284 HYDRAULICS AND ITS APPLICATIONS 



Differentiating this with respect to -j, and equating the result to zero 

 we have the condition that the K. E. should be a maximum. This gives 1 





the dimensions being taken in ieet. 



If for example the pipe supplying the nozzle of a Pelton wheel be 1 foot 

 in diameter and 500 feet long, the maximum K. E. is delivered when 



a ~ I 



iv- 



8 X 500/ 

 and if/ = '01 this becomes 



a d 2 



By substituting this value of -r or of -=-5 in equation (7) above, the value 



A JLJ 



of this K. E. is given. 

 Thus (K. E.) max . 



o 



H 



= 395 X -158 -j 4 X -01 X 500 X ('158) 2 \ ft. Ibs. per sec. 



1 



= 62-4 ' H 



1-50 



= 34 H* ft. Ibs. per second. 



If the Pelton wheel have an efficiency of 80 per cent, the work done by 

 the wheel per second will be given by 



8 X 34 H% ft. Ibs. 

 27-2 3 

 = -KKH horse-power 



- '0495 H^ horse .power, 



_ 4fl a*\_a 3 



~ -' X 



Equating this to zero we have 



12 f I tf = 1 + *JJtf 

 D ' A 1 I) A* 



a? D 



With a circular noz/,le this makes d *= * 



