till it meets some other feature that interferes with its progress. Since the amount of water flowing before the jump is the same as that downstream, the product of velocity v and depth h in a uniform channel must be the same before and after the jump. So we have v1h1 = v2h2 34

Water Watching Knowing the depth and speed before the jump, we can work out the velocity at the new depth. The water loses energy in the jump, and it is often very turbulent in the process. So a hydraulic jump is sometimes used to tame a flow which might otherwise produce unwanted scour downstream. Because of this you may sometimes come across an obstruction specially built into a fast flow, or even a series of walls or weirs, running across the stream. •

Channel bed

Watching the motion of water in a brook can reveal some of the unevenness of flow caused by changes in the bed, so that even though the water is cloudy you can guess at the nature of the bottom. In estuaries, where the water is tidal, the bottom can be inspected at low tide. As the water recedes you can walk out over the sand or mud or rocks in places and see how small channels are formed to take the outgoing water. Where the bottom is mud, be careful at all times to avoid regions where the mud is deep and treacherous. If there is weed about, it will be found that generally speaking the weed tends to grow on firmer bottom, and weed-free areas may be very soft. So as a general guide it is better to walk where there is weed. Splatchers, or pieces of flat board fixed to the feet, are sometimes useful for walking more comfortably where you have to walk on mud, and it is generally advisable to carry a stick. You can use this to probe the ground ahead. Where the bottom is sandy, it is usually firm; but occasionally this can be deceptive. Quicksands are areas that will not support people, water being liberally mixed with the sand, perhaps due to a spring there. The rising water separates the grains, producing a dangerous water-sand combination. You can easily sink in this. Sometimes you may see a reed or near-vertical twig, whose lower end is stuck in the bottom, with the upper end above the surface, waving across the flow with a regular rhythm. This is an interesting effect due to the eddies being thrown off behind the stick as the water passes. The eddies are cast off on alternate sides, and go off downstream like a street of little whirlpools. These cause the stick to be pushed first one way and then the other, and the movements may build up to a large to and fro swing. This is the same thing that produces a note from a string in a breeze, the so-called Aeolian harp. It is related to a special number in fluid studies called the Strouhal number. •

Vortices

Vortices or whirlpools form when water is caused to rotate, and these are most often seen in the house, when water drains from the bath or sink. There are two distinct kinds of vortex, free and forced.

35

Water Watching A forced vortex occurs when the water is forcibly whirled round, as when you stir a cup of tea. You can see that the level is higher at the rim than at the centre, the surface being basin-shaped, and nearly flat in the middle. On the other hand, the free vortex in the bath is flat at the outside, and steeper towards the centre. You can sometimes see free vortices in bodies of water which are draining through a hole, drawing it down and forming the characteristic whirling trumpet shape. You are unlikely to see many forced vortices, as these occur chiefly inside centrifugal pumps. If you look at a centrifugal pump you will see how the casing is like a snail's shell, water being sucked into the centre and whirled around the spiral casing so that the pressure rises towards the outside. More information about vortices is given in the glossary under "whirlpools". •

Pumps

Pumps are machines for putting energy into water. They are mostly centrifugal pumps, where water enters at the centre or eye of the pump, is rapidly spun round inside the casing, and forced out at the rim. You may see reciprocating pumps sometimes. In these there is a piston, moving to and fro to draw in water on a suction stroke and push it out on the delivery stroke. With these, high delivery pressures can be achieved in compact pumps at low speeds. Centrifugal pumps require high speeds or large diameters to produce high pressures, unless they use several stages, the outlet from one leading to the inlet of the next stage. You can usually recognise these by the number of snail-shaped casings that contain the rotating parts. Some small pumps use a rotor with flexible blades, running in an eccentric casing. Here the water enters between blades at one point, and discharges at a point further round the casing where there is an outlet, the outer casing here being nearer to the centre of the rotor. The water is virtually "squeezed" through the pump. The peristaltic kind of pump uses a rotating set of rollers. These press on a flexible pipe to squeeze a fluid along the pipe. These suit small deliveries, and are perhaps most often seen in applications such as pumps for small quantities of blood, oil and other liquids. Where the fall in height of the bed of a river increases, the speed of the flow naturally increases, since the difference in head between two points a given distance apart is greater here. The steeper the slope the greater the increase of speed. In rocky gullies air is entrained in the water as it bounces among the obstructions, providing magnificent and often awe-inspiring spectacles. Where this "white water " occurs there are often to be found adventurers in flimsy boats enjoying the thrills of making their way 36

Water Watching downriver successfully (more or less). This is tremendous fun, but it does demand skill and daring, as well as a protective hat and a masochistic outlook.

