Problem 5.10 - Problem 5.10 Given Approximate profile for a...

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Problem 5.10 [Difficulty: 2] Given: Approximate profile for a laminar boundary layer: u Uy δ δ cx (c is constant) Find: (a) Show that the simplest form of v is v u 4 y x (b) Evaluate maximum value of v/u where δ = 5 mm and x = 0.5 m 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 2 1 2 2 2 1 cx Uy cx Uy dx d u x u 2 3 2 cx Uy x u y v The partial of u with respect to x is:
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