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 \(r\).