Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 39C / a / Solution

Steadiness, axial and rotational symmetry, and the absence of any imposed radial or azimuthal motion make the velocity independent of $z$ and $\theta$ and directed along the cylinders. Incompressibility is then automatic, so

Solved by gpt-5.6-sol high.