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Problem 5.15 - Problem 5.15 Given Steady incompressible...

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Problem 5.15 [Difficulty: 3] Given: Steady, incompressible flow in x-y plane: v B x y 3 B 0.2 m 3 s 1 Find: (a) the simplest x component of velocity for this flow field (b) equation of the streamlines for the flow (c) plot streamlines through points (1,4) and (2,4) Solution: We will check this flow field using the continuity equation 0 t w z v y u x Governing Equations: (Continuity equation) Assumptions: (1) Incompressible flow ( ρ is constant) (2) Two dimensional flow (velocity is not a function of z) 0 y v x u Based on the two assumptions listed above, the continuity equation reduces to: 2 3 Bxy y v 2 3 Bxy y v x u The partial of v with respect to y is: Therefore from continuity: Integrating this expression will yield the x-component of velocity: u x 3 B x y 2 d f y ( )
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