A simple model for a tornado is a central core of radius \(R\) rotating at an angular velocity of \(\Omega\) and an outer region. The flow is assumed to be tangential in both regions. Derive an expression for the tangential velocity and radial pressure distribution in the tornado. In particular, find an expression for the pressure at the eye of the tornado. This pressure will be found to be below atmospheric pressure and is responsible for all the damage caused by the tornado.

Hint: solve the problem as a two-region case, with an inner core with the solution domain of \(0 \leq r \leq R\) and an outer core \(R \leq r \leq \infty\). Also use the condition that the velocity and pressure are continuous functions of the radial position.

As a numerical example, consider a tornado with a core radius of \(60 \mathrm{~m}\) with the maximum wind speed of \(100 \mathrm{~km} / \mathrm{h}\). Find the pressure at the eye of the storm.