664 



HYDKAULICS AND ITS APPLICATIONS 



Putting K = I, i.e., neglecting losses in the whirlpool chamber, this 

 reduces to 



, _ ?/ 3 2 (2 - c 2 ) -/ 3 2 c 2 cosec 2 y - 2 u 3 f 3 cot y (1 - r 2 ) 



2 (% 2 u 3 / 3 cot y) 



Assuming / 3 = J u 8 , the following table traces the variation in this 

 efficiency with a change in y in the ideal cases when K = 1, and when 



From these results it is evident that with an efficient whirlpool 

 chamber there is very little advantage to be gained by giving the 

 vanes any considerable backward curvature. Moreover, as these 

 efficiencies do not take into account friction losses which increase 

 as y diminishes, the actual advantage is less than appears from the 

 table. 



(3) Pump with Guide Vanes or Diffuser Ring. As previously mentioned, 

 experiments tend to show that with well designed guide vanes on the 

 discharge side of the wheel, up to 75 per cent, of the kinetic energy of 

 discharge may be converted into pressure energy, so that the gain of 



energy per pound in the guide passages will be given by - ^ 



where k has a maximum value of about '75. 



The total gain of pressure head in the pump is now equal to 

 k (w 3 2 -f- /a 2 ) i u f H~ /a 2 ~ /s a cosec 2 y __ jp i ^ 



2 # Zg % g 



Assuming v = / 2 and putting w 3 = u 3 / 3 cot y, we get : 



k (ti-s - / 3 cot y) 2 + % 2 - / 3 2 cosec 2 y + fc/ 3 2 = 20 IV (20) 

 or 2 g H' = u 3 z (k + 1) +/s 2 cosec 2 y (k - 1) - 2 k u 3 f 3 cot y. 



1 No whirlpool chamber. 



