Problem 5.57 - Problem 5.57 Given Find[Difficulty 3 Steady...

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Problem 5.57 [Difficulty: 3] Given: Steady, two-dimensional velocity field represented above Find: Ax B () y C Solution: We will apply the acceleration definition, and determine the streamline slope. t V z V w y V v x V u Dt V D a p Governing Equations: (Particle acceleration) Assumptions: (1) Two-dimensional flow (velocity is not a function of z) (2) Incompressible flow y V v x V u a p Based on the above assumptions the particle acceleration reduces to: Substituting in the field:    j y A i AB x A j A Ay i A B Ax a p ˆ ˆ ˆ ˆ 2 2   j y A i AB x A a p ˆ ˆ 2 2 2 s m ˆ 0533 . 0 ˆ 12 . 0 j i a p 2 s m ˆ 0800 . 0 ˆ 08 . 0 j i a p At (x,y) = (0m, 4/3m) At (x,y) = (1m, 1m) 2 s m ˆ 160 . 0 ˆ 04 . 0 j
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