HYDRAULICS teach us to ascertain the velocity and impetus of fluids when in motion, and serves as the basis for com puting the powers of various machinery acted upon by running water.
The first principle we shall inculcate in this service is, that water, being an in elastic fluid, (though many have thrown away much time in the attempt to prove the contrary,) can only be set in motion by two causes, viz. the increased pressure of the air, as in the air-vessels of fire-en gines, and by gravitation ; that is, where it is liberated from confinement, and al lowed to descend to an inferior level. In the former case, water may be made to rise by machinery suited to the purpose ; in the latter, it will inviolably seek a low er situation.
The velocity of water, proceeding through a hole in the side of a vessel, is ever proportioned to the distance of the aperture from the level of the fluid, the square root of the intermediate space be ing the guide. It must, however, be re collected, that in consequence of the de crease of that space, as the water is let out, the pressure becomes gradually less ; therefore the medium, or mean distance, between the surface and the vent whence the water issues, will be found, in gene. ral, a oorrect standard. Hence we see, that, in order to force double the quan tity of water through the lowest of two apertures, the distance must be quadru pled. For if a hole made at C in the pipe A B, fig.L will supply one gallon of water in a minute ; to draw double that quantity in the same time, the low er hole, D. must measure from the sur face, B, four times as much as from C to the surface.
This establishes the above position, and proves, besides, that the force is equal to the velocity, as indeed we know to result in every branch of mechanism.— To shew this, let the pipe, A B, be per forated in several parts, as at C D E ; the first, i. e. C, being one foot ; that at D be ing four feet ; and that at E being seven feet below the surface, B ; between E and A we will suppose only one foot in, terval, so that D may be in the centre of the height A B. Draw the horizontal line, A F, and from D describe the semi. circle, B G A, having D G equal to D A, or D B, for its radius. Now the water will, as it flows from D, describe a para bola, and will fall upon the line, A F, at such a distance from A, as will be equal to double the radius, D G. In like man
ner the water flowing from the aperture, C, will reach that point, viz. K, on the hori zontal A F, which may measure the sine, C H, on the same semicircle: and the sine of the arc taken opposite to E, i. e. E L, is equal to the sine, C H, the water rushing from E will intersect, or meet, the water falling from C, at the point K. It is to be observed, that the parabolic curve of the water proceeding from C to K has a greater tendency to gravitation than that issuing from E, which rushes with far more force, and consequently has a greater tendency to an horizontal direction. For the aper ture at C is only acted upon by a column of one foot deep, i.e from B to C, but the column of water from B to E measures seven feet. We have already stated, that the velocity is equal to the square root of the column's height above the aperture.
It is the peculiar property of fluids to preserve their level, notwithstanding any varieties of course, or inequality of eleva tion. Thus, supposing the pipe, A B C D, fig. 2, to be bent into the form required for passing over declivities, as shown: the water will rise to the height, A D ; but where the channel exceeds the level of that line, there will be a break in the course of the fluid, such as appears at 13 : yetthe course may descend to any depth, as at C, provided the pipe be brought back to the original height. If either end be in the smallest degree lower than the other, the water will sink to the level of the lower retaining brim. And if the sup ply be continual, the water issuing from the lowest end will mount nearly to the level of the source. This isthe principle on which fountains are in general found. To effect this, however, the pipe should be small, so as to contract the issue of the fluid, and to give it greater velocity, by causing it to expose a smaller surface for the air to press upon. This contraction should not be carried to excess; else the water would want force to pass through the atmosphere, and, being subdued, would break into drops, and fall without gaining any height. The conduit-pipe is usually made about five diameters of the fountain-pipe ; under such proportions the water will ordinarily flow so freely as to give a good jet.