Problem 2.242

Under standard conditions helium fills up the space between two long coaxial cylinders. The mean radius of the cylinders is equal to \(R,\) the gap between them is equal to \(\Delta R,\) with \(\Delta R \ll R .\) The outer cylinder rotates with a fairly low angular velocity \(\omega\) about the stationary inner cylinder. Find the moment of friction forces acting on a unit length of the inner cylinder. Down to what magnitud \(e\) should the helium pressure be lowered (keeping the temperature constant) to decrease the sought moment of friction forces \(n=10\) times if \(\Delta R=6 \mathrm{~mm} ?\)