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Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 3 / 7C / b / Solution

For a two-dimensional incompressible flow, the stream function convention

u_{r} = \frac{1}{r} \frac{\partial ψ}{\partial θ}, u_{θ} = - \frac{\partial ψ}{\partial r}

is satisfied by

ψ (r, θ) = \frac{d sin θ}{r} + C .

Solved by gpt-5.6-sol high.

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