Hydraulic Jump Calculator
Compute conjugate depth (sequent depth) of a hydraulic jump in a horizontal rectangular channel from the upstream Froude number — with energy loss, efficiency, jump-length estimate, and USBR jump-type classification.
Calculator
Upstream Froude number Fr₁ (dimensionless)–
Conjugate depth y₂–
Rasio y₂/y₁–
Downstream velocity v₂–
Downstream Froude number Fr₂ (dimensionless)–
Jump height hⱼ = y₂−y₁–
Energy loss ΔE–
Efisiensi E₂/E₁–
Jump length L ≈ 6·y₂ (empirical)–
–
Jump length is estimasi empiris (Bradley & Peterka: L/y₂ ≈ 6.0–6.1) — not an exact theoretical result. Applies to horizontal rectangular channels without significant friction.
Jump profile diagram
Formulas used
Fr₁ = v₁ / √(g · y₁)
y₂/y₁ = ½·(√(1 + 8·Fr₁²) − 1) — persamaan Bélanger (momentum)
ΔE = (y₂ − y₁)³ / (4·y₁·y₂) — specific energy loss
E = y + v²/(2g) — specific energy; efficiency = E₂/E₁
L ≈ 6·y₂ — empirical (not theory)
Assumptions: rectangular channel, horizontal bed, hydrostatic pressure distribution, wall friction neglected, jump occurs over a short distance. Fr₁ ≤ 1 means subcritical/critical flow — no jump.
Jump-type classification (USBR / Bradley & Peterka 1957)
| Fr₁ | Type | Ciri |
|---|---|---|
| ≤ 1 | No jump | Aliran subkritis/kritis |
| 1 – 1.7 | Undular | Gelombang permukaan, disipasi < 5% |
| 1.7 – 2.5 | Weak | Small surface roller, 5–15% dissipation |
| 2.5 – 4.5 | Oscillating | Unstable, large downstream waves, 15–45% dissipation |
| 4.5 – 9 | Steady | Stabil, performa terbaik, disipasi 45–70% |
| > 9 | Strong | Kasar tapi disipasi 70–85% |
See also
- Open Channel Flow (Manning) Calculator — debit & kedalaman normal saluran terbuka.
- Froude Number Calculator — Fr = v/√(gL) for ships & channels.
- Broad-Crested Weir Calculator — broad-crested weir discharge.
Scope limits: this tool computes lompatan hidraulik klasik (conjugate depth, ΔE, length, classification) in rectangular channels. General Froude numbers (ships, hydraulic depth) are in the separate Froude tool; Manning discharge is in Open Channel Flow.
Pertanyaan umum
What is a hydraulic jump?
A hydraulic jump is the sudden transition from supercritical flow (fast, shallow, Fr > 1) to subcritical flow (slow, deep, Fr < 1) in an open channel, marked by a steep rise in water surface with a turbulent roller. The phenomenon is used to dissipate water energy downstream of dams, sluice gates, and spillways so it does not scour the channel bed.
How do you calculate the conjugate depth y₂?
For a horizontal rectangular channel, use the Bélanger equation from momentum conservation: y₂/y₁ = ½·(√(1+8·Fr₁²)−1), with Fr₁ = v₁/√(g·y₁). Example: y₁ = 0.5 m and v₁ = 6 m/s (g = 9.80665 m/s²) → Fr₁ = 2.7096, then y₂ = 0.5 × ½·(√(1+8×2.7096²)−1) = 1.6822 m. The calculator above computes it automatically.
Does the Froude number have units?
No. The Froude number Fr = v/√(g·L) is a dimensionless number — the ratio of inertial to gravitational forces. Hence Fr₁ and Fr₂ in this tool are shown without units; the label indeed reads “dimensionless,” not an omission.
What are the types of hydraulic jumps?
USBR (Bradley & Peterka, 1957) classifies five types by Fr₁: undular (1–1.7), weak (1.7–2.5), oscillating (2.5–4.5), steady (4.5–9), and strong (> 9). Each range’s upper bound is inclusive — e.g. Fr₁ of exactly 2.5 is still a weak jump.
When does a hydraulic jump NOT occur?
If Fr₁ ≤ 1 (subcritical or critical flow), there is no jump: y₂ = y₁ and no energy is lost. Example: y₁ = 2 ft, v₁ = 8 ft/s → Fr₁ = 0.9973 < 1, so the flow stays tranquil with no jump.
How much energy is lost in the jump?
Specific energy loss ΔE = (y₂−y₁)³/(4·y₁·y₂). In the example y₁ = 0.5 m, v₁ = 6 m/s: y₂ = 1.6822 m so ΔE = 0.4911 m, with efficiency E₂/E₁ = 78.97%. The larger Fr₁, the greater the energy dissipation.
How long is a hydraulic jump?
Jump length cannot be derived from theory — the empirical Bradley & Peterka estimate is used: L ≈ 6·y₂ (typical range 6.0–6.1 × y₂). In the anchor example (y₂ = 1.6822 m), L ≈ 10.0933 m. This tool labels it explicitly as an empirical estimate.
Calculation example downstream of a sluice gate?
A sluice gate discharges v₁ = 6 m/s at depth y₁ = 0.4 m: Fr₁ = 3.0294 → oscillating jump, y₂ = 1.5253 m, ΔE = 0.5839 m, 73.88% efficiency. Downstream depth must be at least y₂ for the jump to form at that position.
What does a strong jump (Fr₁ > 9) look like?
Example: y₁ = 0.3 m, v₁ = 20.5827 m/s → Fr₁ = 12. Conjugate depth y₂ = 4.9434 m (16.4779× ratio), ΔE = 16.8771 m, only 22.94% efficiency. The flow is rough and churning, but dissipates the most energy.
How is this different from the Froude and Open Channel Flow calculators?
The Froude Number calculator computes the general Fr = v/√(gL) (ships, hydraulic depth) with flow-regime classification; Open Channel Flow computes Manning discharge and normal depth. This tool specifically computes hydraulic jumps: conjugate depth, ΔE, length, and the five USBR jump-type classifications — which neither of those tools computes.
Results are educational/preliminary-engineering — verify with a full hydraulic analysis for water-structure design.
Free tool by NRTechStudio