Page:The American Cyclopædia (1879) Volume IX.djvu/129

 HYDROMECHANICS 121 the centre of buoyancy B to the left, the point M might remain at nearly the same distance from G, because it would also move to the left. But if the inclination of the vessel in the same direction carried the centre of buoyancy FIG. 15. Fio. 16. to the right, the height of the metacentre M would dimmish until it would be in G, when the equilibrium would be indifferent, and at last below G, when the ship would turn over. It is desirable to have the metacentre as far as possible above the centre of gravity, and this condition is secured by bringing the cen- tre of gravity to the lowest practicable point, by loading the ship with the heaviest part of the cargo nearest to the keel, or by employing ballast. II. HYDRODYNAMICS, although it em- braces many of the principles of hydrostatics, treats more particularly of the laws of liquids in motion. One of the most important prin- ciples of hydrodynamics is that which deter- mines the velocity of jets which issue from orifices at various depths in the sides of ves- sels containing liquids, and depends upon the laws of hydrostatic pressure. If an orifice is made in the side of a vessel containing a liquid, the liquid will issue from it with a velocity equal to that which a heavy body would ac- quire in falling through the vertical distance between the surface of the liquid and the ori- fice. If the jet is directed upward, it will as- cend, theoretically, to a level with the surface of the liquid ; but practically it will fall short of this in consequence of friction at the orifice, and of the resistance offered by the air. At first sight it would appear that the velocity of efflux would be proportional to the pressure, but an analysis of the case, aside from the test of experiment, will show that this cannot be, for in no instance can the jet be projected higher than the surface of the liquid. If, in general terms, the velocity of a jet were in pro- portion to the pressure at the point of issue, a column of mercury would throw a jet with 13 times the velocity that an equal column of wa- ter would ; but it must be perceived that a column of mercury can only propel a jet as high (theoretically) as the surface, and there- fore to the same height as an equal column of water can. Now, there can be no doubt that the pressure of mercury at the same depth is 13 times that of water ; but mercury, being also 13 times as heavy as water, has 13| times as much inertia, and therefore requires so many times as much force to give it the same initial velocity. The velocity with which a liquid escapes from an orifice varies as the square root of the depth below the surface ; so that when the points of escape are 1, 4, 9, and 1C ft. in depth, the initial velocities will be as 1, 2, 3, and 4. This is the celebrated theorem of Torricelli, which he deduced from the laws of falling bodies. As the velocity of a falling body is in proportion to the time of its fall, it will be in proportion to the square root of the height fallen through, and is represented by the formula V = v'tyh, in which g is the ac- celerating force of gravity (= 32-2), and h the height. (See MECHANICS.) A jet issuing from the side of a vessel describes, theoretically, a parabola, precisely as in the case of a solid projectile ; for the impelling force and the force of gravity act upon the jet in the same manner, and the resultant force gives it the same direction. The range, or distance to which the jet is projected, is greatest when the angle of elevation is 45, and is the same for elevations which are equally above or below 45, as 60 and 30. The resistance of the air however alters the results, and the statement is only true when the jet is projected into a vacuum. If a vessel filled with water have orifices made in its side at equal distances in a vertical line from the top to the bottom, a stream issuing from an orifice midway between the surface and the bottom will be projected further than any of the streams issuing from the orifices above or below. This may be de- monstrated by the adjoining diagram, fig. 17. Let a semicircle A F E be described on the side of a vessel of water, its diameter being equal to the height of the liquid. The range of a jet issuing from either of the orifices B, C, or D will be equal to twice the length of the ordinates B F, C I, or D K respectively ; and therefore jets issuing from B and D will meet at a point H on a level with the bottom, and twice the length of the ordinates B F and D K. Now, as the ordinate C I is the great- FIG. IT. est, the range of the jet issuing from C will he greater than that of any other jet. The amount of water escaping in one second from an orifice would, theoretically, be equal to a cylinder having a diameter equal to that of the orifice, and a length equal to the distance