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)