Rapids Steep changes of level produce rapids or falls worthy of attention. The flow rate is high, and often one finds a hydraulic jump at the foot of the steep part, where the streaming water erupts into a foaming increase of depth, to comparatively placid flow downstream. In salmon streams the fish have to leap these hazards to reach the upper parts of the stream for spawning, and at such times of the year onlookers are attracted to the falls.

Waterfall A large vertical drop in the bed of a river converts a smooth stream into a vertical aerated curtain of great appeal. Some of these waterfalls, or cataracts, are famous for their height, or the volume of the discharge. As the water falls it goes faster under the influence of gravity, and the result can be a brilliant sheet of changing texture and colour. Each unit of water that falls through a distance h gains wh units of energy during the fall. Most of this energy is converted into heat as it strikes the tailwater, though the amount of heat is comparatively little, and the "boiling" water below the fall is not due to the temperature of the water but the turbulence produced by the impact.

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Water Watching

Foot of Waterfall •

Turbines

Energy can be put into water by increasing the head, for example with a pump. To get energy out we decrease the head. This can be done by a device such as a waterwheel or turbine. The early waterwheels were (and some still are) open and visible to the passerby. Here a stream of water at a particular level flows to a lower level, yielding energy to the wheel. They may be overshot, breast-shot or undershot. Water-watchers are well advised to seek them wherever they may be, for they are few in number, and getting fewer. They are delightful to watch, especially when working. The larger ones are powerful and surprisingly efficient. After all, the power is freely available from the water as it moves along its cycle from ocean back to ocean. Built very strongly, and running comparatively slowly, they are reliable and long-lasting.

Waterwheel All that is demanded from the operator is maintenance work, such as keeping the leet free from obstruction, pouring some lubricant on the bearings, and perhaps fitting a new cog or two at long intervals. This is much less expensive than maintenance on a modern machine, though the power output is of course much lower. 38

Water Watching A cog is a wooden tooth which is set in the rim of a wheel. Once cogs have worn in they are very good at conveying the power from one wheel to another. Modern gearing uses teeth of cycloidal or involute form, and wooden cogs tend to wear into this kind of shape. They are surprisingly quiet in action. Modern water-turbines are usually difficult to see, as they are enclosed. They are like rotary pumps working in reverse. In some the water strikes a series of buckets mounted in the rim of a wheel, and in others the casing runs full, the water flowing over suitably shaped vanes, compelling the set of vanes to move by reaction. There is little for the water-watcher to see, though the general appearance of the machinery is one of quiet clean efficiency. The discharge from some turbines can be spectacular though, as not all of the energy in the water can be removed. Modern turbine design demands careful attention to detail if the machines are to be efficient. One aspect of great importance is the way in which the water flows through the passages. Where the water moves fast the pressure is low, and if it falls too far the water boils or evaporates and bubbles of vapour form there. This is called "cavitation". Further along the passage, where the pressure is greater, such bubbles may collapse with considerable violence and there can be serious damage from the impact as the unyielding water batters that part of the machinery. The design of pump impellers and ship propellers calls for great care to avoid the damaging effects of cavitation. If you get a chance to look at the propellor of a ship or a small boat you might see some pitting if the blades are not suitably designed for their duty. This pitting is not to be confused with the holes formed by electrolytic attack, which arises when dissimilar metals are immersed in an electrolyte, such as salt water. You may find lumps of zinc fastened beneath the waterline as "sacrificial" items. These will be eaten away in preference to the more expensive items like propellors.

39

Wave Motion Ups and downs of the water surface are familiar as waves, and when they are very small we recognise them as ripples. These are surface waves, but there is another kind which cannot be so easily seen. They occur below the surface, and are called compression waves. We shall look at these first. •

Compression waves

If you take a pipe full of water, and you suddenly force a plunger into one end, you momentarily squash the water touching the plunger. Because water is elastic, or springy, this compressed slice of water bounces, and in doing so squeezes the next slice of liquid. This in its turn rebounds, and in this way a shock wave or compression wave passes along the pipe through the water. If the other end is plugged, this compression wave will be reflected, and start to come back again along the pipe to the plunger. Making a series of sudden thrusts like this we can send a train of waves through the water. The same sort of thing happens if we smack the surface of a pond, say. Quite apart from the ripples which may be produced, there is a shock wave starting at the point of impact and travelling downwards and outwards through the water. Poachers are well aware of the way these waves of high pressure go through water. By causing an explosion in a lake or a stream, they can produce a severe wave of compression which can stun fish near the point where they set off the detonation. The unconscious fish float to the surface, where the poachers can gather them, and scamper away with their catch before the bailiffs catch them. It is this process of compression waves travelling through water which enables sounds to be transmitted below the ocean surface. Whales and other sea creatures emit sounds, which are trains of compression waves, to communicate with others. These sounds or wave trains can pass through water for long distances before they peter out. You can try this for yourself in the swimming pool. Diving under, you can make sounds that can be picked up by a friend swimming nearby. •

Water hammer

One way of producing a compression wave in a pipe that is running full is by suddenly shutting a valve, so that the flow comes to an abrupt stop. In some houses, quickly closing a tap can produce a series of sound waves that go to and fro along the pipe, and the noise can be very loud. It sounds as if the pipe system is being attacked by a series of hammer blows, and this is called "water-hammer". It is not advisable to do this deliberately, as the pressure rise at the wave front can be high enough to cause a burst. Opening a tap usually stops the noise at once. Water hammer can be cured by putting a restriction in the line, or just closing down the stopcock a little.

