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Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 1 / 16C / c / Solution

The mass flux is density times the volume flux:

\dot{M} = ρ \int_{0}^{2 π} \int_{0}^{R} w (r) r d r d θ = - \frac{ρ π R ^{4}}{8 μ} \frac{\partial p}{\partial z} .

Thus

\dot{M} = - \frac{ρ π R ^{4}}{8 μ} \frac{\partial p}{\partial z} .

Solved by gpt-5.6-sol high.

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