Problem 2.20

A horizontal cylinder closed from one end is rotated with a constant angular velocity $\omega$ about a vertical axis passing through the open end of the cylinder. The outside air pressure is equal to $p_{0},$ the temperature to $T,$ and the molar mass of air to $M .$ Find the air pressure as a function of the distance $r$ from the rotation axis. The molar mass is assumed to be independent of $r$.