Problem 5.32 - Problem*5.32[3 Approximate profile for a...

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Problem *5.32 [3] Given: Approximate profile for a laminar boundary layer: u U 2 y δ y δ 2 δ cx (c is constant) Find: (a) Stream function for the flow field (b) Location of streamlines at one-quarter and one-half the total flow rate in the boundary layer. Solution: We will generate the stream function from the velocity field. x v y u Governing Equations: (Definition of stream function) Integrating the x-component of velocity yields the stream function: ψ y U2 y δ y δ 2 df x () U δ y δ 2 1 3 y δ 3 fx If we set ψ 0 at y0 the stream function would be: ψ U δ y δ 2 1 3 y δ 3 The total flow rate per unit depth within the boundary layer is: Q ψδ ψ 0 U δ
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