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 \(\sigma=\) \(=\eta r(\partial \omega / \partial r)\)