Problem 6.103

Problem 6.103 - Problem 6.103 [Difficulty: 3] Given: Data...

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Problem 6.103 [Difficulty: 3] Given: Data from Table 6.2 Find: Stream function and velocity potential for a vortex in a corner; plot; velocity along one plane Solution: From Table 6.2, for a vortex at the origin ϕ r θ , () K 2 π θ = ψ r θ , K 2 π ln r = Expressed in Cartesian coordinates ϕ xy , q 2 π atan y x = ψ , q 4 π ln x 2 y 2 + = To build flow in a corner, we need image vortices at three locations so that there is symmetry about both axes. We need vortices at ( h , h ), ( h ,- h ), (- h , h ), and (- h ,- h ). Note that some of them must have strengths of - K ! Hence the composite velocity potential and stream function are ϕ , K 2 π atan yh xh atan + atan + + + atan + = ψ , K 4 π ln 2 2 + 2 + 2 + + 2 + 2 + + 2 2 + = By a similar reasoning the horizontal velocity is given by

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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 6.103 - Problem 6.103 [Difficulty: 3] Given: Data...

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