378 



or 



HYDKAULICS AND ITS APPLICATIONS 



Efficiency (max.) = 



v = 2 n 

 X " (1 - cos a) 



1 COS a 



This is a maximum for a = 180, i.e., with a series of hemispherical 

 cups and then equals unity. With a series of flat plates having normal 

 incidence a = 90 and the efficiency equals '5. 



ART. 108. IMPACT ON ONE OF A SERIES OF KECURVED VANES WHOSE 

 DIRECTION OF MOTION MAKES AN ANGLE WITH THAT OF THE JET. 



This problem is one of much importance in the design of impulse 

 turbines. Let a be the angle between the directions of v and of u, and 



FIG. 169. 



let 6 be the total angle through which the vane is recurved (Fig. 169). 

 Then if, as is usual, the incidence is tangential, the relative velocity v r of 

 jet and vane at impact is given by 



v* = v* + u? %vu cos a (triangle a b c.) 



and, neglecting friction and eddy losses, the relative velocity at discharge 

 will be the same as this. 



