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Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 1 / 16D / Solution

For steady inviscid flow, Bernoulli's equation along a streamline is

p + \frac{1}{2} ρ ∣ u ∣^{2} + χ = constant .

Writing steady Euler flow in divergence form and integrating over

V

gives

\int_{\partial V} (ρ (u \cdot n) u + p n + χ n) d S = 0

by incompressibility and the divergence theorem.

Solved by gpt-5.6-sol high.

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