A laminar boundary layer of thickness is modelled by the parabolic profile u U = 2 (…

PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

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

Problem

A laminar boundary layer of thickness δ=6.0 mm\delta = 6.0\,\mathrm{mm} is modelled by the parabolic profile uU=2(yδ)−(yδ)2,0≤y≤δ,u=U for y>δ,\frac{u}{U} = 2\left(\frac{y}{\delta}\right) - \left(\frac{y}{\delta}\right)^2, \qquad 0 \le y \le \delta, \qquad u = U \text{ for } y > \delta, where UU is the free-stream speed. Find the displacement thickness δ1\delta_1, the momentum thickness δ2\delta_2, and the shape factor Hsh=δ1/δ2H_{\rm sh} = \delta_1/\delta_2 for this profile.

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