For this question, $3$ marks will be awarded for rigour, precision, explanation and presentation.

Further, if in your solution you introduce any new notation not given in the question, then please

remember to define it$.$

The streamlines of a smooth planar fluid flow are the smooth curves traced by the fluid's individ$-$

ual particles. The vectors of the flow's velocity field are the tangent vectors of the streamlines.

Suppose that the smooth planar flow takes place over a non$-$empty, open, simply connected

region $Rsube{R}^2,$ the flow's velocity field $F$ is smooth throughout $R,$ and the divergence of $F$ is

non$-$zero throughout $R.$ Under these assumptions, prove that none of the streamlines of the

smooth planar flow in $R$ are closed.