4-26 Mr. Ivory's Notes relating to 



right tube; then, according to the authors mentioned, the 

 centrifugal pressure at the orifice will be equal to 



lg~ x ~^~' 



being the difference between the pressures at the distances r 

 and ? J , from the axis. 



II. Velocity with which the Fluid issues from the horizontal 

 Arm, supposing that v is the absolute Velocity of the Ori- 

 fice, 

 The velocity required is produced by the pressure of the 

 fluid in the upright tube increased by the centrifugal pressure. 

 Wherefore if h denote the length of the upright tube, sup- 

 posed to be kept constantly full, the sum of the two pressures 



mentioned will be = h + jj- ; and, if V denote the velocity 

 of the effluent water, we shall have, 



Tg 

 And, if we put & = 4 gf 9 then 



V 2 =* 4 £(/*+/) 



V 2 =*g(h+-^) = 4gh + v> 



III. Demonstration of Daniel Bernoulli's Proposition respect- 

 ing the Reaction of effluent Water (or, Cor, 2. prop. 36. 

 lib. 2. Principia). 

 Suppose that water issues from a small orifice in the side, 

 or bottom, of a vessel which is kept full ; let k be the height 

 of the surface above the level of the orifice: then, 2 V gk is 

 the velocity in a second with which the water issues ; and, if 

 a be the area of the orifice, the quantity of water discharged 

 in a second is equal to the prism a x 2 4/ g k ; and, as the 

 water issues with the velocity 2 \/ g k, the quantity of motion 

 in the water discharged in a second is equal to, 



a x2 \/gkx2\/gk = 2akx2g; 



and the same quantity of motion; viz. 2akx2g, is evidently 

 the reaction of the water projected in a second. But the prism 

 or weight, 2 a k 9 by falling, produces a quantity of motion equal 

 to 2akx2g in a second : wherefore the reaction of the pro- 

 jected fluid is equal to the weight 2 a k ; that is, to the weight 

 of a prism of the fluid having its base equal to the orifice a, 

 and its altitude equal to 2 k. 



This proposition supposes that the water has acquired its 

 complete velocity of projection, due to the head k. Before the 



efflux 



