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Problem 5.86

# Problem 5.86 - Problem 5.86 Given Find[Difficulty 3...

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(a) Whether or not this is an irrotational flow (b) Stream function for the flow Problem 5.86 [Difficulty: 3] Given: Velocity field approximation for the core of a tornado Find: Solution: We will apply the definition of rotation to the given velocity field. V 2 1 Governing Equation: (Definition of rotation) z k r e r e r ˆ 1 ˆ ˆ (Definition of "del" operator) r r e e e e ˆ ˆ ˆ ˆ (Hints from text) Assumptions: (1) Steady flow (2) Two-dimensional flow (no z velocity, velocity is not a function of θ or z)  e V e V z k r e r e r r r ˆ ˆ ˆ 1 ˆ ˆ 2 1 From the definition of rotation: Employing assumption (2) yields: e V e V r e r V e r V e e e V e V r e r e r r r r r r r r ˆ ˆ 1 ˆ ˆ
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