2. Consider a tornado. (a) Derive an expression for the distribution of pressure as a function of radial distance r from the center of the tornado. Assume that the velocity in the tornado is given by vr, where v is the azimuthal wind and is a constant. Assume that the temperature does not vary within the tornado. Your answer should be p = something where that something depends on r. Hint: You must assume sort of balance, and it might also be useful to use the ideal gas law to substitute for p. (b) Given the expression you derived in (a), calculate the pressure at the center of the tornado if the temperature is 288 K and the pressure and wind speed at 100 m from the center are 1000 hPa and 100 ms, respectively.