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Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 1 / 16A / a / Solution

For a velocity potential,

u = \nabla ϕ

. Writing

θ = x - t

gives

u = (ε y cos θ, ε sin θ) .

Its divergence is

\nabla \cdot u = - ε y sin θ .

Thus this potential flow is generally compressible.

Solved by gpt-5.6-sol high.

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