 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2008/k/1/iii/solution

For steady inviscid flow of constant density without a body-force potential, Bernoulli's theorem gives

\frac{p}{ρ} + \frac{1}{2} ∣ u ∣^{2} = constant along each streamline .

The constant can differ between streamlines, because this flow has nonzero vorticity. Dotting the steady Euler equation with

u

gives

u \cdot \nabla (p / ρ + ∣ u ∣^{2} /2) = 0

, which proves precisely the along-streamline form.

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