Hydraulic jumps in rectangular channels

Hydraulic jump in a rectangular channel, also known as classical jump, is a natural phenomenon that occurs whenever flow changes from supercritical to subcritical flow. In this transition, the water surface rises abruptly, surface rollers are formed, intense mixing occurs, air is entrained, and often a large amount of energy is dissipated. In other words, a hydraulic jump happens when a higher velocity, v1, supercritical flow upstream is met by a subcritical downstream flow with a decreased velocity, v2, and sufficient depth. Numeric models created using the Standard Step Method or HEC-RAS are used to track supercritical and subcritical flows to determine where in a specific reach a hydraulic jump will form. There are common hydraulic jumps that occur in everyday situations such as during the use of a household sink. There are also man-made hydraulic jumps created by devices like weirs or sluice gates. In general, a hydraulic jump may be used to dissipate energy, to mix chemicals, or to act as an aeration device.To produce equations describing the jump, since there is an unknown energy loss, there is a need to apply conservation of momentum. To develop this equation, a general situation in which there may or may not be an energy loss between upstream and downstream, and there may or may not be some obstacle on which there is a drag force Pf is considered. however, for a simple or classic hydraulic jump the force per unit width(Pf) equals 0. From there the momentum equation, and the conjugate depths equation can be derived.