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Hydraulic Jump Calculator

Calculate sequent depth, energy loss, jump length, and classify jump type in rectangular channels for hydraulic jump analysis.

Hydraulics & Water Resources Hydraulic engineers, water resources engineers, students Commercial Intent: MODERATE

Engineering Formulas

Froude Number

Fr₁ = V₁ / √(g Γ— y₁) Frβ‚‚ = Vβ‚‚ / √(g Γ— yβ‚‚)
Fr: Froude number (dimensionless)
V: Flow velocity (m/s)
g: Gravitational acceleration (9.81 m/sΒ²)
y: Flow depth (m)

Sequent Depth Equation

yβ‚‚ = y₁ Γ— 0.5 Γ— (√(1 + 8 Γ— Fr₁²) βˆ’ 1)
yβ‚‚: Sequent depth after jump (m)
y₁: Inflow depth before jump (m)
Fr₁: Inflow Froude number

Energy Loss

Ξ”E = (yβ‚‚ βˆ’ y₁)Β³ / (4 Γ— y₁ Γ— yβ‚‚)
Ξ”E: Energy loss across jump (m)
y₁: Inflow depth (m)
yβ‚‚: Sequent depth (m)

Specific Force

F = 0.5 Γ— Ξ³ Γ— yΒ² + (Ξ³ Γ— QΒ²) / (g Γ— A)
F: Specific force (N)
Ξ³: Specific weight of water (9810 N/mΒ³)
y: Flow depth (m)
Q: Discharge (mΒ³/s)
A: Flow area (mΒ²)
g: Gravitational acceleration (m/sΒ²)

Engineering Notes

A hydraulic jump can only form when Fr₁ > 1 (supercritical inflow).
The steady jump (Fr 4.5–9.0) provides the most stable energy dissipation and is preferred for stilling basin design.
Jump length formulas are empirical; USBR recommends 6.9Γ—(yβ‚‚βˆ’y₁) for Fr 4.5–9.0.
Oscillating jumps (Fr 2.5–4.5) produce surface waves and may require wave suppressors.

Assumptions

β€’ Rectangular, horizontal channel section
β€’ Steady flow conditions
β€’ Negligible friction losses along the jump
β€’ Hydrostatic pressure distribution before and after jump
β€’ Uniform velocity distribution at sections

Common Mistakes

βœ• Using sequent depth equation for non-rectangular channels
βœ• Forgetting to check Fr₁ > 1 before applying jump equations
βœ• Confusing jump length with sequent depth
βœ• Applying the 6.9Γ—(yβ‚‚βˆ’y₁) length formula outside its valid Fr range

Frequently Asked Questions

What is a hydraulic jump?

A hydraulic jump occurs when supercritical flow (Fr > 1) transitions to subcritical flow (Fr < 1), causing a sudden rise in water surface with turbulent energy dissipation. It commonly occurs downstream of spillways, sluice gates, and in stilling basins.

What is sequent depth?

Sequent depth (yβ‚‚) is the conjugate depth after the hydraulic jump β€” the depth required to satisfy the momentum equation for a given inflow Froude number. It is always greater than the inflow depth (y₁).

Why are hydraulic jumps used in stilling basins?

Hydraulic jumps dissipate excess kinetic energy from supercritical flow, preventing scour and erosion downstream of hydraulic structures. Stilling basins are designed to contain and stabilize the jump within a controlled region.

What does the Froude number tell us about jump type?

The Froude number determines the jump type: Fr 1.0–1.7 (undular), 1.7–2.5 (weak), 2.5–4.5 (oscillating), 4.5–9.0 (steady), and >9.0 (strong). Steady jumps at Fr 4.5–9.0 are preferred for energy dissipation in stilling basins.

References & Standards

USBRChow (1959)
Chow (1959)
Open-Channel Hydraulics β€” definitive reference on hydraulic jumps
USBR
Design of Small Dams β€” stilling basin design standards
Hager (1992)
Energy Dissipators and Hydraulic Jump β€” modern analysis

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