Problem 5.11 - Problem 5.11 Given: [Difficulty: 3]...

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Problem 5.11 [Difficulty: 3] Given: Approximate (parabolic) profile for a laminar boundary layer: u U 2 y δ y δ 2 δ cx (c is constant) Find: (a) Show that the simplest form of v for incompressible flow is v U δ x 1 2 y δ 2 1 3 y δ 3 (b) Plot v/U versus y/ δ (c) 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 1 3 2 2 2 1 2 2 cx y y U dx d u x u The partial of u with respect to x is: Now since δ 1 2 x 1
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Problem 5.11 - Problem 5.11 Given: [Difficulty: 3]...

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