Blasius equation ($f^{\prime \prime \prime }+\frac{1}{2}f{f}^{\prime \prime }=0$)

For a steady incompressible viscous boundary layer over a flat plate with constant outer speed $U$, the stream function $\psi =\sqrt{\nu Ux}f(y\sqrt{U/(\nu x)})$ reduces the Prandtl boundary-layer equation to the displayed ordinary differential equation. The wall and outer conditions are $f(0)=f^{\prime }(0)=0$ and $f^{\prime }(\infty )=1$. The wall shear is $\rho U\sqrt{\nu U/x}{f}^{\prime \prime }(0)$, so its integral on one plate face of length $L$ is $2\rho U^{2}L{f}^{\prime \prime }(0)/\sqrt{UL/\nu }$. Both equally exposed faces contribute twice this value.