THE CENTRIFUGAL PUMP. 291 



Let h be the height to which the water is raised, meas- 

 ured from the level of the water in the well to the centre 

 of the orifice of discharge, v the velocity of discharge through 

 the orifice, and V the velocity of the orifice in its circular 

 path, as in Art. 158. Then the work due to the centrifugal 

 force must equal the work of raising the water through the 

 height h, increased by the work stored in the water at 

 efflux ; therefore 



(1) 



and v V= W* tyli- V 



[as in (2) of Art. 158]. 



Now the work applied per second to raise each lb. of 

 water must equal the work in raising the water through the 

 height //, increased by the work remaining in the water 

 after leaving the machine. Hence 



(v - F) 2 

 applied work = h + - = ' 



"9 



__-_!. (s) 



9 



The useful work is h foot-pounds per second ; therefore 



efficiency = -. - (3) 



= 1 - ^ - etc., (4) 



which increases towards the limit 1 as F increases towards 

 infinity. Neglecting friction, therefore, the maximum 

 efficiency is reached when the pump has an infinitely great 

 velocity of rotation, as in the case of the reaction wheel. 



