Hydraulic Jump
A hydraulic jump is a phenomenon in open-channel flow where rapidly flowing supercritical water (Froude number > 1) abruptly transitions to slower subcritical flow (Froude number < 1), accompanied by a significant rise in water depth and intense turbulence. The jump dissipates a large amount of kinetic energy as heat and sound, making it useful as an energy dissipator downstream of spillways, weirs, and sluice gates to protect channel beds from erosion. The sequent (conjugate) depths before and after the jump are related by the Belanger equation.
Key Formula
y2/y1 = (1/2) × (-1 + sqrt(1 + 8·Fr1²))
LaTeX: \frac{y_2}{y_1} = \frac{1}{2}\left(-1 + \sqrt{1 + 8\,Fr_1^2}\right)
| Symbol | Meaning | Unit |
|---|---|---|
| y_1 | Upstream (supercritical) flow depth | m |
| y_2 | Downstream (subcritical) sequent depth | m |
| Fr_1 | Upstream Froude number = V₁ / √(g·y₁) | dimensionless |
| V_1 | Upstream mean flow velocity | m/s |
| g | Acceleration due to gravity | m/s² |
Worked Example
Problem
Water flows at depth y₁ = 0.30 m with velocity V₁ = 4.5 m/s in a wide rectangular channel (g = 9.81 m/s²). Confirm the flow is supercritical and find the sequent depth y₂.
Solution
Froude number: Fr₁ = V₁ / √(g·y₁) = 4.5 / √(9.81 × 0.30) = 4.5 / √2.943 = 4.5 / 1.715 = 2.62 > 1 → supercritical (hydraulic jump will form). Sequent depth ratio: y₂/y₁ = (1/2) × (−1 + √(1 + 8 × 2.62²)) = 0.5 × (−1 + √(1 + 8 × 6.864)) = 0.5 × (−1 + √(56.91)) = 0.5 × (−1 + 7.544) = 0.5 × 6.544 = 3.272. Sequent depth: y₂ = 3.272 × 0.30 = 0.982 m.
Answer
y₂ ≈ 0.98 m; Fr₁ = 2.62 (supercritical upstream)
Classification of Hydraulic Jumps by Upstream Froude Number
| Jump Type | Fr₁ Range | Description | Energy Loss |
|---|---|---|---|
| Undular jump | 1.0 – 1.7 | Slight undulations, no roller | Very small (< 5%) |
| Weak jump | 1.7 – 2.5 | Small rollers, smooth surface | Small (5–15%) |
| Oscillating jump | 2.5 – 4.5 | Irregular, jet oscillates | Moderate (15–45%) |
| Steady jump | 4.5 – 9.0 | Well-defined, stable | High (45–70%) |
| Strong jump | > 9.0 | Very turbulent, rough surface | Very high (> 70%) |
Interactive Tools
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Related Terms
Manning's Equation
Manning's Equation is an empirical formula used to calculate the average velocity and discharge of water flowing in an open channel under uniform flow conditions. Developed by Irish engineer Robert Manning in 1889, it relates flow velocity to the channel's hydraulic radius, bed slope, and a roughness coefficient (Manning's n) that accounts for the resistance caused by the channel boundary. It is the most widely used formula in open-channel hydraulics for the design of drainage channels, rivers, culverts, and sewers.
Bridge Design
Bridge design is the engineering discipline concerned with planning, analysing, and sizing all structural and non-structural components of a bridge to carry specified traffic, wind, seismic, and thermal loads safely and economically over its design life. The process involves selection of bridge type (beam, arch, truss, cable-stayed, suspension), site investigation, load calculations to relevant codes (IRC in India, AASHTO in the USA), structural analysis, material design, and consideration of aesthetics, constructability, and durability. Bridge design integrates structural mechanics, geotechnical engineering, hydraulics, and materials science.
Road Design
Road design (highway engineering) is the branch of civil engineering that deals with the geometric layout, pavement structure, drainage, and traffic capacity of roads and highways to provide safe, comfortable, and efficient movement of vehicles. Geometric design encompasses horizontal alignment (curves), vertical alignment (gradients and vertical curves), sight distances, and cross-sectional elements such as lane widths, shoulders, and median widths. Pavement design involves determining the thickness and composition of surface, base, and sub-base layers to carry traffic loads over the design life without failure; Indian standards are governed by IRC codes.
The term 'hydraulic' is from the Greek 'hydraulikos' (water organ), combining 'hydor' (water) and 'aulos' (pipe). 'Jump' describes the sudden rise in water surface. The phenomenon was first mathematically described by Italian engineer Giorgio Bidone in 1820, and the depth relationship (Belanger equation) was formalised by Jean-Baptiste Charles Joseph Belanger in 1838.