658 



HYDRAULICS AND ITS APPLICATIONS 



M 3 2 + /2 2 ,/3 2 cosec 2 y -f- k r } 2 



2 8 (. 3 t / 3 cot y) 

 where 7c has the value indicated in the preceding article for the type of 

 pump under consideration. 



The various cases will now be considered in greater detail, and as, 



except for very low lifts, -^ is small in comparison with H' while v is 



9 



approximately equal to/ 2 , the foregoing expressions will be simplified by 

 writing 



a 2 ff cosec 2 y . ( increase of pressure ) TT , . 



f- 1 , , . . ,, 1'L ieei 

 2 g ( after leaving impeller ) 



A i W /a 2 cosec 2 y 4- A; ?' 3 2 



ana ?/ = ~- -'- (121 



2 MS ( UQ Ja cot y) 



(1) Pump without Special Provision for Utilizing the Kinetic Energy 

 of Discharge from the Impeller. Here k = o, and if the pump be working 

 so that water enters without shock, 



~ * cosec 



While 

 so that 



3 (u 3 cot y 

 ' = w 3 2 -/ 3 2 cosec 2 y 

 = V " 



H' + f "cosec 

 If y = 90, ?'.^. with radial vane tips. 



(18) 



(14) 

 (15) 



a value which is always less than 50 per cent. 



If y is very small cosec y = cot y (approx.) and we have 



UQ 



Since / 3 cot y or/ 3 cosec y approximates more nearly to u a as y diminishes, 

 the theoretical efficiency in this case approximates to a value unity. 



Usually / 3 is taken as some definite fraction, commonly from \ to j of 

 A/2 g H', and the following table shows how rj f varies with y for these 

 values of / 3 . 



