Problem *5.33[Difficulty: 3]Given:Approximate profile for a laminar boundary layer:uUsinπy2δδcx(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.xvyuGoverningEquations:(Definition of stream function)Integrating the x-component of velocity yields the stream function:ψyU sinπy2δdfx()2Uδπcosπy2δfxIf we setψ0aty0the stream function would be:ψδπcosπy2δThe total flow rate per unit depth within the boundary layer is:Qψδψ0δπcosπ2cos 0δπAt one-quarter of the flow rate in the boundary layer: Q14δπUδ2
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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.