660 HYDRAULICS AND ITS APPLICATIONS 



On differentiating equation (17) with respect to H', we finally get : 

 d_Q _ _ <l A 2 in 2 



and, therefore, other things being equal, , will have its least value 



when sin y has its greatest value, i.e., when y 90 ; that is to say, the 

 change in delivery head corresponding to a change in the volume] 

 delivered by the pump, will be least when radial tipped vanes are- 

 ussd. 



This is of importance in the case of a high-lift pump used for boiler 

 feed purposes where the quantity pumped may be varied, but where the 

 delivery pressure is required to remain approximately constant, and for 

 this purpose radial vanes are most suitable. The same reasoning applies 

 to the case of pumps for elevator work, where the delivery pressure is to 

 bs approximately constant. 



Also, where a pump is required for dry dock or similar work, the 

 possibility of obtaining a large increase in Q as II diminishes with the] 

 emptying of the dock, renders the radial vane type most suitable, forj 

 although the increased volume necessitates a largely increased power,, 

 this is in general unimportant as compared with the reduction in the 

 time necessary to empty the dock. 



W 7 here a pump is electrically driven, however, this large increase in 

 power with a reduced head involves the danger of overloading the motor 

 and this is more particularly the case when induction motors are usefl 

 and where speed variation is in consequence impossible. In such a case 

 backward curved vanes are essential, for, since the horse power is proper- ] 

 tional to H' Q and therefore to 



H' As sin y V "a 2 20 If 

 we get, on differentiating, 



d (H' Q) _ ( u/ 3 (i H' | 



This expression diminishes with y, and indicates that the rate of increase 

 of the horse-power with a diminution of head is less the smaller the value 

 of y. 



Again, with a pump initially designed to work against a certain head, 

 if the vanes are radial, the possible diminution in speed is very small, but 

 increases as the backward curvature of the vanes increases. With radial 

 vanes, indeed, the pump ceases to lift altogether when the speed falls 

 slightly below that corresponding to normal working. It follows that 

 where the working head cannot be accurately predetermined, the pump 



