THEOKY OF TUEBINE DESIGN 559 



so that the peripheral speed for maximum efficiency is approximately 

 half that due to the supply lead. 



Since the kinetic energy rejected at discharge increases with an increase 

 in / 3 , it is necessary to keep this as small as possible, so that in practice 

 the vanes are usually designed to give k a value between \ and J, while /g 

 is given a value about *40 V 2 g H'. On this assumption, we have 

 w 2 * = C*x2gH'-tf 

 = 2gH f I <7 V 2 -16} 

 = -781 X 2 g H' 

 /. w 2 = -884 V 2 g H'. 



Again, = tan a 



a = 24 24' (approximately). 

 Assuming k = J, and writing (2) in the form 



_ IT, (1 ~ IP)/,* 



Vi ~ "2 2tt> 2 

 thia becomes on substituting 



u a = ^{ l+ftan 2 a } 



= -577 iv z = '525 C v V 2 g H' ; 



so that the peripheral speed of the wheel is slightly greater than half 

 that corresponding to the supply head. 

 Again, since /a cot ft = w^ u% 



= tog (1- -577) 

 we have cot ft = '423 cot a 



-s 



.-. ft = 47 (approximately). 

 Again, /a = % tan y 



fo 



= 1*2 . tan y. 



7*2 



In the case of an axial flow turbine r a = r 2 , so that 



/s = *a tan y 



tan a 



i 



tany = -^ = 



1*2 Oil M?2 



= ;=== tan a = -393 

 /. y = 21 30' (approximately). 



