All-101 71 



ourselves to the determination of the boundary layer contribu- 

 tion and to an indication of the ensuing difficulties. 

 Carry out the following three steps: 



(a) Let X = e {;, i.e., stretch x coordinate near x = 0. 



(b) Substitute v^ 2 = ^'^^^ ^12' '^ ^ e^^-^Y* 



(c) Keep the leading terms of the equations. 

 The equations then reduce to 



nsyvi = h^^ 



-1/3 



ins6e v, + nsyU]_ = - h-, + nsv-... 



u, ,- + 



^Iv = iYh2 



1^ ly 



yvg = I (h-Lj. + h^^) 



-1/3 - 



i6£ V2 + yu2 = - -t (h^y + h2y) + Vg^^ 



""2^ "" ^2y " " ^^^^2 • 

 Eliminating all the unknowns except h25 we find 



^2Km " ^2^^ - h2^ + L h2 = 



where !/■:> p t 



6, = 16 e"^-^, L = iyy (ns + i) . 

 1 I 



Solutions are 



ho = S C. e ^ 

 "^ 1=1 ^ 



where the Dj_ are the roots of 



L p 

 D - 6-,D - D + L = 0. 



