That a column of water will stand at exactly the same level as any other with which it communicates, may be seen still more simply by placing a glass tube, open at each end, in a basin of water. However the tube may be inclined or bent, whether its lower end is wide or narrow, the column of water inside it will be at exactly the same level as the water outside it. Yet, of course, the rigid glass walls of the tube cut off all communication between the column of water inside it and the rest, except at the bottom.
In a well-ordered town, water is supplied to every house and can be drawn from taps placed in the highest stories. These are fed by pipes which lead from a cistern at the top of the house. This water is brought from a large pipe, or main, in the street, by a smaller house-pipe, which is often made to twist about in various directions before it reaches the cistern at the top of the house into which it delivers the water. If you followed the main, you would find that it took a long course up and down, beneath the pavement of the streets, until at last it reached the water-works. Here you would find that the main was connected with a reservoir; and either this reservoir is at a greater height than any of the cisterns into which the water is delivered, or there is some means of pumping the water from it to that height on its way to the main. Thus the reservoir, the main, and the house-pipe form one immense U-tube, and the water in the house-pipe tends to rise to the same level as that of the water in the reservoir, and hence flows into the cistern when the supply-pipe is open.
28. The Transference of Motion by Moving Water: the Momentum of Moving Water.
Suppose a wooden vat with a horizontal tap, the sectional area[[3]] of the tube of which is one square inch, inserted close to the bottom, to be filled with water up to 100 inches above the tap. Then supposing the tap to be shut, the pressure upon its sectional area will be 25,250 grains, or rather more than three pounds and a half—and there is the same pressure on every square inch of the bottom of the vat.
[3]. The sectional area of a tube is the surface occupied by its cavity when it is cut across. It would be represented by the surface of a piece of cardboard, like the wad of a gun, just large enough to go into the tube.
If the tap is now turned, the water nearest to it being unsupported on its outer side, the pressure on the inner side sets it in motion, and it flows out in a stream. At first the stream shoots out violently and the water is carried to a long distance. That is to say, the weight of the column of water 100 inches high acts as a force, or cause of motion, upon the water nearest the tap, and this water is forced out with a velocity depending on that force in a horizontal direction. Now suppose that you take a common toy cup-and-ball and bring the ball into the way of the stream of water. The stream will at once strike the ball and drive it in the same direction as that which it is itself taking. The power which the moving water has of transferring or communicating motion to a body which is at rest, but free to move as the ball is, is due to its momentum. The greater the mass of the stream and the more rapidly it moves, the more motion will it communicate to the ball, or the heavier the ball it will move. Close to the mouth of the tap the direction of the stream is horizontal; but it very soon begins to bend downwards, and describing a rapid curve, comes to the ground. It does this for just the same reasons that a stone thrown horizontally describes a curve; and at length strikes the ground; and, in fact, the stream may be regarded as so much water thrown horizontally.
These reasons are two: firstly, as soon as the water has left the tap it is an unsupported heavy body; and, as such, it begins to fall to the ground. Secondly, the momentum of the water is continually being diminished by the resistance of the air through which it passes. For, although the air which surrounds us is so thin and movable a body that we ordinarily take no notice of it—the fact that it offers resistance to bodies which move through it is easily observed; as, for example, in using a fan. The water has to overcome this resistance, and its momentum is proportionally diminished.
If, when the water leaves the tap, the air and gravitation were alike abolished, the water, keeping its momentum, would travel for ever in the same direction.
As the water runs out, it will be observed that the velocity of the stream becomes less and the curve which it describes sharper, so that it comes to the ground sooner; and finally, when the vat is nearly empty, the stream falls nearly vertically downwards. The reason of this is that the level of the top of the water is gradually lowered; consequently, the height of the column which presses on the water close to the tap is gradually lessened, and therefore its weight is diminished. But this weight or pressure is the cause of the motion of the water, and as the cause diminishes the effect of that cause must diminish. Therefore the momentum of the water is gradually lessened and it is carried less and less far horizontally in the time which it takes to fall to the ground: until finally, it acquires no appreciable horizontal motion at all, and so falls vertically downwards from the mouth of the tap.