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Water Watching In open water pressure waves can pass without any indication on the surface that this is happening. In a submarine, the noise of propellors overhead is easily heard, and submarine crews who want to avoid detection have to maintain silence, because any sounds they make can be picked up by surface vessels. An attacking ship can toss overboard containers of explosive known as depth charges. These cause explosions, sudden rises of pressure, below the surface. The pressure waves produced like this go through the water and strike the submarine. If the pressure wave is not dissipated, diminished by distance, submarine craft can suffer severe damage, and may be crippled or destroyed. Sound waves in air can sometimes be heard at a distance when sent across the surface of water. People aboard small boats driven by a noisy outboard engine have to shout to make themselves heard; yet often they can be heard clearly aboard other craft some distance away. The sound is carried by a series of pressure waves in the air, and the smooth surface of the water does little to reduce the energy of those waves. •

Surface waves

Although the subject of surface waves has been mentioned in earlier chapters these alterations in the surface of water deserve separate treatment. The disturbances range from very tiny ripples to enormous ocean swells and powerful rollers. They may have smooth well-defined shapes, or break into great masses of tumbling foam. Here we are concerned with what can be seen by the watcher, who is above the surface. Those who like activity among the breakers, though, can enjoy some fascinating views looking up at the waves from underneath. Basically, a surface wave is a vertical oscillation, bobbing up and down, which usually occurs as one of a series of similar disturbances at the surface of the water. So a train of waves consists of undulations or swells following one another, where the surface moves up and down, usually regularly.

Wave train approaching shore The water at the surface may not be displaced horizontally, but move rhythmically in a vertical line. This can be seen if a stick is tossed into a train of waves. The stick doesn't seem to go anywhere as the train of waves passes it. 41

Water Watching •

Wave power

In the great open spaces of the oceans long trains of waves move along steadily over great distances, and the impressive size of the wave-train depends upon the "fetch", or stretch of water over which the wave is driven. So those coasts that face the open seas can suffer heavy destructive pounding. If the shore is steep, the waves can be formidable, but on gently shelving shores the energy is gradually dissipated till the tide line peters out in small ripples. The alternating pounding and sucking action of the great combers is very powerful, and this can change the appearance of a beach in a few hours. Where the beach is sandy or pebbly, enormous volumes of beach material can be shifted by the mighty wave forces during a storm. People who live in sea-side resorts know only too well the power behind water on the move. Protection of the coast from the deadly attacks of waves costs a lot of money and constant care. All over the world winter storms call for extra vigilance. When waves occur in deep water you can imagine the particles of water near but below the surface moving up down and sideways in a kind of circular motion, becoming elliptical nearer the bottom. The shape of the free surface at any instant is generally trochoidal . You can draw a trochoidal shape on paper if you make a small cardboard disc and mark a point P on its edge. Roll the disc, without slipping, along a horizontal ruler and mark the position of P on the paper at a number of intervals. If the points so marked are then joined by a smooth curve the result is a trochoid. You may care to experiment with a point not on the edge but somewhere else on the disc, to see the difference this makes to the shape of the curve. If you make a series of little holes at various distances from the edge, you can draw a lot of trochoidal curves by poking the pencil point through the holes. If there is a sudden discharge into a channel, such as one might get by opening a sluice gate, a hump of water appears, which travels along the waterway. The height and shape of this wave doesn't alter much if the channel section doesn't change. If the end of the channel is closed, then the wave may be reflected, keeping its form and speed more or less as it bounces back. In some rivers a solitary wave can form at the mouth when the tidal rise occurs. A wave, sometimes with steep sides, then travels up the river. In some cases this wave can be dangerous and destructive. The behaviour of a solitary wave in a channel is a good subject for laboratory work, and the books and papers about water studies contain much information on this. For the water-watcher who wants to try a few experiments the ripple is a good place to start. A stone tossed into a placid stretch of water will produce a set of circular ripples. These wavelets move outwards from where the stone entered. If knots are tied at known intervals in a piece of floating line pointing to the centre, then you can find the 42

Water Watching horizontal distances between successive crests, and their speed, an interesting piece of experimental work.

