376 HYDRAULICS AND ITS APPLICATIONS 



In genera], with a plate having a diameter from two to three times that of 

 the jet, the total pressure exerted will exceed 90 per cent, of the theoretical. 



ART. 107. IMPACT ON MOVING VANES. 



Let v be the velocity of the jet in feet per second. 



,, u be the velocity of the vane in the direction of motion of the jet. 

 Then the relative velocity of jet and vane = v u. 



FIG. 168. 



(1) Impact on a single vane curved through an angle a, and moving in the 

 direction of the jet (Fig. 168). 



Here the weight of water i TT7 . . 

 ,.,.,, \ W A (v u} Ibs. 



striking the vane per sec. I 



Initial momentum in) W A (v u} v 

 direction of motion I g 



Final velocity in direc-) 



, \ . \ = U + (V - u) COS a 



tion oi motion j 



. . Final momentum in | W A j , 



-,. ,. ,. \(v u) u 4- (v uY cos a i 



direction of motion ) // 



.'. Change of momentum) W A ,. 



. ,,. ,. ,. f = - \( v ~ u ) L v u ( v u ) cos a 



in this direction g 



rr xl / \ O / - \ 



= : (v u)* (1 cos a) 



/ 



W A 

 . ' . Work done on vane = - - (v u? (1 cos a) u ft. Ibs. per sec. 



, r 



Initial kinetic energy of) W A v 3 .. 



, - it. IDS. 



jet 2 g 



-p^v, . 2 (v ?j.) 2 (1 cos a) ?/ 



.*. Efficiency = - ^ - = r;. 



