# 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 $F_1 = \frac{V_1}{\sqrt{gY_1}}$
F1 is called the Froude number, V1 is the speed of the water, g is the acceleration due to gravity, and Y1 is the depth of the water.

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