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Unformatted text preview: way from u x + v y = 0. Consider now a more general approach to solving this equation in terms of the similarity solution ( x, y ) = F ( x ) f ( ) , where = y/g ( x ) The more general far eld boundary condition ~u ( U ( x ) , 0) as y/ leads to the condition F ( x ) = U ( x ) g ( x ) (in class we had U ( x ) = U = const). Show that this leads to the equation f 2- 1 + U U g g ff 00 = 1 + f 000 g 2 U , where the prime is the derivative with respect to the appropriate single variable ( x or ). Show that a similarity solution is only possible if either U ( x ) ( x-x ) n or U ( x ) e x , where x , n, and are constants. 4. For the case U ( x ) = Ax n ( A > 0) in the previous problem, show that g ( x ) x (1-n ) / 2 . By choosing g ( x ) = s 2 ( n + 1) Ax n-1 derive an ordinary dierential equation for f ( ) (the Falkner-Skan equation)....
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This note was uploaded on 07/23/2008 for the course MATH 505 taught by Professor Belmonte,andrewl during the Fall '07 term at Pennsylvania State University, University Park.
- Fall '07