Circular ripples •

Sand ripples

On suitable bottoms of tidal waters you can sometimes see sand-ripples when the water has receded. These are caused by the rolling action of the water as it moves across the bottom. As the water approaches the granule it is slowed at its base and speeds up over the top. So the pressure is increased below and decreased above. This provides lift, and the granule rises. This changes the pressure distribution round the granule and it falls again. So the grains are rolled along the bottom, and in rolling they form ridges at rightangles to the flow. This is a simplified description of the action, and the water-watcher will find interesting variations in the patterns when walking out across the sand at low water. •

Wave frequency

The frequency of waves is how often the water moves up and down in a certain time. A set of waves at one frequency, added to another set with its own frequency leads to changes in height with yet another, the "beat" frequency. So at equal intervals there will occur a larger than usual wave, as the two crests come together.

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Water Watching

At the seaside, where the beach is attractive to swimmers, bathers sometimes call the unusually large wave the "seventh wave", though its frequency depends upon the frequencies of the individual trains, and may be every ten or any other number. The bather sees waves approaching in regular order, and then, every now and again there is this extra large one. This can be a danger for small children, who may be caught unawares and swept off their feet. A boat afloat in waves rises and falls rhythmically as it crosses the crests and troughs, a motion which can be comforting and restful to a seasoned mariner, but a matter of some unhappiness for those who suffer from seasickness. The regular rise and fall is in no way dangerous for the well-found vessel moved by a simple wave-train travelling the length of the ship. It is said to pitch and toss, and many people enjoy this. Standing on deck, looking ahead, you can gently rock your body to and fro with the same frequency, so that you are always upright, and the ship seems to rock round you, with the horizon staying in one place. Some people are sick because they rock with the ship, so that the horizon itself seems to heave up and down, not a very pleasant feeling. When the waves run at right angles to the ship's course the vessel rolls, and the roll can on occasion build up to a perilous angle. This occurs when the natural period of roll of the vessel is close to that of the wave train. The natural period of roll for a boat, from side to side, differs from that for pitching. Given an opportunity, you can easily test this by rocking a rowing boat sideways, and then trying to rock the bows up and down. You will not find it easy to rock the boat end-for-end, but should find it fairly simple to roll it from side to side, even right over if you keep it up. Boats which are pitching into waves may sometimes be turned sideways, so that they fall into the troughs of the waves. This is called "broaching" and can sometimes be unpleasant in heavy weather. The frequency of the waves and the rolling frequency of a 44

Water Watching boat might be nearly the same, and then the situation is dangerous, as the boat may be rolled so far as to capsize. Here again, if you stand on deck and swing your body so that it remains at right-angles to the horizon, the vessel will roll around you, and the horizon will remain still. You can stroll along the deck, leaning first one way and then the other in rhythm with the ship's motion. This may remove altogether the nausea of sea-sickness. When a series of waves is crossed by another similar one at a large angle difficult conditions can arise. Such a combination of waves can produce lumpy formations, the surface rising like a collection of pyramids, great lumps of water each surrounded by a trough. The ridges of one set of waves are cut into slices by the ridges of the other train, so that a ship no longer has an easy rhythmic motion. It is thrown up by a heap of water in an awkward manner without a clear direction of motion. Such nasty conditions can be met off coastal promontories, where currents from each side of a headland meet one another at certain states of the tide. At such times wise skippers of small craft avoid areas with that kind of reputation. For the water-watcher, it can be instructive to stand on a cliff and see the wave action at various times of different tide and weather. At slack water the behaviour is very different from that when the currents are running. In calm conditions, too, such waves as are seen differ greatly from those driven by high winds. When we cast a stone into a pond the resultant ripples arise from the depression and consequent upwards displacement of the water at the point of entry. When we see waves approaching shore from seaward we are usually looking at wind-driven waves, and when these have been travelling many miles they have had an opportunity to build up. You may sometimes see the effect of fetch in an estuary. Wind-driven waves across the water are likely to be smaller than those that run up the estuary, just because the fetch is longer up the estuary than across it. To see a classic train of waves one needs to go to sea, and experience the steady repeated rise and fall, uninfluenced by coastal effects. It is instructive, too, to visit areas where surfing is popular, for here the large combers roll in and break as the water reaches the shallows. The shapes of the waves can be clearly seen and enjoyed, either in the water or not. As a large wave approaches the beach, the deeper parts of the water are slowed by the rising shore, and the upper surface rides on over this lower water. So the shape of the wave is bent, and the crest may roll along over the top of a hollow in the water; thus a curling formation occurs. The front of the wave then becomes unstable, and starts to break up. Air bubbles are caught in the water, and this gives the water its white appearance. The movement inside the wave is violent; and the foam is a mixture of air and water which can ride along with the wave front till it reaches the shore. The behaviour of waves can be studied in rivers, at sea, on the shore, or at home in the bath. Surface waves can be produced by wind or other disturbance, and compression 45

