and the relation 



26, 



1+ 



1+ 



26 cos Y 



-, 1/2 



(26) 



The equivalent irrotational flow is determined by the values of v(s,6) 

 By (23) , we have 



(l+k6) r. 



v(s,6) = - J 1^ (ru) dn = J 1^ 



[r(U-u)-rU] dn 



h ('^y^i) - ' k (-0^) - f^ !f (u -^ ^) (27) 



where U = U(s,6). In the irrotational flow about the body without a bound- 

 ary layer, with velocity components (U ,V ) , (27) becomes 







(l+k6) r^ Vj(s,6) =-11- [rU^(s,n)] 



dn 



■=--^i^(^oV -|^^(Ui-^^) 



since (9U^/3n) „ = 0, and U^(s,n) = U^(s,0) + 0(6 ) =. U^(s). If the 

 i n=U 1 i 1 



boundary layer is thin, then U (s) = U and the first term of the right 

 member of Equation (27) can be interpreted as that contributing an addi- 

 tional flux due to the boundary layer. We define the additional normal 

 velocity V' due to the boundary layer by 



(1+^^) ^6^' = k (-o"^i) 



(28) 



10 



