a cosh (2^-5)- 1 a a 



On the y-axis w = and 



v^'^A cotll [44i] 



On the walls at y = i a/2, y = and 



u=lA tanh !I^ [44]] 



a a 



(B) Line Source in a Stream Between Parallel Walls 



If a uniform flow parallel to the walls is superposed, the resulting formulas can be written, 

 in terms of real constants V and a real positive constant g: 



= ii/a, + ^ fk-I in/cosh ^ - cos ^) 1 I [44k] 



\j, = 4^ -^ £ [7 - ^""' (t-n ^/tanh ^) ] | [441] 



u=i/-l+— M^ sinh 1) , 'o=-—r, sin [44m,n] 



l_ 2a\H a /J 2aH a 



The uniform velocity that is here superposed is V{l + g/2a), but the resultant stream velocity 

 at x = + ^ is U, since, as ^-~, w--^. As x-*-^, u^-U (1 + g/a). On the walls at y = ±a/2, 



tz=[;[-l+-£(tanh?^-l]] [4*0] 



„=[/r_l + l jboth2^-l)] [44p] 



On the a!-axis 



and a stagnation line occurs at a; = Xq where 



a:^=— tanh-l — ^ [44q] 



^ n 2a+ g 



103 



