The pressure forces acting on the control volume surface are equal to the 

 time rate of change of linear momentum, M, of the fluid within the control 

 volume. For steady incompressible flow, one obtains 



S +S +S_ Control volume C.V. 



- j (p!t)dS =~ J M d\r 



"^ ^^ ^'^ Control v'"" 



/ V • V V 

 *C." 



/ 



(A-1) 



= p J V • V V d\r 



c.v. 



= P J V (V'n)dS 



On the body surface, it is required that V'n=0. The force acting on 

 the body is 



= / 



or, from Equation A-1, 



F = I pn dS 



F = - J [pn + pV(V'n)]dS 

 S +S^ 



00 Q 



The pressure is related to the velocity by means of the Bernoulli theorem 

 as 



p = - p_ V'V 

 2 



and so the force may be expressed entirely in terms of the velocity on the 

 boundaries S and S , as 



^ = J [P- (V'V) n - p"v(V'ri)] dS (A-2) 



70 



