Hydraulic Jump Calculator (Sequent Depth, Energy Loss & Jump Type)

How it works

Fr₁ = V₁ / √(g·y₁) · Bélanger equation: y₂ = (y₁/2)·[√(1 + 8·Fr₁²) − 1] · V₂ = V₁·y₁/y₂ · head loss ΔE = (y₂ − y₁)³ / (4·y₁·y₂) · critical depth yc = (q²/g)^(1/3), q = V₁·y₁ · jump length ≈ 6·y₂ · power = ρ·g·Q·ΔE.

When fast, shallow supercritical flow (Froude number above 1) meets slower, deeper subcritical flow — below a spillway, a sluice gate or a steep chute — it rises abruptly in a turbulent roller called a hydraulic jump. Momentum is conserved across the jump but energy is not, which is why stilling basins use jumps to dissipate energy before water reaches an erodible channel. The Bélanger equation gives the sequent (conjugate) depth for a horizontal rectangular channel; the USBR classification by Fr₁ describes the jump’s character, with steady jumps (Fr₁ 4.5–9) giving the best stilling-basin performance.

Worked example

Water leaves a sluice gate 0.3 m deep at 6 m/s in a 2 m wide channel. Fr₁ = 6/√(9.81 × 0.3) = 3.50, an oscillating jump. y₂ = 0.15 × (√(1 + 8 × 3.50²) − 1) = 1.342 m, so the water jumps 1.042 m, slowing to 1.34 m/s. The head loss is (1.342 − 0.3)³/(4 × 0.3 × 1.342) = 0.702 m — 32.9% of the upstream energy — and the jump is roughly 6 × 1.342 = 8.05 m long.

Sources: Hydraulic jump — Bélanger equation and classification · US Bureau of Reclamation — Hydraulic Design of Stilling Basins and Energy Dissipators (Engineering Monograph 25)

Frequently asked questions