= Solution
In <steady flow>, the <Euler equations for an inviscid fluid> and part (a) give
$$
\nabla H=\mathbf u\times\boldsymbol\omega,\qquad H=\tfrac12|\mathbf u|^2+\frac p\rho+\Phi.
$$
Taking the dot product with $\mathbf u$ yields $\mathbf u\cdot\nabla H=0$, because a <cross product> is perpendicular to its first factor. Part (b) therefore gives \b[Bernoulli's quantity along streamlines]:
$$
\boxed{\tfrac12|\mathbf u|^2+\frac p\rho+\Phi=\text{constant on each streamline}.}
$$
For rotational flow these constants can differ between <streamlines>, since $\mathbf u\times\boldsymbol\omega$ need not vanish and therefore $\nabla H$ need not be zero. Special rotational flows can still have one global constant when that cross product vanishes; the general conclusion is only constancy along individual <streamlines>.
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