HYDRODYNAMICS treats of the laws of the motion of liquids; the flow of water from orifices and in pipes, canals, and rivers; its oscillations or waves; and its resist ance to bodies moving through it. The term hydraulics is sometimes applied to the same subjects, from the Greek word autos, a pipe. The application of water as a mov ing power forms the practical part of the subject.—In what follows, the illustration is taken from the case of water, but the principles established are true of liquids in general.
three apertures, D, C, E, are made at different heights in the side of a vessel filled with water, the liquid will pour out with greater impetuosity from C than from D, and from E than from C. The velocity does not increase in the simple ratio of the depth. The exact law of dependence is known as the theorem of Torricelli; the demonstra tion is too abstruse for introduction Here, but the law itself is as follows: "Particles of fluid, on issuing from 071 aperture, possess the same degree of velocity as if they had fallen freely, in vacuo, from a height equal to the Lance of the suKface of the fluid above the center of the aperture." The jet from C, for instance, has the same velocity as if the particles composing it had fallen in vacuo from the level of the liquid to C. Now, the velocity acquired by a body in falling is as the time of the fall; but the space fallen through being as the square of the time. it follows that the velocity acquired is as the square root of the space fallen through. In the first second, a body falls 16 ft.. and acquires a velocity of 39 feet. If E, then, is 16 ft. below the level, a iet D Urgin„1],.filows at the rate of 32 ft.; and if D is at a depth of 4 ft., the velocity' of dIM 1e half the Velocity of that at E, or .16 feet. In general, to find the velocity for any given height; multiply the height by 2X32, and extract the square root of the product. This rule may be expressed by the formula a =i/vF,h, in which a signifies the velocity of the issue, g the velocity given by gravity in a second, or 32 ft., and is the height of the water in the reservoir above the orifice. This last
thy is technically called the head or charge.
That this theory of the efflux of liquids is correct, may he proved by experiment. Let the vessel, MB, have an orifice situated as at o; the water ought to issue with the velocity that a body would acquire in falling from 31 .to the level of o. Now. it is established in the doctrine of projectiles (q.v.), that when a body, is projected vertically upwards with a certain velocity, it ascends to the same height from which it would require to full in order to acquire that velocity. If the theory, then, is correct, the jet ought to rise to the level of the water in the vessel at 31. It is found in reality to fall short of this; but not more than can be accounted for by friction, the resistance of the air, and the water that rests on the top in endeavoring to descend. When the jet receives a very slight inclination, so that the returning water falls down by the side of the ascending, ten in. of head of water may be made to give a jet of nine inches. A stream of water spouting out horizontally, or in any oblique direction, obeys the laws of projectiles, and moves in a parabola; and the range of the jet for any given velocity and angle of direction may be calculated precisely as in projectiles. The range of horizontal jets is readily determined by practical geometry. On AB describe a semicircle; from D, the orifice of the jet, draw DF perpendicular to AB, and make BK equal to twice DF; then it can be proved by the laws of falling bodies and the properties of the circle, that the jet must meet BL in the poinCK. If BE is equal to AD, the perpendicular EH is equal to DF; and therefore a jet from E will have the same range as that from D. Of all the perpendiculars, CG, drawn from the middle point C, is the greatest; therefore, the jet from C has the longest possible range.