In the Couette viscometer $($shown below$),$ the liquid whose viscosity is to be measured is filled

between the two concentric cylinders, the inner one rotating with a constant angular velocity $$ while

the outer one is restrained by a torsional spring. The torque, $T,$ acting on the outer cylinder is

measured. Assuming the flow to be steady, laminar, incompressible and purely circular and

independent of $z,$ obtain an expression for $$ in terms of $T,,R_i$ and $R_{\text{@}}($radii of inner and outer

cylinder$).$ Also, show that for $\frac{R_i}{R_o}1,$ the velocity profile is approximately linear.