By using Navier Stokes equation and Continuity equation solve this problem.Correct solution needed here.

(n) In the Couette viscometer shown below, the fluid is filled between two concentric cylinders. The inner cylinder rotates at an uniform angular velocity , while the outer one is restrained by a torsional spring. The torque T acting on the outer cylinder is measured by means of the deflection of the spring. Assuming the flow to be steady, laminar, purely circular, and independent of z, obtain an expression for in terms of the torque T on the outer cylinder, angular speed and geometric parameters. Show that if the gap between the two cylinders is small, the velocity profile is approximately linear. (use Navier-Stokes and continuity equations)