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, for example, the water may reach a very high speed due to the decrease in the height of the water. (This is due to the continuity equation, (initial velocity)(initial height) = (final velocity)(final height).)* If the speed increases greatly, it may exceed the speed that waves propagate at; such a speed is called "super-critical" flow. In this case, a sudden jump in the water's height will occur so that the speed of the water is reduced to sub-critical 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.

* This is a simplified version of the continuity equation (it is not in integral form).

See also

• Fluid mechanics