Waves and ripples in water, air, and æther

by Sir J. A. Fleming

Fig. 28.

At this point we must make a digression to explain a fundamental law concerning fluid flow in tubes. Suppose we have a uniform horizontal metal tube, through which water is flowing ([see Fig. 28]). At various points along the tube let vertical glass pipes be inserted to act as gauge or pressure-tubes. Then when the fluid flows along the horizontal pipe it will stand up a certain height in each pressure-tube, and this height will be a measure of the pressure in the horizontal pipe at the point where the pressure-tube is inserted. We shall notice that when the water flows in the horizontal pipe, the water in the gauge-pipes stands at different heights, indicating a fall in pressure along the horizontal pipe. We also notice that a line joining the tops of all the liquid columns in the pressure-pipes is a straight, sloping line, which is called the hydraulic gradient. This experiment proves to us that when fluid flows along a uniform-sectioned pipe there is a uniform fall or decrease in pressure along the pipe. The force which is driving the liquid along the horizontal pipe is measured by the difference between the pressures at its extreme ends, and the same is true of any selected length of the horizontal pipe.

It will also be clear that, since water is not compressible to any but the very slightest extent, the quantity of water, reckoned, say in gallons, which passes per minute across any section of the pipe must be the same.

Fig. 29.

In the next place, suppose we cause water to flow through a tube which is narrower in some places than in others ([see Fig. 29]). It will be readily admitted that in this tube also the same quantity of water will flow across every section, wide or narrow, of the tube. If, however, we ask—Where, in this case, will there be the greatest pressure? it is certain that most persons would reply—In the narrow portions of the tube. They would think that the water-particles passing through the tube resemble a crowd of people passing along a street which is constricted in some places like the Strand. The crowd would be most tightly squeezed together, and the pressure of people would therefore be greater, in the narrow portions of the street. In the case of the water flowing through the tube of variable section this, however, is not the case. So far from the pressure being greatest in the narrow portions of the tube, it can be shown experimentally that it is precisely at those places it is least.

This can be demonstrated by the tube shown in [Fig. 29]. If water is allowed to flow through a tube constricted in some places, and provided with glass gauge-pipes at various points to indicate the pressure in the pipe at those places, it is found that the pressure, as indicated by the height of the water in the gauge-glasses at the narrow parts of the tube, is less than that which it would have at those places if the tube were of uniform section and length, and passed the same quantity of water. We can formulate this fact under a general law which controls fluid motion also in other cases, viz. that where the velocity of the liquid is greatest, there the pressure is least. It is evident, since the tube is wider in some places than in others, and as a practically incompressible liquid is being passed through it, that the speed of the liquid must be greater in the narrow portions of the tube than in the wider ones. But experiment shows that after allowing for what may be called the proper hydraulic gradient of the tube, the pressure is least in those places, viz. the constricted portions, where the velocity of the liquid is greatest. This general principle is of wide application in the science of hydraulics, and it serves to enable us to interpret aright many perplexing facts met with in physics.

We can, in the next place, gather together the various facts concerning fluid flow which have been explained above, and apply them to elucidate the problems raised by the passage through water of a ship or a fish.

Let us consider, in the first place, a body totally submerged, such as a fish, a torpedo or a submarine boat, and discuss the question why a resistance is experienced when an attempt is made to drag or push such a body through water. The old-fashioned notion was that the water has to be pushed out of the way to make room for the fish to move forward, and also has to be sucked in to fill up the cavity left behind. Most persons who have not been instructed in the subject, perhaps even now have the idea that this so-called “head resistance” is the chief cause of the resistance experienced when we make a body of any shape move through water. A common assumption is also that the object of making a ship’s bows sharp is that they may cut into the water like a wedge, and more easily push it out of the way. Scientific investigation has, however, shown that both of these notions are erroneous. The resistance felt in pulling or pushing a boat through the water is not due to resistance offered by the water in virtue of its inertia. No part of this resistance arises from the exertion required to displace the water or push it out of the way.

The Schoolmen of the Middle Ages used to discuss the question how it was that a fish could move through the water. They said the fish could not move until the water got out of the way, and the water could not get out of the way until the fish moved. This and similar perplexities were not removed until the true theory of the motion of a solid through a liquid had been developed.