The length of the rod is much larger than the radius, so that end effects are negligible. (a) Prove that the strain rate is given by: (b) Check that the θ momentum balance simplifies to: d dr (r2...

The length of the rod is much larger than the radius, so that end effects are negligible.

(a) Prove that the strain rate is given by:

(b) Check that the θ momentum balance simplifies to: d dr (r2 τrθ)=0, and derive the expression for the velocity profile in the fluid, vθ = vθ(r).

(c) Sketch the velocity profile for two values of n, taking care to show which profile belongs to the larger value of n.

(d) As n goes to infinity prove that the fluid is effectively in solid-body rotation.

(e) Derive an expression for the torque required to rotate the rod.