Question $2$: Potential Flow $-$ Vortices

a$)$ A hurricane is comprised of a compound vortex. Explain what this means and sketch the velocity and pressure fields for this natural phenomenon.

$[4]$

b$)$ A tornado is represented by a combination of a sink, of strength $2,500\frac{m^2}{s}$ and a free vortex of circulation, $=6,000\frac{m^2}{s}.$ Compute the velocity and gauge pressure at a distance $10$ m from the centre. Is the flow compressible at this distance from the centre?

$[6]$

Note that: $,{}_{sink}=\frac{m}{2},$ and ${}_{\text{f}\text{r}\text{e}\text{e}\text{v}\text{o}\text{r}\text{t}\text{e}\text{x}}=\frac{lnR}{2}$