$1\mathrm{.}3.$ Find the pressure $p$ both inside and outside the core of the

Rankine vortex $(1\mathrm{.}23).$ Show that the pressure at $r=0$ is lower than that

at $r=$ by an amount ${}^2{a}^2($hence the very low pressure in the centre

of a tornado$).$ Deduce that if there is a free surface to the fluid and

gravity is acting, then the surface at $r=0$ is a depth ${}^2\frac{a^2}{g}$ below the

surface at $r=($hence the dimples in a cup of tea accompanying the

vortices that are shed by the edges of the spoon$).$