How to Use Hydraulic Jump Calculator
The Hydraulic Jump Calculator solves the sequent-depth, velocity and energy-loss relationships for a rectangular open-channel hydraulic jump, based on the Bélanger momentum equation.
- Choose input mode — select “depth + velocity” if you know the upstream depth y₁ and velocity V₁, or “flow rate + width” if you have discharge Q and channel width b.
- Enter upstream conditions — provide y₁ and the second variable in consistent SI units.
- Read the conjugate depth y₂ in the result panel along with the Froude number Fr₁.
- Check downstream velocity V₂, computed from the continuity equation.
- Review the jump type — undular, weak, oscillating, steady or strong — classified automatically by Fr₁.
- Read energy dissipation ΔE and the energy-loss percentage, useful for stilling basin sizing.
Formula & Theory — Hydraulic Jump Calculator
The Hydraulic Jump Calculator applies the Bélanger equation, derived from integrating the momentum equation across a rectangular cross-section:
Fr₁ = V₁ / √(g·y₁)
y₂/y₁ = ½ · ( √(1 + 8·Fr₁²) − 1 )
V₂ = V₁ · y₁ / y₂ (continuity)
ΔE = (y₂ − y₁)³ / (4·y₁·y₂) (head loss)| Symbol | Meaning | SI Unit |
|---|---|---|
| y₁, y₂ | Upstream and sequent (conjugate) depths | m |
| V₁, V₂ | Upstream and downstream mean velocities | m/s |
| Fr₁ | Upstream Froude number (dimensionless) | — |
| ΔE | Specific energy dissipated | m |
| g | Gravitational acceleration (9.81) | m/s² |
Jump types by Fr₁: undular 1.0–1.7, small surface waves, minimal loss; weak 1.7–2.5, smooth rise, ≈15–20 % loss; oscillating 2.5–4.5, unstable jet, avoid for design; steady 4.5–9.0, best basin performance, 45–70 % loss; strong >9.0, rough and violent, >70 % loss.
Use Cases for Hydraulic Jump Calculator
- Stilling basin design — size the apron length at the toe of spillways, chutes and drop structures to confine the jump and prevent scour.
- Energy dissipation analysis — quantify how much incoming kinetic energy is converted to heat and turbulence, reducing erosive power downstream.
- Weir and drop-structure aprons — locate the jump toe and select a suitable floor depth or deflector block arrangement to contain the jump.
- River training and grade control — predict the natural jump position under design discharges for bank and bed stabilisation works.
- Laboratory and teaching flumes — verify Bélanger theory against measured sequent depths and energy profiles in undergraduate hydraulics courses.
- Flood routing — track jump migration under varying discharge to avoid structural overloading at channel transitions.