V(s,6) 



|v(x,r) 

 I — ►uCx, 



r) 



Figure 5 



Let us apply the Gauss flux theorem to the volume of the body of 

 revolution generated by the profile r = f(x), extending from the nose to a 

 transverse section at x, assuming that the flow about the body is generated 

 by an axial source distribution M (x) . Since r = f(x) is a stream surface, 

 the flux theorem gives 



47T 



X f 



/ Mq dx = J 



2iTru (x,r) dr 



(36) 



Here [u (x,r), v (x,r)] denote the velocity components of the irrotational 

 flow when the given profile is a stream surface, as distinct from the 

 components (u,v) of the equivalent irrotational flow. Differentiating (36) 

 and integrating by parts, we then obtain 



Mq(x) 



1 d_ 

 4 dx 



Uj(x,f)- 



t 



I 



dr 



(37) 



13 



