Take $x$ vertically downward along the wall and $y$ normally outward, with the wall at $y=0$ and free surface at $y=h$. The expected steady velocity is $\mathbf u=u(y)\mathbf e_x$: it vanishes at the wall and is opposed by an upward air shear $ku(h)$ at the surface. Gravity supplies the downward body force $\rho g\mathbf e_x$, while the surface normal stress is the atmospheric pressure $p_0$.


Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ib / Paper 1 / 17D / a / Solution

 Solution (source code)