Chemical and Physical Papers. 87 



any head (A) is equal to the revolutions (iVi) for one-foot head 

 multiplied by VA."* 



This relation ■ might also have been shown by means of curves 

 from the test at hand. 



EQUATION BETWEEN HORSE-POWER, REVOLUTIONS AND HEAD. 



2 7rrLN 

 (15) Brake horse-power = P= 



33,000 



where r = Length of brake-arm in feet. 

 L = Load on the brake in pounds. 



We have shown that under the usual assumed conditions of 

 maximum efficiency and constant <?, ]Vi=]Vi ^|/l and P=P\ h^f\ 

 so that equation (15) may be written in the form — 



T~, . ,..,1^2 -rL CL ^ ^ 2- r 



tor simplicity let 7— — r-y = -^— . where C = — = a constant, 



^ -^ 33,000/1 h 33,000 



, -^ 

 and — - = n = revolutions per minute under one-foot head. 



C L 

 Plotting the values of -r- as the vertical ordinates and of {n) for 



the horizontal ordinates for the various heads previously considered, 

 figure (6) will result. In this as in figure (2) the points for heads 

 above 60 feet fall along a general line, which has been drawn in: 



The product of the horizontal and vertical ordinates of any point 

 on this curve will be the brake horse-power of the wheel under one- 

 foot head and having the revolutions indicated by its horizontal 

 ordinate. 



. The general algebraic formula connecting two variables such as 

 — r— and (?i) is — 



(17) CL 



—j— = a + on + en- +, etc., 

 ti 



where a, h, 0, etc., are constants. 



It was found that an equation having three terms on the right 

 side of the equality sign gave a curve which corresponded suf- 

 ficiently close to the experimental curve for practical purposes. 



The constants a, h and c were obtained by choosing three points 

 on the experimental curve and substituting the values of their co- 

 ordinates in the general equation above. The resulting three sim- 

 ultaneous equations were solved, giving as the equation of the curve: 



CL 



(18) -- = . 000106 -.0000009376w-.00000000266w-^. 

 h 



*" Water Power Eng-ineering, " by Mead. 



