Hydraulic jump

A hydraulic jump in the river

A hydraulic jump is a discrepancy in water depths. When water in a stream flows over a rock, the water may reach supercritical speed - that is, the speed of the water may exceed the speed that waves propagate at. If so, there will be a sudden change in the water's height so that the speed of the water is reduced to subcritical speed.

The equation that governs this phenomena is:

${\frac {H_{2}}{H_{1}}}={\frac {1}{2}}({\sqrt {8{F_{1}^{2}}+1}}-1)$

where $F_{1}={\frac {V_{1}}{\sqrt {gY_{1}}}}$
$F_{1}$ is called the Froude number, $V_{1}$ is the speed of the water, $g$ is the acceleration due to gravity, and $Y_{1}$ is the depth of the water.