Hydraulic Jump Calculator
Calculate downstream depth, velocity, Froude numbers, energy loss, efficiency, discharge, and dissipated power based on upstream conditions, channel width, gravity, and fluid density. Hydraulic Jump Calculator helps hydraulic engineers, designers, and students analyze energy dissipation and flow transitions in open channels.
Highlights
- Calculate downstream sequent depth and hydraulic-jump strength.
- Determine upstream and downstream Froude numbers for flow classification.
- Estimate discharge and flow velocities in rectangular channels.
- Measure energy loss, jump efficiency, and dissipated power.
- Estimate hydraulic-jump length for practical channel design.
Table of Contents
How Hydraulic Jump Calculator Works?
A hydraulic jump is a rapid transition from shallow, fast, supercritical flow to deeper, slower, subcritical flow in a rectangular open channel. The calculator uses the upstream depth, upstream velocity, channel width, fluid density, and gravitational acceleration to determine the sequent depth, flow characteristics, energy dissipation, and estimated jump length.
The upstream Froude number compares inertial effects with gravity effects:
For the upstream section, V1 is the mean velocity, y1 is the upstream depth, and g is gravitational acceleration. A hydraulic jump generally requires supercritical upstream flow, commonly represented by Fr1 greater than 1.
The downstream, or sequent, depth is calculated from the rectangular-channel momentum relationship:
Here, y2 is the downstream depth. The sequent depth ratio, y2/y1, indicates jump strength: a ratio near 1 represents a weak jump, while a larger ratio indicates a stronger transition.
Continuity gives the discharge and downstream velocity:
In these equations, b is channel width and Q is volumetric discharge. The downstream Froude number is then evaluated using V2 and y2.
Specific energy is the sum of flow depth and velocity-head terms:
The calculator determines upstream and downstream specific energy, then calculates the specific energy loss:
Jump efficiency expresses the remaining specific energy as a percentage of the upstream value:
Energy dissipation power combines the specific energy loss with discharge, density, and gravity:
The estimated jump length is based on a commonly used screening approximation:
The main calculated quantities are summarized below.
| Output | Calculation basis |
|---|---|
| Downstream depth | Rectangular-channel sequent-depth relationship |
| Depth ratio | y2/y1 |
| Downstream velocity | Continuity, Q/(b y2) |
| Froude numbers | V/√(g y) |
| Specific energies | y + V2/(2g) |
| Energy loss | E1 − E2 |
| Dissipated power | ρgQΔE |
| Estimated jump length | Approximately 6y2 |
Inputs may be provided using the supported depth and width units of m, cm, mm, ft, or in; velocity units of m/s, ft/s, km/h, or mph; density units of kg/m³, g/cm³, or lb/ft³; and gravitational acceleration units of m/s² or ft/s². Outputs include the supported depth, velocity, discharge, energy, power, and efficiency units listed by the calculator.
Practical Use Cases
Hydraulic engineers can estimate the downstream depth, Froude numbers, energy loss, and dissipated power when analyzing a hydraulic jump in a rectangular channel. These results help assess whether the transition provides adequate energy dissipation and whether downstream flow conditions are compatible with the channel layout.
Dam and spillway designers can use the calculator to obtain a preliminary sequent depth and jump length below a spillway or outlet structure. The energy-loss and power outputs provide an initial indication of the dissipative demand placed on the stilling basin.
Irrigation and drainage designers can evaluate flow transitions in canals, chutes, and drainage channels by entering the upstream depth, velocity, and channel width. The depth ratio and downstream velocity help identify potential changes in water-surface elevation and flow regime.
Water-treatment and process engineers can estimate discharge and hydraulic energy dissipation in channels where turbulence and mixing are important. Fluid density can be specified for fluids that differ substantially from typical fresh water.
Civil engineering students and instructors can compare upstream and downstream Froude numbers, verify the sequent-depth equation, and study how velocity, depth, gravity, and channel width affect hydraulic-jump behavior.
Field and design reviewers can use the calculator as a rapid screening tool for checking reported depths, velocities, discharge, specific energies, and approximate jump length before performing a detailed hydraulic model or site-specific design.
Accuracy and Limitations
The calculator is accurate for the idealized one-dimensional hydraulic-jump model in a prismatic rectangular channel, using hydrostatic pressure, steady flow, continuity, and momentum conservation. It assumes negligible friction and bed-slope effects across the jump and estimates jump length as approximately six times the downstream depth, so the length should not replace a site-specific design or physical model. Results can be less representative for irregular or nonrectangular channels, strongly curved or sloping channels, submerged jumps, rapidly varying inflow, significant air entrainment, nonuniform velocity profiles, or conditions where the upstream Froude number is not greater than 1. Because dissipated power is proportional to density, gravity, discharge, and energy loss, errors in any of those inputs directly affect the power result.
Quick Examples
Example #1: Standard Concrete Flume
Analyzes a typical hydraulic jump in a rectangular open channel carrying water under standard gravity.
Example #2: Metric Laboratory Experiment
Examines a smaller-scale hydraulic jump using centimeter dimensions and a controlled laboratory flow.
Example #3: Imperial Irrigation Channel
Evaluates hydraulic-jump energy dissipation in an irrigation channel using imperial input units.