Water Watching waves by the movement of something solid. Wherever you see them, they are one of nature's free entertainments. •

Viscous fluids

Before ending this chapter on waves it might be worth looking briefly at another aspect. Although water-watchers are concerned chiefly with water, comparison of its behaviour with other liquids can be instructive. For waves, as an example, what happens in "thick" liquids like tomato soup and thick sauces is easily seen to be very different from what we see in water. Thick liquids are said to be "viscous", and they resist rapid changes in surface shape. For example, the viscosity of glycerine is about 800 times that of water. Tension at the surface, too, can alter things. A liquid of high surface tension floating on another liquid alters the reaction of that surface to disturbances of any kind. If oil is spread over rough water the surface tension and the viscosity of the oil are such that the waves are not so readily produced or maintained. This fact is well-known to sea-faring people. In rough conditions broken water can be smoothed out by pouring oil onto the water. It at once spreads out on the surface and effectively smothers the bumpiness. Oil, being less dense than water, floats, and since it doesn't mix it stays on the surface. It spreads out over a large area forming a very thin layer, and stays there for a long time. When shipping discharges oil at sea this can be very damaging to sea creatures, birds in particular. You can see oil on the surface because of the rainbow colours that are reflected from the surface. A bird, alighting on such a surface, finds its plumage clogged, and cannot fly properly, leading to an unpleasant death. In its attempts to clean itself, it may get the oil into its stomach, too. Legislation exists to control such discharges of oil, but it is difficult to make sure the laws are obeyed. If oil and water are agitated violently, they can form what is called an "emulsion". The oil is broken up into tiny globules which are scattered throughout the water. To form an emulsion requires much energy. When oil is spread upon water an emulsion is not formed unless there is fierce movement, such as you see on rocky shores during violent storms. This has been, necessarily, an incomplete look at waves, but they form such an absorbing field of study for the water-watcher that you are pretty well bound to carry your investigations further. If you don't mind a little mathematics you will find the work done by people like Reynolds and Froude very informative.

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Glosssary BACKWATER CURVE A backwater is the stretch of water we meet when we go up stream from any point towards the source of the flow, the head water. The term is also used to describe a creek or an inlet from the main flow, where the water may be stagnant for part of the time. When an obstruction is placed across a channel, the depth at that point is changed, and the effect is felt for some distance upstream. If the depth of the flow is measured, or calculated, at a number of different points upstream of the obstruction we can draw a curve to show this variation in depth.

This is called a "backwater curve". It is important when a weir, for example, is to be built across a stream. It tells us about any resultant risk of flooding upstream. BROWNIAN MOVEMENT Very fine particles in suspension in a liquid are not at rest but move about in an irregular manner. Such colloidal particles are in effect being bombarded by the molecules, and this agitation can be seen, using a microscope. The movement takes its name from the botanist, Brown, who noticed this in 1827. BUBBLE A bubble is formed when a quantity of fluid is enclosed in another fluid with which it does not mix, for example, an air bubble in water. The bubble is generally spherical, but the surface tension of the water is such that the bubble is like an elastic bag, capable of much deformation. When many bubbles are in close contact they form a froth. Where they touch there can be no more than three bubbles in contact with each other, the lines of contact running out at 120 degrees from one another. A froth can remain as such for long periods in calm water, but is readily broken up and dispersed in turbulent flow. 47

Water Watching

Froth BUOY Almost any floating object can be used as a buoy. What distinguishes it is being moored or fixed to the bottom. Yachtsmen and fishermen lay down mooring buoys of great variety. Fishermen may use any floating object to mark where they have laid lobster pots. Navigation buoys are large standardised buoys indicating the channel by colour and shape. Generally, the red ones

Port hand buoy are to the left side of the channel when entering an estuary, and the green ones to the right

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Water Watching

Starboard hand buoy Mooring buoys are usually large and marked as such. BUOYANCY Any object thrust into water pushes the surface out of position, because it displaces some of the fluid; and this volume of water is thus raised above the normal surface. So it presses down on the water beneath. The pressure at any point below the surface is equal in all directions, but increases with depth. Hence the force pushing upwards below the object is greater than that pressing downwards on the upper part. The net force is thus upwards, and this force is called "buoyancy". If the weight of the object is less than the weight of the displaced water it will rise until the displaced volume of water has the same weight as the object. A floating object which is displaced downwards will move up on release, and may bob up and down before it stops, the frequency of oscillation depending upon the properties of the fluid and the object itself. CORIOLIS EFFECT Think about a particle of water moving over the earth's surface in a northerly direction, in the northern hemisphere say. It has, in its new position, an eastward velocity greater than the ground beneath. Relative to the earth it appears to be swinging to the right. Again, if water or air moves eastwards, its velocity relative to the axis of the earth is greater than the ground beneath it, so it tends to move "uphill" to the south, where the earth's velocity is greater. Hence it appears to veer to the right. It will be found that free initial movement in any direction invariably produces a rightward swing, in the northern hemisphere. This apparent desire for moving water to swerve to the right means that it tends to form a vortex, running counter-clockwise, the so-called "Coriolis" effect. The same reasoning applied in the southern hemisphere produces a clockwise vortex. Sections through such swirls are trumpet-shaped. They are called "free" vortices, or whirlpools, and the fluid flows in towards the centre, following a spiral path. 49

Water Watching A weather map shows the effect of the Coriolis acceleration by the inward spiral of air masses around a depression.

