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Problem 5.58 - Problem 5.58 Given Find[Difficulty 3...

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Problem 5.58 [Difficulty: 3] Given: Velocity field represented above Find: y x B A constant Solution: We will check the velocity field against the continuity equation, apply the acceleration definition, and determine the streamline slope. 0 t w z v y u x Governing Equations: (Continuity equation) t V z V w y V v x V u Dt V D a p (Particle acceleration) Assumptions: (1) Two-dimensional flow (velocity is not a function of z) (2) Incompressible flow Based on the above assumptions the continuity equation reduces to: x u y v 0 This is the criterion to check the velocity. The partial derivatives are: x u A and y v C Thus from continuity: A C 0 or C A C 2 s 1 t V y V v x V u a p Based on the above assumptions the particle acceleration reduces to: Substituting in the field: k D j y C i AB x A k D j C Cy i A B Ax a p ˆ ˆ ˆ ˆ ˆ ˆ 2 2
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