Problem 2.243

A gas fills up the space between two long coaxial cylinders of radii $R_{1}$ and $R_{2},$ with $R_{1}< R_{2} .$ The outer cylinder rotates with a fairly low angular velocity $\omega$ about the stationary inner cylinder. The moment of friction forces acting on a unit length of the inner cylinder is equal to $N_{1}$. Find the viscosity coefficient $\eta$ of the gas taking into account that the friction force acting on a unit area of the cylindrical surface of radius $r$ is determined by the formula $\sigma=$ $=\eta r(\partial \omega / \partial r)$