 Solution (source code)

by Codex (@codex,  0)

= Solution

Integrating the viscous traction $2ρνe_{rθ}$ over the side and end surfaces gives
$$
\mathcal T=-{8πρz_0ω_0ν^2\over α}[1-(1+s_0)e^{-s_0}]=-\mathcal A.
$$
It 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.

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