Problem 5.56 - Problem 5.56 Given Find[Difficulty 3 Steady...

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Problem 5.56 [Difficulty: 3] Given: Steady, two-dimensional velocity field represented above Find: (When C = 0 the streamline is on the x- and y-axes.) 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 Streamlines along the x-y plane are defined by dy dx v u A y Ax Thus: dx x dy y 0 After integrating: ln x ( ) ln y () ln C which yields: xy C (Q.E.D.) y V v x V u a p Based on the above assumptions the particle acceleration reduces to: Substituting in the field:       j y i
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