CENTRIFUGAL PUMPS 



647 



while u 2 = peripheral velocity of impeller at entrance. 

 i/ 3 = peripheral velocity of impeller at exit. 

 )8 = vane angle at entrance. 

 y = vane angle at exit. (Fig. 319.) 



In this discussion it is assumed throughout that the pump runs full at 

 all speeds within its working limits, the theory ceasing to apply if 

 any action of the nature of cavitation take place. The further assump- 

 tions are made that each particle of water, immediately before entering 

 the wheel, is moving radi- 

 ally, and that its initial 

 velocity of whirl w 2 is zero, 

 and also that all particles 

 of water on leaving the 

 impellers have the same 

 velocity and are moving in 

 directions which make the 

 same angle with the tan- 

 gent to the periphery at 

 the point of discharge. 



Form of Vanes. Just as 

 in the case of the turbine 

 all shock at entrance to the 

 vanes is to be avoided, 

 and, assuming radial flow 

 at the entrance, this gives 

 as a necessary condition 



for entry without shock- 



/I?' 01 o \ FlG - 319. Velocity Diagram for Vanes of 



Pump. 



/a = 2 tan /3. 

 The relative velocity of water and vane at entrance is then given by 



2 v r = / a cosec j3 = A// 2 2 -f- ^a 2 - 



If the angle /3 does not satisfy the above condition, there will be loss 

 by shock at entry. The magnitude of this may be approximately calcu- 

 lated, for the relative velocity of water and vane in the direction of rotation 

 before entering the wheel is i< 2 , while the relative velocity in the same 

 direction after entry is / 2 cot ft. The loss of head due to this change in 

 relative velocity is then approximately equal to 



fa -y/?) 2 fe et . (p . 83) . 

 The greatest source of loss in the pump, as compared with the turbine 



