= Inviscid falling jet and radial impact film
{title2=$u^2=u_0^2+2g(H-z),\quad \pi R^2u=\pi a^2u_0$}
A steady incompressible jet at atmospheric <pressure> conserves <Bernoulli's equation> and <volume flux>. Its radius contracts as $R=a[u/u_0]^{-1/2}$. After impact, a thin nearly horizontal axisymmetric film has $2\pi rhv=\pi a^2u_0$. Evaluating <Bernoulli's equation> on its <free surface> gives $v^2=u_0^2+2g(H-h)$, hence $a^4/(4r^2h^2)=1+2g(H-h)/u_0^2$. This inviscid thin-film description applies away from the impact region and does not describe a dissipative hydraulic jump.
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