Problem 5.82

Problem 5.82 - Problem 5.82 Given Find[Difficulty 2 Flow...

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(a) Fluid rotation (b) Circulation about the curve shown (c) Stream function (d) Plot several streamlines in first quadrant Problem 5.82 [Difficulty: 2] Given: Flow field represented by a velocity function. Find: Solution: We will apply the definition of rotation and circulation to the given velocity field. V 2 1 Governing Equation: (Definition of rotation) s d V (Definition of circulation) Assumption: Steady flow  k By Bxy Ax z y x k j i ˆ 2 1 0 ˆ ˆ ˆ 2 1 2 s ft rad ˆ k y From the definition of rotation: da cd bc ab s d V s d V s d V s d V From the definition of circulation we break up the integral:   Bxydy dx Ax j dy i dx j Bxy i Ax s d V 2 2 ˆ ˆ ˆ ˆ The integrand is equal to: Therefore, the circulation is equal to: Γ x a x b x Ax 2 d y b y c y Bx y

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Problem 5.82 - Problem 5.82 Given Find[Difficulty 2 Flow...

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