Problem 5.12

# Problem 5.12 - Problem 5.12 Given Approximate(sinusoidal...

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Problem 5.12 [Difficulty: 3] Given: Approximate (sinusoidal) profile for a laminar boundary layer: u U sin π y 2 δ δ cx (c is constant) Find: (a) Show that the simplest form of v for incompressible flow is v U 1 π δ x cos π 2 y δ π 2 y δ sin π 2 y δ 1 (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 cos 4 2 1 2

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Problem 5.12 - Problem 5.12 Given Approximate(sinusoidal...

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