Chemical and Physical Papers. 85 



the water in the bucket, and to the fact that the reversed stream of 

 water must clear the next bucket, this ratio is something less than 

 one-half. 



It is evident efficiency will fall off as we either increase or de- 

 crease the value of the ratio of bucket velocity to spouting velocity 

 from this most eflBcient value. 



In figure (2) the values of the ratio of bucket velocity to theo- 

 retical or spouting velocity (called^) have been plotted horizon- 

 tally and the efficiencies vertically for every increase of 10 feet in 

 head between 20 and 157.7 feet. A single line averaging the heads 

 above 60 feet has been drawn. It will be noticed the points for 

 any one head may fall both above and below this line, so that for 

 the practical working limits of the wheel the efficiency varies as 

 the ratio ("i^). 



RELATION OF HORSE-POWER AND HEAD. 



The theoretical horse-power of a wheel =-^^k"= -^-^' where (w) = weight 



ooU o . o 



of discharge in pounds per second. 



(3) The actual or brake horse-power =P= \-^ ' where (E)= efficiency. 



o o 



Combining (1) and (3): 



(4) p^ cayl2grh-i/^E 



8.8 ' 



It is apparent if c and E are constants, and if <^ remains con- 

 stant, the power of the wheel will be in direct proportion to the 

 three-halves power of the head, or — 



(5) ^ - -^• 



This reduces to — 



Pi h 3/2 



(6) P = 



In figure (8) brake horse-power has been plotted vertically and 

 velocity ratio {'P) horizontally for each of the heads considered in 

 figure (2). The maximum horse-power for each head occurs at 

 practically the same value of ^ ( = 0.45 ). 



The values of brake horse-power for each head, when ^ = 0.45, 

 was used to plot the curves of figure (4). In figure (4) a straight 

 line was first obtained by using the three-halves powers of the 

 heads and brake horse-powers as coordinates; the curve between 

 head and brake horse-power being drawn from this line, and the 

 experimental points then put in. This curve shows the brake 

 horse-power will vary as the three- halves power of the head when 

 •^ is a constant. 



