THEOKY OF TURBINE DESIGN 



535 



This gives the velocity of whirl, and the peripheral speed of the wheel 

 for maximum efficiency, in terms of the available head H. r 



The effect of any variation in a or (3, on the peripheral speed for maxi- 

 mum efficiency, is shown in the following table, which gives the theoretical 

 values- of k (where ii z = k V 2 g H') in the case where / 2 = f 3 . 



On the assumption that w 3 = o and that the loss at entrance is zero, the 

 maximum theoretical efficiency w of a turbine is given by 



WQ 



1 - 



_ work done per second by water _ g 



energy supplied per second W Q H ' 



tan a 

 tan ft 



/ 1 _ tana \ 

 V tan B I 



21- 



\ , V r a 

 ) "' O~.r2 



tan a 



tSajS/ ' &3 2 ?' 3 2 

 1 



1 i i / ^2 ?2 \ 2 tan 2 a 

 + i U7^) 1 _tana 



(10) 



tan 



This gives the hydraulic efficiency of the machine, and does not take 

 into account losses due to mechanical friction in the turbine. The actual 



