Problem 5.28 - Problem *5.28 [Difficulty: 2] Stream...

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Problem *5.28 [Difficulty: 2] Given: Stream function for an incompressible flow field: ψ U r sin θ () q 2 π θ Find: (a) Expression for the velocity field (b) Location of stagnation points (c) Show that the stream function is equal to zero at the stagnation points. Solution: We will generate the velocity field from the stream function. r V r V r 1 Governing Equations: (Definition of stream function) Taking the derivatives of the stream function: V r U cos θ q 2 π r V θ U sin θ e U e R q U V r ˆ sin ˆ 2 cos So the velocity field is: To find the stagnation points we must find the places where both velocity components are zero. When
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