666 HYDKAULICS AND ITS APPLICATIONS 



TTf 



H' be replaced by , the deductions also apply to the compound 



pump. 



The work done on the shaft per Ib. of water,) n w 3 u- A , 

 neglecting frictional losses, is now given by} g 



the manometric efficiency r?' bv - 



" n iv 3 u 3 



while neglecting friction ^the power required) W Q TV r> TT p 

 to drive the pump 550 V ' 



B - H - P - 



ART. 178. GENERAL EQUATION FOR PUMP. 



From equation (11), p. 658, we have 



2 g H' = 7/ 3 2 + kv - / 3 2 cosec 2 y 

 for any pump, and since v 3 ' 2 = iu^ -f- / 3 2 



= (WB /3 cot y) 2 + yij 2 

 the foregoing relationship can be written 



2(/ H' = A % 2 + B u 3 / 3 + C/ 3 2 



= a A 72 + 6 N Q -f c (/. 



Where AT = revs, per min. ; Q = discharge ; and where A, B, C, a, b, c, 

 are constants for any particular pump. It follows that if the speed, the 

 discharge, and the head be measured for three different speeds, discharges, 

 or heads, the values of these constants may be obtained and the discharge 

 calculated for any other speed or head and vice versa. 



ART. 179. PERIPHERAL SPEED OF A PUMP. 

 If H' = total head pumped against, including friction head, we have 



us (MS /a cot y)' 



so that with a perfect pump in which all losses were negligible, the 

 peripheral velocity of the vanes at discharge would be given by 



w-a Oa /a cot y) = g If. 



and with radial vanes we should have u 3 = */ g H'. As y diminishes 

 the peripheral speed increases, while any diminution in efficiency 

 naturally necessitates a higher peripheral speed again, so that actually 

 we have MS = k ^/ g //', where k depends upon y ; upon the value adopted 

 fory 8 ; and upon the type of pump. In practice it. is usual to make 

 / 3 from [*2 to '3] u 3 , the co-efficient increasing from about "21 when 

 y = 15 to '29 when y = 90, while k is given a value between 1'2 and 



