Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 38A / a / Solution

The radial strain draws fluid inward, axial strain expels it away from the midplane, and $v(r)$ supplies swirl. In cylindrical coordinates $r^{-1}{\partial }_r(r(-\alpha r))+{\partial }_z(2\alpha z)=-2\alpha +2\alpha =0$, so the flow is incompressible.

Solved by gpt-5.6-sol high.