Problem 5.34

Problem 5.34 - Problem *5.34 [Difficulty: 3] Given: Data on...

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Problem *5.34 [Difficulty: 3] Given: Data on boundary layer Find: Stream function; locate streamlines at 1/4 and 1/2 of total flow rate Solution: uxy () U 3 2 y δ 1 2 y δ 3 and δ x () c x For the stream function u y ψ U 3 2 y δ 1 2 y δ 3 Hence ψ y U 3 2 y δ 1 2 y δ 3 d ψ U 3 4 y 2 δ 1 8 y 4 δ 3 fx Let ψ = 0 = 0 along y = 0, so f( x ) = 0, so ψ U δ 3 4 y δ 2 1 8 y δ 4 The total flow rate in the boundary layer is Q W ψδ ψ 0 U δ 3 4 1 8 5 8 U δ At 1/4 of the total ψψ 0 U δ 3 4 y δ 2 1 8 y δ 4 1 4 5 8 U δ 24 y δ 2 4 y δ 4 5 or 4X 2 24 X 5 0 where X 2 y δ The solution to the quadratic is X 24 24 2 44
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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