CENTRIFUGAL PUMPS 653 



In the forced vortex we have, considering the points (2) and (3) : 



W 2 



while due to relative outward flow we have 



W 2 g 2 g 



. 1/8 1/2 _ CO 2 Qy* ?2 2 ) _ V*3^ -- U^ . ^ 



20 



2 - 22 ,., 



Summing these and writing p 3 = p' 3 + p" Bt etc., we get the total 

 difference in pressure between the inlet and discharge edges of the vanes, 



a z_ 2 /a 2 cosec 2 y ( . 



~~ ~~ 



EXAMPLE. 



A pump, 1 foot diameter at inlet, 2 feet diameter at outlet. 6 inches 

 broad at inlet, 4 inches at outlet, discharges 5'0 cubic feet per second, 

 when making 200 revolutions per minute. Determine the rise in pressure 

 in passing through the wheel, and hence, neglecting all frictional losses, 

 the head pumped against. Assume y = 25 and neglect the effect of the 

 vane thickness. 



Here Q=/aXwXj=/ 8 X2irXj 



/. / a = i? = 3-18 f.s. / 8 = J = 2'386 f.s. 





Again, M . 8 = X b 1 Q X 2 = 20-96 f.s. 



and cosec 2 y = 5 '6 



Pt-Pt (20-96) 2 + (3-18) 2 - (2'386) 2 X 5*6 



_ A , Q . 



64-4 



.'. rise in pressure, p% p% = 6*48 X 62*4 = 404 Ibs. per square foot. 

 Head pumped against = 6'48 feet. 

 (b) Change of Pressure in Volute Chamber. Writing the gain of head in 



k k I'- 2 



this chamber as -^ (W + /a 2 ) feet = -^ - feet we have 



Total gain of pressure) !(,, si/-? 9 i j 



in pump =2-p^ + 3 2 +^-/^cosecVJft. (4) 



Experiments show that K has a value often as low as -10. With a well- 



