Air at ( , ) flows at over a flat plate

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity

Fluid Dynamics, Ch The boundary layer: Prandtl's equations and the Blasius solution

Problem

Air at 20∘C20^{\circ}\mathrm{C} (ρ=1.20 kg m−3\rho = 1.20\,\mathrm{kg\,m^{-3}}, ν=1.51×10−5 m2 s−1\nu = 1.51\times10^{-5}\,\mathrm{m^2\,s^{-1}}) flows at U=5.0 m s−1U = 5.0\,\mathrm{m\,s^{-1}} over a flat plate. At x=0.20 mx = 0.20\,\mathrm{m} from the leading edge: ((a)) use the diffusion-convection scaling estimate δ∼x/Rex\delta \sim x/\sqrt{Re_x} (no numerical coefficient) to estimate the layer thickness; ((b)) use the Blasius result δ99=4.9x/Rex\delta_{99} = 4.9x/\sqrt{Re_x} to compute the actual 99%99\% thickness, together with the wall shear stress τw=0.332ρU2/Rex\tau_w = 0.332\rho U^2/\sqrt{Re_x} and the displacement thickness δ1=1.7208x/Rex\delta_1 = 1.7208x/\sqrt{Re_x}; ((c)) state the ratio δ99/δ\delta_{99}/\delta, and comment on what the scaling estimate of part (a) does and does not give correctly.

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