Problem *5.37[Difficulty: 3]Given:Rigid body motion in Example Problem 5.6erCVˆC0.3m2sFind:(a) Stream function for the flow field(b) Volume flow rate per unit depth between r = 0.20 m and 0.24 m(c) Sketch velocity profiles along a line of constant θ(d) Check the volume flow rate calculated from the stream function by integrating the velocity profilealong this line.Solution:We will generate the stream function from the velocity field.rVrVr1GoverningEquations:(Definition of stream function)Assumptions:Incompressible flowFlow is in the r-θplane onlyIntegrating the θ-component of velocity yields the stream function:ψrCrdfθ()Cln rfθNow take the derivative of the stream function:Vr1rdfdθ0Therefore,fθ() C1ψCln rC1The volume flow rate per unit depth is:Qψr2
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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.