### Hydraulic Jumps Explained

Fig. 1: A Standing Wave (aka Stationary hydraulic jump) occurs when a flow of liquid at high velocity discharges into a zone of the river or engineered structure which can only sustain a lower velocity

A hydraulic jump is a phenomenon common in open channel flow. If flow before the jump is supercritical, a jump will occur and flow after the jump will be subcritical. The jump destroys excess energy (velocity).

In lamens terms, a hydraulic jump occurs when fast moving liquid (in the supercritical state) contacts slow moving liquid, which converts some of the flows kinetic energy (i.e. speed) into potential energy (i.e. height).

### Hydraulic Jump Equations:

#### Depths

y_2 = -\frac{y_1}{2} + \sqrt{\left(\frac{y_1}{2}\right)^2 + \frac{2V_1^2y_1}{g}}

where

• y2 = depth after the jump (ft)
• y1 = depth before the jump (ft)
• V1 = velocity before the jump (fps)
• y2 & y1 = are called conjugate depths

#### Head Loss

h_L = \frac{(y_2 - y_1)^3}{4y_1 y_2}

where

• hL = head loss in the jump (ft)

#### Energy Loss

HP = \frac{\gamma Q h_j}{550}

where

• HP = energy dissipated by the jump (hp)

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