IMPACT OF JETS 377 



For maximum efficiency -, = 



.-. 2(v u) 2 4(9 M)W = 



either v u or v w = 2 u 

 so that v = 3 u. 



In the first case the velocity of the jet is unchanged and the work done 

 on the vane is zero. In the second case we have : 



Work done on vane = - - ( - v \ ^ ^ (1 cos a) ft. Ibs. per sec. 

 9 ^ ** / * 3 



= 27 - v 8 (1 cos a) ft. Ibs. per sec. 



o 



.-. Efficiency (max.) 07 (^ ~ cos a )- 



This has its greatest value when a = 180, and then equals ^=. 

 When a = 90, i.e., in the case of normal impact on a single flat plate, 

 we have, as before, the maximum efficiency when u = 5, and then 



efficiency (max.) = -~=. 

 a % 



(2) Impact on a Series of Moving Vanes. 



If, instead of a single vane, we have a series of vanes successively 

 placed in the path of the jet at frequent intervals, the weight of water 

 striking these vanes per second becomes W A v Ibs. 



If the vanes form surfaces of revolution having their axes in the line 

 of action of the jet, neglecting losses due to splash we have, if a be the 

 angle through which the stream is deflected : 



Change of momentum ) , . 



per second in direction r = - - (v ?/) (1 cos a) 

 of jet 



. * . Total pressure on vanes = - - (v u) (1 cos a) Ibs. 



tS 



Work done on vanes per 1 W A v u , 



second f '- -j <* " a) < X - cos > ft lbs - 



ro/v, 2 (v n) (v -) (1 cos a) 

 .'. Jiniciency = ^ L 



For maximum efficiency y-^ = 

 . * . v (v ) r u 



