Problem 5.78 - Problem 5.78 Given Find[Difficulty 2...

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(a) Expression for the velocity field (b) Rate of rotation (c) Stream function Problem 5.78 [Difficulty: 2] Given: Velocity field for motion in the x-direction with constant shear Find: Solution: We will apply the definition of circulation to the given velocity field.  0 t w z v y u x Governing Equations: (Continuity equation) V 2 1 (Definition of rotation) Assumptions: (1) Steady flow (2) Incompressible flow     i x f Ay V ˆ The x-component of velocity is: uy A df x () Ay f x Since flow is parallel to the x-axis: k A x f Ay z y x k j i ˆ 2 1 0 0 ˆ ˆ ˆ 2 1
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