Sand in cutting hard Material. 341 



and^= BJ 



.\ substituting in (2), we have 



•--P=\/-.v (4) 



V 9 



This, then, shows the relation between the pressure, velocity, 

 and nature of the body. 



If u is the velocity of impact and X 1 , d' are the elasticity and 

 density for the other body, we have 



P =^£. { u-v); 



V9 



and if the bodies are of the same material, we shall have 



u 



v =% 



If, however, they are of different materials, 



/Xd /7Jd' t v 



.-.v= y**' u, .... (5) 



from which v may be found when u is known. 



We now come to the case of a liquid When a liquid is pro- 

 jected against a surface, the pressure must be such as to overcome 

 the momentum of the liquid ; and in the case of continuous mo- 

 tion, if the pressure were uniform over the surface in contact we 

 should have 



v 2 d 2 

 P=2j-v* ....... (6) 



And in the case of impulsive motion it is clear that the pressure 

 cannot be less than this. 



Hence if a stream of fluid B strikes a solid A, we have at the 

 first instant 



2(7 v ' V a 



'-9 v 9 



from which we can find v when u is known. 



