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 $\Delta R=6 \mathrm{~mm} ?$