This is the same effect in air as one sees in water. The tornado is an extreme example. DENSITY Density is a measure of the amount of matter in unit volume of the material. This can be expressed in units of mass per unit volume or, more usually, units of weight per unit volume. Density varies with temperature, and may be different in different parts of a body of water. The warmer liquid, being less dense, floats upward, displacing cooler water, so giving rise to vertical and hence horizontal currents. Ships which travel to tropical regions, where the water is warmer and so less dense, float lower in the water there, and the difference may be considerable. On the side of the hull, near the water-line, you may sometimes see short horizontal lines painted there, to show the designed depth of immersion in home and tropical waters. It has been suggested that the mysterious loss of shipping in the "Bermuda triangle" might be due to massive upsurges of gas from the sea bed there which so reduce the effective density of the sea as to cause serious loss of buoyancy for vessels designed to float on "solid" water. In some parts of the ocean layers of water of differing densities occur. A submarine vessel can lie submerged, "floating" at the surface of separation of such layers.

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Water Watching DIMENSIONLESS NUMBERS Certain combinations of physical quantities exist whose values control the kind of movement of water, and of bodies moving in water. The value of such a number does not depend upon the units used, since they "cancel out". Here are some dimensionless numbers whose values are of interest to those who study water. The Reynolds number NR is given by vd/, and is a criterion of the kind of flow. If d is the diameter of a pipe, for example, then a value of NR less than 2,000 is indicative of laminar flow. Above this value the flow is likely to become turbulent. Notice that for a given pipe carrying water the product VD is constant for a given Reynolds number. So an increase in either the velocity or the pipe diameter can swing the flow from laminar to turbulent conditions. The quantity v/÷(gL) is the Froude number. NF is concerned with gravitational effects, where L is a typical length. When the Froude number approaches one we meet critical conditions, as for example in a channel, taking the depth y for the typical length. When NF = 1 we have v = ÷(gy), or y = v / g. So the critical depth is related to the velocity of flow. Where the depth changes abruptly, as at a hydraulic jump, it passes through the critical depth, the velocity changing accordingly. When surface tension is a factor the Weber number NW, given by, Lv/ is involved. So it comes into calculations when studying droplets, flow over weirs under small heads, spread of thin layers, and ripple formation. Here is the surface tension coefficient. A body moving through water meets a resistance or drag R, depending upon its shape, the frontal area and the velocity. The combination R/ Av is called the Newton number NN , and its value is a measure of the drag R on the body, A being typically the crosssectional area. The Strouhal number NS, (fL/ v) relates the frequency f of transverse oscillations of a rod of diameter L to the speed v of the flow in which it is immersed. This refers to the way a stick wobbles when dragged through water. It is easily felt when a rod is towed through water so that the flow is across the stick. You can see how the wobbles alter as the speed is changed. Where the elastic properties are of importance, the Mach number, NM, can be regarded as the speed of an object compared with the speed of sound in the water. It tells us something of the forces involved. This number can be written as v÷( /K), where K is a measure of the elasticity of the water. When the speed of an immersed object is such that the Mach number approaches one a very large increase in resistance arises. It may help you to understand this if you watch a boat accelerating to a speed at which the bow wave builds up and forces the vessel to be constantly climbing this "hill" of water. At this speed the resistance is high, and 51

Water Watching further speed increase demands a very big increase of thrust unless the boat can "plane", or skim along the surface. This is the same number that we hear about in connection with supersonic flight of aircraft. There are other dimensionless numbers used in the study of water, and those mentioned above are merely a sample. The study of dimesnionless numbers is a powerful tool DOWSING Although many are not convinced, this is a well-authenticated method of detecting the presence of underground water by walking over the ground with some sensitive indicator. It has been suggested that some emanation from below ground affects the diviner so that the muscles twitch and thus cause movement of the twig or other divining tool. One way is to hold in each hand a couple of lengths of metal rod, bent into the shape of the letter "L", the short lengths clutched vertically in the fist, with the longer ends horizontally pointing forward, and free to swing.

Dowsing rods The presence of underground water will cause the rods to swing as you pass over the water. It may need some practice, and it doesn't seem to work for everyone, but the number of people for whom it does work is surprising. Similar reactions occur with any delicately set unstable arrangement. A popular one is a forked hazel twig, pointing upwards, the ends held with the thumbs pushing upwards against the grip of the fingers on the inside pulling down.

