Question

4. A tornado rotates with constant angular velocity o. Show that the surface pressure at the center of the tornado is given by: where po is the surface pressure at a distance ro from the center and T is the temperature (assumed constant). If the temperature is 288 K, pressure at 100 m from the center is 102 kPa, and wind speed at 100 m from center is 100 ms'1, what is the central pressure?

Answer 1

Given that: A tornado rotates with constant angular velocity Let 'r' be the distance from axis of rotation of tornado. v^2/r = 1/e partial differential p/partial differential r = omega^2 r p^-1 = RT/p integral_p_0^p d(ln p) = (omega^2/RT) integral_r_0^0 r dr ln(p/p_0) = -omega^2 r_0^2/2RT By Substituting omega^2 r_0^2/2RT < < 1 rightwardsdoublearrow p = p_0 [1 - omega^2 r_0^2/2RT] = 94 kPa