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Introduction to Hydraulic Jumps and Momentum
The phenomenon known as a hydraulic jump occurs when there is a sudden increase in water level during open channel flow. This transpires when a high-speed, supercritical flow upstream is rapidly slowed and forced to change to subcritical flow. During this change in flow condition and concurrent rise of water level, there is a loss of energy and significant turbulence. This jump cannot occur when the Froude number is less than 1 or when the flow is subcritical upstream.

There are numerous scenarios where a hydraulic jump can take place naturally or as a result of a man-made device. One natural example is when a channel transitions from a steep slope, where water velocity is above critical conditions, to a shallower slope that initiates subcritical flow. This will cause a rise in the water surface and loss of energy near the change in reach grade. Hydraulic jumps also occur when a sluice gate produces supercritical flow on a reach with subcritical flow imposed downstream. This flow change causes the sudden jump in water level downstream of the gate. See Figure 1 and Figure 2 below for examples of the scenarios described above.



While energy is lost during a simple, stationary hydraulic jump, momentum is conserved. Momentum is measured as the product of velocity times mass. It is a vector in the same direction as the velocity. Since flow in open channels is generally linear moving from an upstream to a downstream location, the vector quantity is implied and it is assumed that flow downstream is positive. In order to solve for the water surface height upstream and downstream of the jump, the principle of conservation of momentum must be applied. Setting the momenta upstream and downstream of the jump equal to each other will result in an equation relating the two depths. These two subcritical and supercritical depths with the same momentum are referred to as “conjugate depths”.

Knowledge Gap of Hydraulic Jumps in V-Shaped Channels
Currently, most of the literature regarding hydraulic jumps has focused on rectangular channels , with some attention to circular and trapezoidal cross sections. In the case of a rectangular channel, the following equation can be used to easily solve for the momentum and the conjugate depths on either side of the jump. The units are L3/L or L2.