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Ae311_fall_2011_hw_4 - Prof Daniel J Bodony AE311 Fall 2011...

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Prof. Daniel J. Bodony AE311, Fall 2011 HW #4 Due 5 pm Wednesday, October 5, in the AE311 dropbox Problem 1 Recall Problem 3 from HW2 where you were given an approximate form of the velocity profile in a boundary layer for the flow of water over a flat plate with zero pressure gradient: u ( x , y ) U = 2 parenleftBigg y δ ( x ) parenrightBigg 2 parenleftBigg y δ ( x ) parenrightBigg 3 + parenleftBigg y δ ( x ) parenrightBigg 4 0 y δ ( x ) 1 y > δ ( x ) Assuming v ( x , y ) 0, w 0, and that δ ( x ) = A x , where A is a constant, compute the skin friction coe ffi cient as a function of x . What value of A do you need to match the drag you computed in Problem 3, HW2, using the integral momentum equation? Compute and plot the z -component of the vorticity, ω z . Is the flow rotational or irrotational? Sketch what happens to an initially square fluid element with time. Problem 2 Consider the motion of a fluid in one direction only with velocity field u = ( u ( x ) , 0 , 0) T . Calculate the
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