Problem 6.101 - Problem 6.101 [Difficulty: 3] Given: Data...

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Problem 6.101 [Difficulty: 3] Given: Data from Table 6.2 Find: Stream function and velocity potential for a source in a corner; plot; velocity along one plane Solution: From Table 6.2, for a source at the origin ψ r θ , () q 2 π θ = ϕ r θ , q 2 π ln r = Expressed in Cartesian coordinates ψ xy , q 2 π atan y x = ϕ , q 4 π ln x 2 y 2 + = To build flow in a corner, we need image sources at three locations so that there is symmetry about both axes. We need sources at ( h , h ), ( h ,- h ), (- h , h ), and (- h ,- h ) Hence the composite stream function and velocity potential are ψ , q 2 π atan yh xh atan + + atan + + + atan + + = ϕ , q 4 π ln x h 2 2 + 2 + 2 + q 4 π + 2 + 2 + + 2 2 + = By a similar reasoning the horizontal velocity is given by u qx h 2 π 2 2
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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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Problem 6.101 - Problem 6.101 [Difficulty: 3] Given: Data...

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