ON HYDRAULIC PRESSURE. 229 



diately derived from the reaction of the vessel, or of some fixed obstacle ; for 

 "it is obvious that a vertical force, like that of gravity, cannot of itself pro- 

 duce an oblique or a horizontal motion. 



If a small stream descends from the bottom of a vessel, the weight expended 

 in producing its motion is equal to that of a column of the fluid standing 

 on a base equal to the contracted orifice, and of twice the height of the 

 vessel. Thus, if the vessel be 16 feet high, the velocity of the stream will 

 be 32 feet in a second, and a column 32 feet in length will pass through the 

 orifice in each second, with the whole velocity derivable from its weight 

 acting for the same time ; so much, therefore, of the pressure of the fluid in 

 the reservoir must be expended in producing this motion, and must of course 

 be deducted from the whole force with which the fluid acts on the bottom of 

 the reservoir ; in the same manner as when two unequal weights are con- 

 nected by means of a thread passing over a pulley, and one of them begins 

 to descend, the pressure on the pulley is diminished by a quantity, which is 

 as much less than the sum of the weights, as the velocity of their common 

 centre of gravity is less than the velocity of a body falling freely. If the 

 stream issue from the vessel in any other direction, the effect of the dimi- 

 nution of the pressure in that direction will be nearly the same as if the 

 vessel were subjected to an equal pressure of any other kind in a contrary 

 direction ; and if the vessel be moveable, it will receive a progressive or 

 rotatory motion in that direction. Thus, when a vessel or pipe is fixed on a 

 centre, and a stream of water is discharged from it by a lateral orifice, the 

 vessel turns round at first with an accelerated motion, but on account of the 

 force consumed in producing the rotatory motion, in successive portions of 

 the water, the velocity soon becomes nearly stationary. (Plate XXI. Fig. 

 272.) 



From similar reasoning it appears, that the effect of a detached jet on a 

 plane surface perpendicular to it must be equivalent to the weight of a 

 portion of the same stream equal in length to twice the height which is 

 capable of producing the velocity. And this result is confirmed by expe- 

 riments : but it is necessary that the diameter of the plane be at least four 

 times as great as that of the jet, in order that the full effect may be produced. 

 When also a stream acts on an obstacle in a channel sufficiently closed on 

 all sides to prevent the escape of any considerable portion of water, its 

 effect is nearly the same as that of a jet playing on a large surface. But if 

 the plane opposed to the jet, be only equal to it in diameter, or if it be 

 placed in an unlimited stream, the whole velocity of the fluid column will 

 not be destroyed, it will only be divided and diverted from its course, its 

 parts continuing to move on, in oblique directions ; in such cases the pres- 

 sure is usually found to be simply equivalent to the weight of a column equal 

 in height to the reservoir, the surface being subjected to a pressure nearly 

 similar to that which acts on a part of the bottom of a vessel, while a stream 

 is descending through a large aperture in another part of it. (Plate XXI. 



Fig. 273.) 



* It is obvious that in all these cases, the pressure varies as the square of 



the velocity, since the height required to produce any velocity is proper- 



