$($a$)$ Show that, for a flow with $U_{}$ proportional to $x^{\frac{1}{3}},$ the wall shear stress ${}_S$ for a laminar boundary layer is constant.

$($b$)$ Calculate ${}_S$ for an airflow for which

$\frac{U_{}}{U_0}=B(\frac{x}{L}{)}^{\frac{1}{3}}$

where $B=$ constant, $U_0\frac{L}{v}={10}^3,\frac{U_0^2}{2}=240Pa,$ and, at $\frac{x}{L}=10,$ the free$-$stream velocity $U_{}=2U_0.$

For either $($a$)$ or $($b$)$ make use of any relevant information from the Falkner$-$Skan solutions.