Hydraulic jump
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:
<math>\frac{H_2}{H_1} = \frac{1}{2}(\sqrt{8{F_1^2} + 1} - 1)</math>
where <math>F_1 = \frac{V_1}{\sqrt{gY_1}}</math>
<math>F_1</math> is called the Froude number, <math>V_1</math> is the speed of the water, <math>g</math> is the acceleration due to gravity, and <math>Y_1</math> is the depth of the water.
* This is a simplified version of the continuity equation (it is not in integral form).