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Water Watching

Dowsing twigs HEAD (or height) The pressure exerted by water is often expressed in terms of the height or head, h, of water in a vertical pipe which would produce that pressure at the lower end. The actual pressure is given by wh, where w is the weight of unit volume of the water, or gh, where is the density and g the gravitational acceleration. HYDRAULIC JUMP When water flows in a channel above a certain critical velocity and meets an obstruction, it may form a vertical wall of water and then flow at a lower rate, below the critical velocity. The height of a jump can be calculated, and its subsequent velocity found.

This is useful in the design of water-courses.

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Water Watching

HYDRAULIC RAM

This is a form of pump, in which a flow of water into and through a chamber is suddenly interrupted by a valve. The resultant rise of pressure drives some of the water up a delivery pipe. The process repeats at a frequency set by the conditions. Where there is a plentiful supply of water this is a simple and effective way of pumping part of the water to a convenient height above the ram. The same term is applied to a piston driven by the pressure of water or some other liquid. HYDRODYNAMICS This branch of the study of fluids is concerned with the forces arising when liquids are moving. Flowing water and machinery are studied under this head. HYDROSTATICS When a fluid is at rest the forces exerted are those due to the static conditions, and the study of this branch of fluid mechanics is called hydrostatics. It comprises the examination of forces on immersed bodies, pressure on walls and dams, and buoyancy. HYPERBOLA The hyperbola is a lovely curve, one of the family of conics, derived from cutting a cone along various planes. The equation of the hyperbola is surprisingly simple. xy = c 54

Water Watching where x and y are variables, and c is a constant. This curve occurs from time to time in the study of fluids. You can easily draw it on a piece of squared paper. For simplicity take 10 as the value of c. Then the equation can be written y = 10/x Now draw up a table showing the values of y corresponding to a number of values of x x

1

2

3

4

5

6

7

8

9

10

y

10.00

5.00

3.30

2.50

2.00

1.66

1.40

1.25

1.10

1.00

You see that as x increases, y decreases, very quickly at first, and then it shrinks less and less rapidly. If very large values of x are put into the equation, the values of y become tiny, approaching zero. We say that the curve is "asymptotic" to the horizontal axis, meaning that it approaches nearer and nearer without actually touching it.. Plotting corresponding values of x and y and running a smooth curve through the points will give you a hyperbola. This particular one fits neatly inside a right-angle, and is called a rectangular hyperbola.

MASS Mass is the quantity of matter in a body. It should not be confused with weight, which is a force. The mass of a body is normally constant, though Einstein has shown that mass and energy are mutually convertible. For the water-watcher, the relevant factor is 55

Water Watching that although the volume of a given quantity of water may change under great pressure, the mass remains constant. NEAP TIDE When the pull of the moon on the waters of the earth is reduced by the sun pulling at right-angles the tidal range is reduced, so that the height of high water is lower, and that of low water higher. In other words there is less difference between the levels at high and low water. These tides are the "neap" tides, and occur regularly about halfway between the times of the "spring" tides.

NOTCH For the measurement of flow in a channel a plate is sometimes fitted across the stream with a sharp-edged triangular or rectangular notch cut in the upper edge. The height of the water-level in the notch is a measure of the rate of flow. It is a simple device, cheap to make and install, and the relationship between height and flow is easily calculated. The equation connecting the height h and volumetric rate of flow Q is Q = k÷h where k is a constant depending upon the characteristics of the notch.

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PRESSURE The intensity of pressure can be expressed as so many units of force on unit area; but in the study of fluids the head h which would produce that pressure is largely used instead. PARABOLA The parabola is perhaps the most often-met conic curve in nature. Its equation is short and powerful. y=ax a being a constant whose value sets the proportions of the curve. The presence of the second power of x gives the curve its special shape, which is that of the trajectory of a projectile, or a jet of water. If we take the simplest case of a as unity the equation becomes y=x and from this we can draw up a table of values for a short range to produce part of a parabola.

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The special characteristics of the parabola are responsible for the beautiful appearance of waterfalls and jets of water.

SPRING TIDE This is the tide resulting from the moon and the sun being in the same straight line on the same side of the earth, so that they both pull together. These tides are higher than usual, and often give rise to flooding and damage to protective works on coasts and river banks.

