Calculate downstream depth, energy loss, jump length, and power dissipated in a hydraulic jump. Supports rectangular, trapezoidal, and triangular channels.
A hydraulic jump occurs when supercritical flow (Fr > 1) rapidly transitions to subcritical flow (Fr < 1). The jump is an extremely turbulent, energy-dissipating phenomenon used in stilling basins downstream of spillways, weirs, and sluice gates to protect channel beds from erosion.
This calculator applies the momentum equation to compute the downstream (sequent) depth y₂ from the upstream depth y₁ and velocity V₁. For rectangular channels, the classic Bélanger equation gives y₂/y₁ = ½(√(1 + 8Fr₁²) − 1). The calculator also extends to trapezoidal, triangular, and circular cross-sections.
Key outputs include the Froude numbers before and after the jump, energy loss, jump type classification (undular, weak, oscillating, steady, or strong), estimated jump length, roller length, and the power dissipated. These values are commonly used to size stilling basins and check whether downstream structures can tolerate the remaining energy. They also help you judge whether a jump is likely to form where you expect or whether tailwater conditions will shift or drown it out.
Use this calculator to estimate sequent depth, jump length, and energy dissipation before committing to a basin layout or checking whether tailwater conditions can hold the jump in place. It is most useful as a first-pass design check for spillways, gates, and channels where uncontrolled supercritical flow could otherwise damage the downstream bed or structure.
Bélanger equation (rectangular): y₂ = (y₁/2)(√(1 + 8Fr₁²) − 1) Froude number: Fr = V / √(gy) Energy loss: ΔE = (y₂ − y₁)³ / (4y₁y₂) Jump length: L ≈ 6.1 × y₂ Power dissipated: P = γ Q ΔE Where: • y₁, y₂ = upstream/downstream depths (m) • V = mean velocity (m/s) • g = gravitational acceleration (m/s²) • γ = specific weight of water (9810 N/m³)
Result: y₂ = 4.93 m, ΔE = 10.8 m, P = 3,820 kW
Fr₁ = 12/√(9.81×0.3) = 6.99. y₂ = (0.3/2)(√(1+8×6.99²)−1) = 4.93 m. ΔE = (4.93−0.3)³/(4×0.3×4.93) = 10.8 m. Q = 12×10×0.3 = 36 m³/s. P = 9810×36×10.8 = 3,820 kW.
The upstream Froude number largely determines the kind of jump you should expect. Weak and undular jumps dissipate little energy, while steady and strong jumps create the turbulence that designers rely on in stilling basins. If the flow lands in the oscillating range, the jump can be unstable and hard to control.
A sequent-depth calculation is only the start. In practice you still need to compare the predicted downstream depth with available tailwater, basin geometry, appurtenances such as chute blocks or end sills, and scour protection downstream. The calculator is best used as a screening and concept-design tool.
The most common mistakes are using velocity where discharge-based section properties are needed, assuming the rectangular formula applies to every section, and ignoring submergence. If tailwater is too high, the jump can drown out and dissipate less energy than the free-jump estimate suggests.
No hydraulic jump forms — the flow is already subcritical. A jump requires supercritical approach flow (Fr > 1). The calculator will flag this condition.
Fr < 1.7: undular (standing waves, little dissipation). 1.7–2.5: weak jump. 2.5–4.5: oscillating (unstable, avoid in design). 4.5–9: steady (most efficient for stilling). > 9: strong (very turbulent, rough surface).
Empirically, L_j ≈ 6.1 × y₂ for a free jump in a rectangular channel. This is an estimate — USBR and other agencies publish refined curves by Froude number.
The jump positions itself where downstream conditions force the flow depth to match the sequent depth. In design, sill blocks and end sills in stilling basins help anchor the jump location.
Energy loss increases dramatically with Fr₁. At Fr₁ = 3, about 25% of energy is lost. At Fr₁ = 9, roughly 70% is dissipated. At Fr₁ = 20, over 85% is consumed by turbulence.
Yes. Non-rectangular channels have different momentum balances. The Bélanger equation is exact only for rectangular sections. For trapezoidal channels, iterative or graphical solutions are needed.