HWset8-S2011 - ASE320 Homework set# 8 Due:...

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Unformatted text preview: ASE320 Homework set # 8 Due: April 21, 2011 1.) For the boundary layer velocity profile given by u/U =y/δ for (y≤δ), find: a. The wall shear stress b. The skin friction coefficient c. The displacement thickness d. The momentum thickness 2.) Assuming that the velocity profile in a laminar boundary layer of thickness δ is given by u/U =2(y/δ)  ­ (y/δ)3, where u is the velocity at distance y from the surface and U is the freestream velocity, demonstrate that a. θ/δ = 31/420 b. Cf = τw/(½ρU 2) = 4ν/(U δ) where θ is the momentum thickness, τw if the viscous stress at the wall, Cf is the local skin friction coefficient at a distance x from the leading edge of the plate, ρ is the density, and ν is the kinematic viscosity. 3.) A flat plate 1m long and 0.5m wide is parallel to a flow of air at a temperature of 25oC. The velocity of the air far from the plate is 20m/s. a. Is the flow laminar or turbulent? (show your work!) b. Find the maximum thickness of the boundary layer c. Find the overall drag coefficient CF, assuming that the transition occurs at the leading edge. d. Find the total drag of the plate if the air covers both sides. 4.) Show how the solution for laminar flow over a flat plate is obtained, that is: δ/x =5.48/Re1/2. Hint: Start with the Momentum Integral Equation (derived in class) for a flow with zero pressure gradient and assume the velocity profile is a polynomial of the form u = a + by + cy2. ∞ ∞ ∞ ∞ ∞ ...
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