176 IMP A CT AGA IX ST AN Y SURFA CE OF RE VOL UTION. 



If the surface is at rest, v^ = 0, and (6) becomes 



P = (1 -cos)v . (7) 



\s 



COR. 2. If a = the area of the cross-section of the 

 stream, and w = the weight of a cubic foot of the water, 

 the weight of the impinging water per second is 



W = (t>qp v t )aw, (8) 



which in (5) and (6) gives 



P= (l-cosaHvT^) 8 > (9) 



y 



and in (7) gives P = (1 cos ) v 2 (10) 



y 



That is, the impulse varies as the square of the rela- 

 tive velocity of the water, and also as the area of the 

 cross-section of the stream. 



COR. 3. The impulse of the same stream of water de- 

 pends principally upon the angle at which the water 

 moves off from the axis after the impact. 

 If the surface BAC is hollow, as in Fig. 

 52, the water after impact leaves the sur- 

 face in a direction opposite to that in 

 which it strikes it, and thus much more 

 work is done on the body with a surface 

 concave to the stream than on one convex 

 to the stream, since the work remaining in 

 the water on leaving the former surface 

 will be less than it is in the water on leaving the latter. If 

 = 180, we have cos a = 1, which in (5) and (6) 

 gives 



P = *(v*v i ),. (11) 