STABILITY We recognise three states of stability, (neutral, stable, and unstable), and three axes about which the body can turn. The three axes are the vertical one, about which the body is said to yaw, the fore-and-aft or rolling axis, and the one across the body, the pitching axis. The stability of the body about each of these axes may be different. 58

Water Watching

If you toss a ball into a pool it will settle in a position of neutral stability. If it is disturbed it will remain in the new position, and not attempt to roll round to its former attitude. This is generally true of any regular body. Other shapes, when disturbed, either oscillate or change to a new attitude. High stability results in rapid return to the normal attitude, and high frequency of oscillations. So although good stability is essential in ships, for example, too much can put a severe strain on the vessel as it attempts rapid rolling or pitching. An informative experiment is to put a rectangular block of wood into water and note the difference between the frequencies of oscillation in rolling and pitching. If you visit a place where many small boats are moored, on a windy day or when the water is rough, you may notice the different frequencies and amplitudes for the different kinds of vessel. SURFACE TENSION Molecules of water, like any other substance, tend to cling together. At the surface they are in contact with those of the air, with which they do not have the same affinity. So they cling together, as if there were a skin on the surface. Although this is tiny, the force can be important sometimes.

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It is noticeable especially in fine tubes, where the tension at the surface inside the tube holds up a volume of water above the level outside of the tube. The height h depends upon the diameter d according to h = k/d where k is a constant. The smaller the value of d, then the greater is h. So the water will rise more in a narrow tube than a wide one. In capillary tubes, with very fine bores, the rise may be striking. When rising damp is seen in a wall, it is the fine interstices in the brick and mortar which give rise to this phenomenon.

VISCOSITY When layers of water slide over one another there is a certain amount of resistance, which varies with temperature, and relative speed of sliding. This is due to a property of the water called "viscosity". If there are no variations of speed within the water there are no viscosity effects. It may be helpful to think of viscous fluids as "thick", and those of low viscosity as "thin". Fluids such as tar and treacle have high viscosity. Petrol and thin custard have low viscosity. VORTICES See "Whirlpools"

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Water Watching WEIGHT The word "weight" should not be confused with "mass". Mass is the amount of matter in a body, whereas weight is the inertia force on that body due to gravity. If m is the mass and g the acceleration due to gravity, then the weight is mg. WEIR A weir is an obstruction in a channel, usually a ledge running across the stream.

Weir It may be used to raise the level upstream of that point, and to measure the discharge. In general, the height h of water over the ledge is a measure of the discharge, which is given by Q = k ÷h. The weir may be straight or have a triangular cut in it, a so-called "vee-notch". WHIRLPOOL When you pull the plug in a basin of water or in the bath, you will see that the water doesn't flow straight down the hole, but in a spiral path, spinning round the drain, forming an eddy or whirlpool. This is a free vortex. It is suggested that this is due to the Coriolis effect, arising from the rotation of the earth, though such an eddy is on so small a scale that the forces are tiny, and it is easy to twirl the water with one's hand to make it go the other way.

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Whirlpool in a bath It is easy to appreciate the terror of the old mariners who feared the "maelstrom", the great whirlpool off the coast of Norway. Any slow-moving ship would have no chance of sailing out of such a whirlpool, but would spin faster and faster towards the centre, where it would be sucked down into the depths. Such a whirlpool is a "free vortex", its section being trumpet-shaped, with the surface outside its influence horizontal.

Water can be forced to flow in either direction if physical means are employed, such as when one stirs a cup of tea. These are "forced" vortices, and the section through such a vortex is quite different, being bowl-shaped. The forced vortex is the kind produced in a centrifugal pump. Water enters the pump at the "eye" of the vortex and as it is whirled around by the impellers the pressure is raised towards the outer part.

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Water Watching Edmund W. Jupp The aim of the "Watching" series is to draw attention to some of the very interesting items around us, things that perhaps we don't notice as much as we might. The first was "Bridge Watching", and when this was put "on the Net" it produced, to the surprise of the author, such a pleasant flood of e-mail that another was written, called "Water Watching". This, too, was kindly received. So it was tempting to continue with the theme. Water watchers enjoy this pleasurable pastime, whatever their educational background; but more knowledge of what to look for will, it is hoped, lead to even more satisfaction. The intention is to encourage interest in looking at water or watery fluids, which are all around us. You don't need any equipment, licences or permits, nor any special qualifications, other than some curiosity, a sense of wonder. The treatment won't be too technical, but hopes to show you how some natural laws control the behaviour and appearance of water. Some knowledge of this can make water so much more fascinating, wherever you see it. There is a great variety of surface water to be seen, waterfalls, streams, rivers, puddles, and lakes; there is rain, snow, hail, frost and dew, as well. The total amount of water on our planet doesn't change. It just goes round and round, in its passage sustaining life in all its forms. Water-watchers can look at it during the different stages of its cyclic tour. So, besides enabling every living thing to exist, water provides free intriguing entertainment, to charm us with its magic. We can all take advantage of it. Author Edmund W. Jupp (BSc (Eng), FIMech E) was born during the First World War in Sussex, England and received his early education at Brighton. After service in the 1939-45 war he worked in engineering and education, and travelled widely. He was appointed Principal of the Technical Institute in Guyana.

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