Edward J. Hickin: River Hydraulics and Channel Form
Chapter 3
The momentum equation for open-channel flow
The momentum equation and the hydraulic jump Hydraulic jumps Deriving the momentum equation Application of the momentum equation to the hydraulic jump
Energy loss in hydraulic jumps Some concluding remarks References
We have seen that the energy equation has many useful applications to a wide variety of flow transition problems. In all cases, however, the solutions depend on the assumption that energy is conserved. If energy actually leaks from the system via frictional head loss the Bernoulli equation will overstate the energy available to the flow and the related predictions of velocity and depth will proportionately be in error. To recall our earlier strategy, we minimize this error by considering only short reaches of channel and only gradual transitions. In certain flow phenomena, however, we simply can no longer ignore the energy losses and we must look to alternative ways of describing the flow.
The momentum approach and the hydraulic jump Hydraulic jumps
One of these cases is the hydraulic jump. Hydraulic jumps mark the flow transition from supercritical to subcritical flow. When subcritical flow accelerates into the supercritical state the transition often is smooth with gradually increasing velocity and decreasing depth bringing about a smooth drop in the water surface until the alternate depth is achieved. Any disturbance to the water surface is smoothed out by the surface or gravity wave propagation mechanism discussed earlier. In these circumstances energy losses are not great and the Bernoulli equation does a
Chapter 3: The momentum equation for open-channel flow
credible job of describing the changes to the flow.
When supercritical flow changes to
subcritical flow, however, there is no smoothing of the water surface upstream of the transition because the high downstream velocity prevents upstream diffusion of the water-surface deformation. As a result the transition to subcritical flow is sudden and marked by an abrupt discontinuity, or hydraulic jump, in the water Hydraulic jump with breaking surge
