442 HYDRAULICS AND ITS APPLICATIONS 



ultimately tend to the circular, and in doing so tend to become 

 unsteady. 



(3) Sharp corners and uneven curves in the buckets cause loss of energy 

 by eddy formation. 



(4) Splash on entering buckets, if unsuitably designed (reduced by 

 reducing the number of buckets). 



(5) The jet, being placed tangential to the pitch circle of the buckets, 

 meets and remains in contact with each bucket in turn through some 

 appreciable angle of rotation. The angle at which the jet meets the 

 bucket, and also the angle of discharge, will in consequence vary as the 

 wheel rotates, and it follows that unless the buckets are designed so as to 

 give normal impact on the ridge and a discharge which is tangential to 

 the wheel, and unless the speed of the wheel is regulated so that the back- 

 ward velocity of discharge is equal to the forward velocity of the buckets, 

 an excess of kinetic energy will be rejected to the tail-race. 



Theoretically, assuming the angle of deflection to be 180 and neglecting 

 the effect of friction, the most efficient speed of the buckets is one half 

 that of the jet (p. 378). When allowance is made for the effect of friction, 

 as on p. 371, the most efficient bucket speed is seen to be slightly less 

 than this. In practice the most efficient bucket speed is found to be from 

 44 to *48 times that of the jet, the higher ratio being possible with the 

 more efficient buckets. 



Efficiency of Pelton Wheel. 



Let u = peripheral speed of buckets at pitch circle. 



2 TT r N 



= ^r where r perpendicular distance from axis of jet tc 

 ou 



centre of wheel ; N = revs, per minute. 

 Let r = initial velocity of jet. 

 Let v> 2 = final absolute velocity. 



Let \v r = relative velocity of jet and bucket at entrance. 

 Let gv r = relative velocity at discharge. 



Let a = mean angle between jet and tangent at point of contact. 

 Let y = total angle of deflection of jet. 

 Then initial velocity of jet in direction of tangent ) 



, - - . |=1? COS a. 



at point of impact 



Component, parallel to tangent at discharge, of | 



final velocity relative to bucket 

 /. Absolute velocity in this direction at discharge = u -\- %u r cos y. 





