se ROYAL SOCIETY OF CANADA 



This is balanced by a dead weight W at the end of the arm JDA. 



.-. IF . DA = -^^^ CD . cos a a — cos cp). 



g cos a \ rj 



Coefficient of discharge c,, = c,c,. 



.-. W . . DA = ' CI) . (1 — cos cp). 



Of these quantities the weight of water W is determined bj weigh- 

 in<'- ; the distances between centres DA and CD are known ; while the 

 ai-ea of the oritice S, the theoretical velocity of ettlux of the water, the 

 angle q) through which the water is turned by the bucket, and the values 

 of <j and p are also known. 



It is difficult to obtain a fair value of the coefficient e„; so the course 

 has been taken of including it in a coefficient CJ, which is that given in 

 the following results as the coefficient of impact. 



.^ _ _ ^ 1 Wg_ 



•■• Cj - c,.C: - ^,^ ■ ^^ _ ^.^. ^^ cpSv'' 



Bvit v'- = 2r//i if h is the head of water in the tank. 

 DA 1 W 



.-. a = 



CD (1 — cos (p) 2c,ipSh 



One object of the experiments described is to deterinine the com- 

 parative effect of the impact of the same jets of water on surfaces of dif- 

 ferent shapes. To make this compai-ison, the forces of impact on the 

 various vanes are compared with the effect on a flat plate, or the case 



71 



where Q—^- 



This gives a further sei"ies of coefficients which may be known as the 

 Comparative Coefficient of Impact. The formula from which they are 

 derived is — 



^* - CD ■ 2capSh 



In the case of the flat vanes the effect of the dead weight of the mass 

 of water on the vane is considered, and the coefficients are given after 

 eliminating this ettect. This is not done for the curved vanes, as it would 

 be a very difficult matter to estimate what the effect due to gravity 

 would be ; and, further, the gravity effect is always with and almost 

 inseparable from the impact effect. 



The velocity has a considerable effect on the coefficient of impact, 

 and so the velocity is given in each case in the tables of results. 



The first table given consists of the coefficients of impact for flat cir- 

 cular plates of various sizes. It affords information as to how the area of 

 flat surface and the velocity affect the actual force of impact. The effect 



