If the body were a circular cylinder of constant radius r , we could 

 immediately determine the source strength m(s) equivalent to the effect of 

 the boundary layer. Application of the Gauss flux theorem gives 



27Tr,V' = 47T(2TTr m) 



and hence by (28) , 



= 7-^ (U6,) 

 4tt ds 1 



(29) 



A generalization of (29) can be derived from the integral-equation 

 formulation of the Neumann problem for the prescribed boundary-layer flux. 

 If P and Q are points on the body surface, we have 



2™(P) = / m(Q) 



^ — dS- + V'(P) 



\ ^PQ Q 



(30) 



The singularity of the kernel when Q coincides with P can be removed by 

 means of the relation, valid at smooth points of the surface, 



/ 



r dS^ = - 2tT 



^^Q ^PQ Q 



(31) 



Thus (30) may be written in the form 



4TTm(P) 



-I 



m(Q) ^ -^ - ni(P) ^ -^ 

 . . ^^ ^PQ ^^Q ^PQ 



dS^ + V'(s,0) (32) 



which suggests the first approximation 



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