Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 38C / b / Solution

Let $U$ be the streamwise speed and $\delta$ the layer width. Continuity gives $v\sim U\delta /x$, while inertia--viscosity balance givesThe imposed stress gives $\rho \nu U/\delta \sim S{x}^{-1/2}$. Eliminating $U$ yieldsandwhich is independent of $x$.