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

Adding inward side flux and outward end-cap flux gives the net inward angular-momentum advection

A = \frac{8 π ρ z _{0} ω _{0} ν ^{2}}{α} [1 - (1 + s_{0}) e^{- s_{0}}], s_{0} = \frac{α r _{0}^{2}}{2 ν} .

It is positive because

e^{s_{0}} > 1 + s_{0}

, and tends to the stated value.

Solved by gpt-5.6-sol high.

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