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# ps_11b - 2.20 Problem Set 11B Name 1 Consider an...

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2.20 Problem Set 11B Name: ____________________ 1. Consider an approximate velocity profile within a laminar boundary layer over a wall given by: 1 £ ¦ ¦ ¤ ¦ ¦ ¥ 2 ax () K y G + b x x (; x ) uy < (1) = Ux y p ( ) x measure of the boundary layer thickness at x . (a) By applying one boundary condition at y = which matches the boundary layer flow with the outer flow Ux ( ) , obtain an algebraic relationship between a and b . (b) Now write both a ( x ) and b ( x ) in terms of a new parameter / ( ) such that the x relationship between a and b found in (a) is maintained. In other words, find a / and b / . (c) Write the velocity profile (1) in terms of / instead of a and b . w (d) Using the assumed velocity profile and the x -momentum boundary layer equation ( ) and bx ( ) ( ) , and ( ) are constants at any given x , and x where / is a y x 2 s u x s u + U dU s u + Q u v = 2 s s y y evaluated at y = 0 , obtain an expression for / in terms of U, , and . Also obtain an expression for the pressure gradient dp / dx in terms of U , U , / , , and . ( Hint : Polhausen approach, but a different profile

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ps_11b - 2.20 Problem Set 11B Name 1 Consider an...

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