Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 314 / 2 / b / Solution

The radial equation can be writtenThus the Bernoulli function is constant on each streamline:The boundary conditions $u\to 0$ and $\rho \to {\rho }_0$ as $r\to \infty$ fix $\mathcal{B}=c_s^2\ln {\rho }_0$.