84 Kansas Academy of Science. 



DISCUSSION OF A PELTON WATER-WHEEL TEST 



MADE AT THE UNIVERSITY 



OF WISCONSIN. 



By Chas. I. Corp, University of Kansas, Lawrence. 



'^I^HIS discussion is the result of a series of tests made at the 

 -■- University of Wisconsin in the summer of 1908. The work 

 was a continuance of au investigation by Prof. D. W. Mead to find, 

 if possible, an algebraic equation between the head, horse-power 

 and revolutions of a water-wheel. 



He shows in his book on Water Power Engineering some rela- 

 tions between discharge, head, velocity-ratio, etc., which hold for 

 the low-head exjoeriments on which he bases his conclusions. 



It is the purpose of this paper to show that, for the Pelton wheel 

 at least, these relations hold for higher heads, and also to work out 

 the equation spoken of above for the wheel used. 



RELATION OF HEAD AND DISCHARGE. 



We know in the case of the nozzle of a Pelton wheel — 



(1) q = ca\2gh 



where q = discharge in cubic feet per second. 

 c = coefficient of discharge. 

 a = area of the nozzle. 

 g — force of gravity. 

 h = head in feet on the nozzle. 



If the buckets of the wheel are sufficiently removed from the 

 nozzle not to affect its discharge and the coefficient of the nozzle is 

 a constant, the discharge will vary as the square root of the head. 

 Figure (1) shows this relation nicely. The experimental points 

 were first plotted, using the square root of the heads as the vertical 

 ordinates and discharges as the horizontal ordinates. If the relation 

 sought holds true these points will lie on a straight line through 

 the origin. This is shown to be the case. The points for the curve 

 between the heads and discharges were taken from this straight 

 line. The points indicated by circles along this latter curve are 

 experimental points. 



RELATION OF RATIO {<P) AND EFFICIENCY. 



Theoretically, the velocity of the buckets of the Pelton wheel 

 should be one-half the theoretical or spouting velocity of the water 

 to work most efficiently. Actually, due to eddies and friction of 



