Past exam of the options I course of the University of Oxford / 2006 / K / K1 / ii / Solution

The complex potential of a two-dimensional potential flow is $w=\varphi +i\psi$, soFor $\mu \ne 0$, a nonzero level $\psi =c$ isThus the streamlines are circles tangent to the horizontal axis at the excluded singular origin, with centers on the vertical axis. Each circle has the origin removed. The zero level is the horizontal axis without the origin, whose positive and negative rays are separate streamlines. Since $w^{\prime }=-\mu /z^2$ is nonzero away from the origin, no other stagnation points intervene. For $\mu =0$ the flow vanishes everywhere off the origin, so the circle description is replaced by the degenerate zero-velocity field.