$2.(30)$ Cyclostrophic balance can be expressed in terms of pressure p and radius r from

the center of circulation as

V $2$

r $=1$

$$p

$$r

where V is the wind speed and is the air density.

A mobile field team observes a tornado that has a wind speed $($tangential$)$ of $120\mathrm{.}0$ m s$1$

and a pressure of $996\mathrm{.}0$ hPa at a radius of $500\mathrm{.}0$ m$.$ Assuming the vortex is in cyclostrophic

balance, integrate the equation to find an expression for the central pressure. You may

assume the density is $1\mathrm{.}0$ kg m$3.$ Hints: You may assume that the tornado rotates

with constant angular velocity $,$ which enables you to express V in terms of and r$.$

Integrate from the edge of the vortex $($radius re and pressure pe$,$ where the e subscript denotes the edge of the vortex$)$ inward to the center $($radius $0$ and pressure p$0).$ Then solve for central pressure p$0.$

Estimate the Rossby number for this situation.