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Problem 5.35 - Problem*5.35 Given Rigid body motion in...

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Problem *5.35 [Difficulty: 3] Given: Rigid body motion in Example Problem 5.6 e r V ˆ ω 0.5 rad s Find: (a) Stream function for the flow field (b) Volume flow rate per unit depth between r = 0.10 m and 0.12 m (c) Sketch velocity profiles along a line of constant θ (d) Check the volume flow rate calculated from the stream function by integrating the velocity profile along this line. Solution: We will generate the stream function from the velocity field. r V r V r 1 Governing Equations: (Definition of stream function) Integrating the θ -component of velocity yields the stream function: ψ r r ω d f θ ( ) ω r 2 2 f θ ( ) Now take the derivative of the stream function: V r 1 r df d θ 0 Therefore, f θ ( ) C ψ ω r 2 2 C The volume flow rate per unit depth is: Q ψ r 2 ψ r 1 ω r 2 2 2 C
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