Hydraulic Jump: Sequent Depth and Energy Loss
Where supercritical flow leaps to a deeper tranquil depth below a chute or culvert.
Example
You enter
- Channel width b (ft) 10
- Discharge Q (cfs) 100
- Upstream (supercritical) depth y1 (ft) 0.8
You get
- Upstream Froude number Fr1 2.4628
- Y2 (ft) 2.415
- De (ft) 0.545
Details, formula, and sources
Belanger's sequent depth y2 = (y1/2)(sqrt(1 + 8 Fr1^2) - 1) and the specific-energy loss dE = (y2 - y1)^3/(4 y1 y2). A 10 ft channel at 100 cfs and a shooting 0.8 ft depth (Fr1 2.46) jumps to 2.42 ft and throws away 0.55 ft of head; push it to 200 cfs (Fr1 4.93) and it jumps to 5.19 ft killing 5.1 ft - which is why a stilling basin is sized to the Froude number, not the flow. Rectangular, horizontal channel; the tailwater must supply the sequent depth. A design aid; the engineer of record governs.
V1 = Q/(b y1); Fr1 = V1/sqrt(g y1) (> 1); y2 = (y1/2)(sqrt(1 + 8 Fr1^2) - 1); dE = (y2 - y1)^3/(4 y1 y2); efficiency = (y2 + V2^2/2g)/(y1 + V1^2/2g).
The Belanger momentum (sequent-depth) hydraulic-jump relation for a rectangular channel and the specific-energy loss, as compiled in Chow's Open-Channel Hydraulics, by name.
The Belanger sequent-depth relation and the jump energy-loss expression are public results in the standard open-channel-hydraulics references.
Estimate. AHJ and licensed professional govern.
Field names used by the API: b_ft, q_cfs, y1_ft, fr1, y2_ft, de_ft
- Sequent depth y2 = (y1/2)(sqrt(1 + 8 Fr1^2) - 1) is the momentum conjugate of the supercritical y1, not the downstream normal depthBelanger / Chow
- Tailwater controls location the tailwater must supply the sequent depth for the jump to sit here; the energy loss grows steeply with Fr1Chow open-channel hydraulics