648 



HYDRAULICS AND ITS APPLICATIONS 



is, however, due to rejection of kinetic energy in the discharge from the 

 impeller, for while this is comparatively unimportant in the turbine, it 

 becomes of the greatest importance in the pump, since it is when leaving 

 the wheel that the water is moving with its maximum velocity, At the 

 best, only a portion of this energy of discharge can be recovered by means 

 of a vortex chamber or guide vanes, and it is therefore advisable to reduce 

 the velocity of discharge to as low a point as is compatible with efficiency 

 in other directions. This may be done by curving the vanes backward at 



their tips, so as to make 

 the discharge angle y 

 (Fig. 320) less than 90. 

 The relative velocity of 

 water and vane at dis- 

 charge then has a tan- 

 gential component in the 

 opposite direction to that 

 of the wheel's rotation, 

 this component increasing 

 as y is reduced, the result 

 being that the absolute 

 velocity of discharge is 

 reduced. Thus, for ex- 

 ample, in Fig. 320 the 

 s'^/f | / triangles of velocity are 



drawn for the cases in 

 which the vanes are re- 

 spectively radial, curved 

 forward at exit, and curved 

 backward at exit. In each 



case the same value has been adopted for / 3 , the velocity of flow at 

 exit, and for w 3 the peripheral velocity of the vanes, while a c represents 

 the direction and the absolute velocity of discharge. 



A comparison of the diagrams will indicate how this diminishes as the 

 angle of backward inclination of the vane tips increases. 



As will be seen later, however, the necessary peripheral speed of the 

 wheel for pumping against a given head increases as y is reduced, and 

 this causes the frictional losses, which vary approximately as w 3 , to 

 increase. 



This backward curvature of the vanes offers a further advantage in that 

 it gives passages of more uniform cross section. This reduces the diver- 



320. Velocity Diagram for Vanes of a Centrifugal 

 Pump. 



