The sink speed scales as $U\sim A/R^2$, so the <Reynolds number> is $Re\sim UR/ν=A/(νR)$. The approximation applies in the high-Reynolds-number region $R\ll A/ν$. Radial inertia scales as $U\,dU/dR\sim A^2/R^5$, so the radial pressure gradient has the same $R^{-5}$ dependence.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 3 / 38A / a / Solution

 Solution (source code)