Wall shear stress (${\tau }_w$)

For a stationary flat plate in a Newtonian fluid, the streamwise shear stress exerted by the fluid on its upper face isThe sign here is positive when the fluid pulls the plate downstream; the plate exerts the opposite tangential traction on the fluid. In a Blasius boundary layer, ${\tau }_w\simeq 0.332057\rho U^2/\sqrt{{\mathrm{Re}}_x}$. A growing boundary layer thickness therefore accompanies decreasing local wall shear stress, because its near-wall velocity gradient becomes gentler. The formal divergence as $x\to 0$ is integrable, but that leading-edge limit lies outside the thin-layer hypothesis.^[ref]

The local skin friction coefficient normalizes wall shear stress by the outer dynamic pressure:For the ideal Blasius boundary layer on one face of length $L$, averaging the local skin friction coefficient gives ${\overline{c}}_f\simeq 1.328230/\sqrt{{\mathrm{Re}}_L}$. The factor of two follows from integrating $x^{-1/2}$, not from counting both plate faces. Drag on two equally exposed faces doubles when the reference area remains that of one face.