Fig. 90.
Let ABC, (Fig. 90) be a recurved tube: if water be poured into one arm of the tube, it will rise to the same height in the other arm. For, the pressure acting upon the lowest part at B, in opposite directions, is proportioned to its depth below the surface of the fluid. Therefore, these depths must be equal, that is, the height of the two columns must be equal, in order that the fluid at B may be at rest; and unless this part is at rest, the other parts of the column cannot be at rest. Moreover, since the equilibrium depends on nothing else than the heights of the respective columns, therefore, the opposite columns may differ to any degree in quantity, shape, or inclination to the horizon. Thus, if vessels and tubes very diverse in shape and capacity, as in Fig. p. 84 be connected with a reservoir, and water be poured into any one of them, it will rise to the same level in them all.
The reason of this fact will be further understood from the application of the principle of equal momenta, for it will be seen that the velocity of the columns, when in motion, will be as much greater in the smaller than in the larger columns, as the quantity of matter is less; and hence the opposite momenta will be constantly equal.
Hence, water conveyed in aqueducts or running in natural channels, will rise just as high as its source. Between the place where the water of an aqueduct is delivered and the spring, the ground may rise into hills and descend into valleys, and the pipes which convey the water may follow all the undulations of the country, and the water will run freely, provided no pipe is laid higher than the spring.
Pressure of water due to its weight. The pressure on any particle of water is proportioned to its depth below the surface. The pressure of still water in pounds per square inch against the sides of any pipe, channel, or vessel of any shape whatever, is due solely to the “head” or height of the level surface of the water above the point at which the pressure is considered and is equal to ·43302 lbs. per square foot, every foot of head or 62·355 lbs. per square foot for every foot of head at 62° F.
The pressure per square inch is equal in all directions downwards, upwards or sideways and is independent of the shape or size of the containing vessel; for example, the pressure on a plug forced inward on a square inch of the surface of water is suddenly communicated to every square inch of the vessel’s surface, however great and to every inch of the surface of any body immersed in it.
It is this principle which operates with such astonishing effect in hydrostatic presses, of which familiar examples are found in the hydraulic pumps, by the use of which boilers are tested. By the mere weight of a man’s body when leaning on the extremity of a lever, a pressure may be produced of upwards of 20 tons; it is the simplest and most easily applicable of all contrivances for increasing human power, and it is only limited by want of materials of sufficient strength to utilize it.