Problem *5.30[Difficulty: 3]Given:Stream function for an incompressible flow field:ψ5Ax2AyA2msFind:(a) Sketch streamlines ψ= 0 and ψ= 5(b) Velocity vector at (0, 0)(c) Flow rate between streamlines passing through points (2, 2) and (4, 1)Solution:We will generate the velocity field from the stream function.xvyuGoverningEquations:(Definition of stream function)Assumptions:Incompressible flow (ρis constant)Flow is only in the x-y planeFor ψ= 0:05AxySolving for y:y52xFor ψ= 5:55AxySolving for y:y52x52m2ss2m52x52m42024105510x (m)y (m)Here is the plot of the two streamlines:ψ=0 is in red; ψ= 5 is in blueGenerating the velocity components from the stream function derivatives:
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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.