Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 38A / d / Solution

Integrating the viscous traction $2\rho \nu e_{r\theta }$ over the side and end surfaces givesIt is always negative. In steady state the cylinder stores no angular momentum, so the divergence theorem for angular-momentum balance requires viscous torque to cancel net advective influx.