86 Kansas Academy' of Science. 



In equation (6), if we make hi = 1 — 



(7) P = Pi /i V^ where Pi = B. H. P. under one-foot head. 

 That is, the horse-power that can be developed at any head will 



equal the power at one-foot head multiplied by h''/-. 



RELATION OP REVOLUTIONS AND HEAD. 



The bucket velocity of a wheel is — 



^D N 



(8) V' = , 



^ ' 12x60 



where N = Revolutions of wheel per minute. 

 D = Diameter of wheel in inches. 



Also spouting velocity is equal- to — 



( 9 ) V = ^lYgh . 

 Combining, ( 8 ) and ( 9 ) : ' 



-DN 



( 10 ) - = ~ = ^. 



V 720 X 8.025 <h 



As equation ( 10 ) is general, it follows that when ^ is constant — 



DN 



( 11 ) — — — = 184.1.6 <(> = a constant. 



\ h 



"The catalogue speed, power and discharge of each series of 

 wheels, as given in the catalogues of the manufacturers, are usually 

 based on the conditions of maximum efficiency and constant <'/'. 



"From the above considerations it follows that in any homogene- 

 ous series of wheels, that is, in any series of wheels constructed on uni- 

 form lines and with dimensions proportional, the wheels of the series 

 are designed to run at the same relative velocity, and therefore — 



"That is to say: In any homogeneous series of turbines " (true, 

 also, of the Pelton wheel ) "the product of the diameter of any 

 wheel {-D), and the number of revolutions {N), divided by \'A, will 

 be a constant, provided 'P remains constant. 



"If, in equation (1*2) D — Di, the equation reduces to — 



(13) ^ = ^ 



"That is to say: The economical speed of any wheel will be in 

 direct proportion to the square root of the head under which it acts. 

 "If in equation (13) A = l, the equation reduces to — 



(14) N=Ni v/i. 



"From which it follows that the revolutions of a wheel {N) for 



