Prandtl Boundary Layer Flow over a Flat Plate

Mechanical Engineering

How It Works

Prandtl's boundary layer theory models viscous fluid flow over a semi-infinite flat plate at high Reynolds numbers. Due to molecular viscosity, fluid adheres to the solid surface under the no-slip condition (u = 0). Viscous shear stresses retard adjacent fluid layers, creating a thin boundary layer thickness (δ) that grows parabolically downstream as viscous diffusion penetrates into the freestream.

Governing Equation
δ(x) ≈ (5.0 · x) / √Re_x , c_f = 0.664 / √Re_x , Re_x = (ρ · U_∞ · x) / μ