Past exam of the probability, statistics and options I course of the University of Oxford / 2008 / K / 1 / iii

For steady inviscid flow of constant density without a body-force potential, Bernoulli's theorem givesThe constant can differ between streamlines, because this flow has nonzero vorticity. Dotting the steady Euler equation with $\mathbf{u}$ gives $\mathbf{u}\cdot \nabla (p/\rho +|\mathbf{u}{|}^2/2)=0$, which proves precisely the along-streamline form.