was seen that this could be accomplished in various ways, such as a source 

 distribution on the given surface and along the wake, a source distribution 

 on the edge of the boundary layer and wake, or by the irrotational flow 

 about the displacement-thickness surface. In none of these irrotational 

 models was it possible to retain the given body as a stream surface. 



Intuitively, it appears desirable to match the boundary conditions on 

 both the body and the edge of the boundary layer and wake, in order to 

 obtain a more realistic irrotational model. We have seen that the vorticity 

 distribution alone yields both the nonslip condition on the body and the 

 boundary condition on EBLW, In the previous models only the boundary condi- 

 tion on EBLW was employed. An additional source distribution, on the body 

 or in its interior is required in order to satisfy the condition that the 

 body remain a stream surface. The condition of zero tangential velocity 

 would not be satisfied, but this seems to be physically less important in 

 an irrotational model. 



The boundary conditions on the body surface S and on EBLW define a 

 Neumann problem which can be readily formulated as a pair or integral equa- 

 tions to be solved simultaneously for a pair of source distributions. The 

 locations of the source distributions may vary, even for a given body, as 

 has already been illustrated. If these are taken to be distributions m(P) 

 on S and y(Q) on T; one obtains the integral equations 



2TTm(P) - J m(P') g^^dSp, - J y(Q') 3^;:-i— dS, 



9n^ r^^. Q' 



2-n\i{q) 



V rpp, P- J dnp rpQ, 



= - U„ 1^ (49) 



3np 



where P and P' denote points on S, and Q and Q' on EBLW, and v(Q) denotes 

 the normal component of the velocity at T, which is assumed to be known. 



19 



