$[1]$ A rotating viscometer consists of two concentric cylinders$-$an inner cylinder of radius $R_i$ rotating at

angular velocity ${}_i,$ and a stationary outer cylinder of inside radius $R_o.$ In the tiny gap between the two

cylinders is the fluid of viscosity $.$ The length of the cylinders $($into the page$)$ is $L.$ Torque $(T)$ is required

to rotate the inner cylinder at constant speed. Showing all of your work and algebra, generate an

approximate expression for $T$ as a function of the other variables. Assumptions: $(1)$ incompressible,

Newtonian fluid, $(2)2$D flow without end effects at top and bottom of the cylinders, $(3)$ linear velocity

profile in the gap, $(4)$ small gap with negligible curvature effect.