= Reflected information in a finite lock release
{title2=$t_{\rm hit}=2t_r[(F+2)/2]^{3/2}$}
A rectangular lock of length $\ell_0$ and depth $h_0$ has rarefaction head speed $-c_0$, where $c_0=\sqrt{g'h_0}$. It reaches a closed rear wall at $t_r=\ell_0/c_0$. The first reflected positive <characteristic curve> follows $x=\ell_0+2c_0t-3c_0t_r^{2/3}t^{1/3}$ inside the undisturbed rarefaction, then crosses the uniform shelf and reaches the front at the displayed time. This marks the end of the initial constant-speed front stage in the ideal fixed-front-Froude model.
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