Hydraulic Jump Calculator
Calculate hydraulic jump characteristics: Froude numbers, sequent depth, head loss, jump efficiency for open channel flow. Free online physics calculator.
About This Calculator
A hydraulic jump is a phenomenon in open channel flow that occurs when flow transitions from supercritical (Fr > 1) to subcritical (Fr < 1). This abrupt change results in a sudden rise in water surface elevation, significant turbulence, and energy dissipation. The Hydraulic Jump Calculator is designed for civil engineers, hydraulic engineers, students, and researchers working on open channel flow problems, spillway design, and channel transitions.
The calculator uses the Froude number equation Fr = v / √(g × y) to determine upstream flow conditions, the conjugate depth equation y₂ = y₁ × 0.5 × (√(1 + 8Fr₁²) - 1) based on conservation of momentum to find the downstream depth, and the head loss formula ΔE = (y₂ - y₁)³ / (4 × y₁ × y₂) to quantify energy dissipation. It also estimates jump length using the empirical relationship L = 220 × y₁ × tanh((Fr₁ - 1) / 22) and jump efficiency as a function of the upstream Froude number.
Results include upstream and downstream Froude numbers (Fr₁, Fr₂), flow velocities (v₁, v₂), sequent downstream depth (y₂), depth ratio (y₂/y₁), head loss (ΔE), jump length (L), jump height (h), and jump efficiency percentage. The calculator also classifies the jump type as undular, weak, oscillating, steady, or strong based on the upstream Froude number range.
Regional Notes
Hydraulic jump analysis is universal and applies worldwide. The calculator uses SI units (m, m³/s, m/s) standard in engineering practice. In the United States, imperial units (ft, ft³/s, ft/s) are sometimes used — engineers can convert inputs using 1 m = 3.281 ft. This calculator is relevant for hydraulic engineering projects globally including dam spillways in India (Bhakra, Hirakud), river training works in the US (Mississippi River), and flood control channels in the UK (Thames Barrier).
Frequently Asked Questions
What is a hydraulic jump in fluid mechanics?
A hydraulic jump is a phenomenon in open channel flow where flow transitions from supercritical (Fr > 1) to subcritical (Fr < 1), causing a sudden rise in water surface with turbulence and energy dissipation. It commonly occurs downstream of spillways, sluice gates, and in natural river rapids.
How do you calculate the Froude number for a hydraulic jump?
The Froude number is calculated as Fr = v / √(g × y), where v is flow velocity in m/s, g is gravitational acceleration (9.81 m/s²), and y is flow depth in meters. For a hydraulic jump, the upstream Froude number Fr₁ must be greater than 1 (supercritical flow) for the jump to occur.
How do you calculate the depth after a hydraulic jump?
The downstream depth (sequent depth) after a hydraulic jump is calculated using the conjugate depth equation: y₂ = y₁ × 0.5 × (√(1 + 8Fr₁²) - 1), where y₁ is the upstream depth and Fr₁ is the upstream Froude number. This equation is derived from the conservation of momentum across the jump.
What are the different types of hydraulic jumps?
Hydraulic jumps are classified by upstream Froude number: Fr₁ < 1.7 (undular jump with small surface waves), 1.7-2.5 (weak jump with low energy loss), 2.5-4.5 (oscillating jump with irregular waves), 4.5-9.0 (steady jump with 70% energy dissipation), and Fr₁ > 9 (strong jump with up to 85% energy loss and high turbulence).
How much energy is lost in a hydraulic jump?
The energy loss (head loss) in a hydraulic jump is calculated as ΔE = (y₂ - y₁)³ / (4 × y₁ × y₂). Jump efficiency ranges from very low (under 20% for undular jumps) to up to 85% for strong jumps (Fr₁ > 9). This energy loss makes hydraulic jumps useful for energy dissipation in hydraulic structures.
What is the length of a hydraulic jump?
The length of a hydraulic jump can be estimated as L = 220 × y₁ × tanh((Fr₁ - 1) / 22), where y₁ is the upstream depth and Fr₁ is the upstream Froude number. This is an empirical relationship based on experimental data and is measured from the toe of the jump to the downstream end of the turbulent region.
What is the difference between supercritical and subcritical flow?
Supercritical flow (Fr > 1) has high velocity and shallow depth, with flow velocity exceeding wave celerity so disturbances travel downstream. Subcritical flow (Fr < 1) has low velocity and greater depth, with disturbances traveling upstream. A hydraulic jump occurs when flow transitions from supercritical to subcritical.
Where do hydraulic jumps occur in practice?
Hydraulic jumps are commonly used in hydraulic engineering applications such as spillway stilling basins to dissipate energy and prevent downstream erosion, below sluice gates and weirs, in sewage treatment plants for mixing, and in natural channels where steep rapids transition to gentle slopes. In India, hydraulic jump stilling basins are used in dam spillways like Bhakra and Hirakud.