HYDRAULICS. 



columns which descend from near the 

 outsides of the vessel, by turning up 

 again to reach the discharging orifice, 

 are thrown into a more direct opposition 

 to the motion of the central descending 

 columns, at the same time that they are 

 themselves constrained to turn suddenly 

 in opposition to their inertia before they 

 can enter the pipe ; and thus the dis- 

 charge is more effectually impeded than 

 if it were proceeding from a mere hole 

 through a thin bottom. 



Sir Isaac Newton investigated the 

 curves in which a fluid will proceed 

 from the interior of a reservoir to a 

 discharging orifice in its bottom, and 

 found that the solid figure produced by 

 the streams flowing from all parts to 

 one common centre, viz. the orifice of 

 discharge as indicated by the dots in 

 B, was an Hyperboloid of the fourth 

 order ; and Venturi, from finding the 

 great difference of discharge through 

 the same area of opening as before 

 stated, determined on applying a dis- 

 eharging-pipe of this, the natural form 

 of flowing water, to the bottom of a 

 reservoir as shown at C, when he found 

 that although the bottom orifice q was 

 the same as before, the quantity dis- 

 charged was increased to ninety-eight 

 quarts in the same period of time : and 

 conceiving that the curve which water 

 naturally assumes in running was con- 

 tinued beyond the point of discharge, 

 he likewise enlarged the lower or dis- 

 charging end of the delivering pipe by 

 making it bell or trumpet mouthed in 

 the same curve, as at D ; and from this 

 form he obtained the maximum quan- 

 tity of water that could be delivered 

 through a given orifice. 



It will be evident that these examples 

 dp not refer to extended lengths of 

 pipe, but merely to the rapid discharge 

 of water from reservoirs, and they are 

 merely given here to show by what 

 simple means the flow of water may be 

 impeded or increased in practice. 



As water in descending is actuated 

 by the same laws as falling bodies, it 

 follows that its motion will become ac- 

 celerated : therefore, in rivers or open 

 channels, the velocity and quantity 

 discharged at different depths would 

 be as the square roots of those depths, 

 did not the friction against the bottom 

 of the channel interfere and check the 

 rapidity of flow which would otherwise 

 take place at that part, but by which 

 a uniform, straight-forward velocity is 



produced. Thus, mfig. 2, if A B C D 

 represents a reservoir of water, and 

 B C G I a canal leading therefrom, and 

 sloping from the prolonged horizontal 

 line A B H, the bottom water at C 



would have a velocity as the square 

 root of the depth B C. The water at E 

 would flow with a velocity proportioned 

 to the square root of the depth F E, 

 and that at G as *Jttl3r, while the top 

 water at I would have a less velocity, 

 or one only equal to the bottom water 

 at E ; because the point E is the same 

 depth as the point I from the level line 

 A B H. The same law holds good 

 with respect to the spouting or flowing 

 of water through jets or adjutages. 

 Thus, if D is a hole made in the side of 

 the vessel of water A, fig. 3, the water 



fa*. 



at D would only be pressed by the sim- 

 ple weight of the perpendicular column 

 of water from A to D ; but when the 

 orifice D is opened and the water is 

 permitted to spout out, its motion 

 throws the whole column into effect, 

 and it will now press upon and dis- 

 charge the water from D, with the 

 same force as if the water had been 

 a solid, descending from A to D, i. e. 

 as the square root of the height A D ; 

 and, for the same reason, any water 

 issuing from other orifices, as C and B, 

 would run in quantities and velocities 

 proportionate to the square root of the 

 depths of such orifices below the sur- 

 face of the fluid. Now the quantity of 

 water spouting from any hole in a 



