Hydraulic Jump Calculator
Compute sequent depth, energy loss, and Froude number for a hydraulic jump in an open channel. Used by hydraulic engineers to design stilling basins and dissipate kinetic energy in spillways.
About this calculator
A hydraulic jump occurs when supercritical flow (Froude number > 1) transitions abruptly to subcritical flow, dissipating energy through turbulence. The sequent (conjugate) depth y₂ is found from the momentum equation: y₂ = (y₁/2) × (−1 + √(1 + 8Fr₁²)), where Fr₁ = V₁/√(g·y₁) is the upstream Froude number. The energy loss across the jump is ΔE = (y₂ − y₁)³ / (4·y₁·y₂). A higher upstream Froude number produces a more violent jump and greater energy dissipation. Engineers classify jumps from undular (Fr ≈ 1–1.7) to strong (Fr > 9). The channel width is used to compute volumetric flow rate Q = V₁ × y₁ × width.
How to use
Suppose y₁ = 0.5 m, V₁ = 4 m/s, and g = 9.81 m/s². First compute Fr₁ = 4/√(9.81 × 0.5) = 4/2.215 ≈ 1.806. Then: y₂ = (0.5/2) × (−1 + √(1 + 8 × 1.806²)) = 0.25 × (−1 + √(1 + 26.09)) = 0.25 × (−1 + 5.204) = 0.25 × 4.204 ≈ 1.051 m. Energy loss: ΔE = (1.051 − 0.5)³ / (4 × 0.5 × 1.051) = 0.166/2.102 ≈ 0.079 m. Enter your own values to size a stilling basin.
Frequently asked questions
What is a hydraulic jump and when does it occur in open channels?
A hydraulic jump is an abrupt transition from fast, shallow (supercritical) flow to slow, deep (subcritical) flow in an open channel. It occurs whenever the upstream Froude number exceeds 1.0 and downstream conditions force a backwater effect, such as below a sluice gate or at the toe of a spillway. The jump converts kinetic energy into turbulence and heat, reducing flow velocity significantly. Engineers deliberately induce hydraulic jumps in stilling basins to protect channel beds from erosion.
How does the Froude number affect the strength of a hydraulic jump?
The Froude number Fr₁ = V/√(g·y) determines the intensity of the jump. When Fr₁ is between 1.0 and 1.7, the jump is undular with small surface waves and minimal energy loss. Between 1.7 and 2.5 the jump becomes weak, and for Fr₁ > 4.5 it becomes oscillating or strong with up to 85% energy dissipation. Higher Froude numbers demand more robust stilling basin designs to contain the turbulence. The sequent depth ratio y₂/y₁ also increases sharply with Fr₁.
Why is energy loss important to calculate for a hydraulic jump design?
Energy loss quantifies how much head is dissipated across the jump, which is the primary purpose of a designed stilling basin. If the basin is too short or the energy loss is underestimated, high-velocity flow can exit and scour the downstream channel bed. Accurately computing ΔE = (y₂ − y₁)³ / (4·y₁·y₂) lets engineers size the basin length, apron thickness, and baffle blocks correctly. Overdesigning wastes construction material, while underdesigning risks structural failure. Regulatory hydraulic models often require documented energy dissipation calculations.