suppose that the radii of curvature are so large compared with the boundary- 

 layer thickness 6, that the curvilinearity of the coordinate system may be 

 ignored. The normal velocity component at n = 6 is then given by 



6 .6 .6 



v(<S) = I ^dn = - I -^dn = -6^ + ^ I (U-u) dn = - 6 -^ 



= r |:^ dn = - f |H dn = - 6 f^ + f- f (U-u) dn = - 6 



J dn I ds ds ds I 







-^^("V' ^1= J (^-^)^- (^> 



where U = u (s,6) and 6, is the displacement thickness. In the irrotational 

 flow about the body, with velocity components U (s,n), V (s,n), we have 

 (3U /9n)^ = where the subscript denotes n = 0. Hence we may put 

 U (s,n) = U (s), since 



Uj(s,n) =. U^(s,0) + n [j^Jq '=■ U^(s,0) = U^(s), < n < 6 



The normal velocity in this irrotational flow, at n = 6, would then be 

 given by V (s,6) =. V (s,0) + 6(8V /3n)„, and hence, since V (s,0) = and 

 3V /3n = - dU /9s, we obtain 



dU 



V^(s,6) ■= - S —!- (2) 



i as 



We also assume that U = u(s,6) = U (s,6) for a thin boundary layer. Thus 

 the first term of the right member of (1) is attributable to this irrota- 

 tional flow, and the second term represents an additional outward flow due 

 to the boundary layer. 



Put V = ^— (U6t) and consider that the "known" values of V on the 

 ds 1 



contour n = 6, the edge of BLW, pose an exterior Neumann boundary-value 

 problem for determining a source distribution m(s) on the surface of the 

 body and (if the body is symmetric) along the centerline of the wake. 



