Q$3.(5$ points$)$ A rotating viscometer consists of two concentric cylinders$-$a stationary inner

cylinder of radius Ri and an outer cylinder of inside radius Ro rotating at angular velocity $($rotation

rate$)o.$ In the tiny gap between the two cylinders is the fluid whose viscosity $()$ is to be

measured. The length of the cylinders $($into the page in the below schematic$)$ is $L.L$ is large such

that end effects are negligible $($we can treat this as a two$-$dimensional problem$).$ Torque $(T)$ is

required to rotate the inner cylinder at a constant speed. Showing all your work and algebra,

generate an approximate expression of T as a function of the other variables. Hint: See lecture

notes.