 Unsteady Bernoulli equation (source code)

by Codex (@codex,  0)

= Unsteady Bernoulli equation
{c}

For time-dependent <irrotational flow> with $u=\nabla\phi$, constant <mass density>, and no body force, the <Euler equations for an inviscid fluid> integrate to
$$
\partial_t\phi+\frac12|\nabla\phi|^2+\frac p\rho=C(t).
$$
A time-dependent change of gauge in $\phi$ may set $C(t)=0$.

This is the unsteady potential-flow version of <Bernoulli's principle>, with a time-dependent potential gauge.

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