Hydraulic Jump Calculator
Your Hydraulic Jump Analysis
What Is a Hydraulic Jump Calculator?
A hydraulic jump calculator evaluates the rapid transition from shallow, fast supercritical flow to deeper, slower subcritical flow in a rectangular open channel. This calculator uses the upstream flow conditions to determine the Froude number and, when a jump can form, calculate its main hydraulic properties.
This hydraulic jump calculator determines whether a supercritical rectangular-channel flow can form a hydraulic jump, then estimates the sequent depth, jump height, energy loss, and jump length. It uses flow rate, channel width, and upstream depth, with an optional tailwater depth to indicate whether the jump can hold, drown, or move downstream.
The calculation assumes a horizontal, rectangular, prismatic channel with hydrostatic pressure distribution. Inputs are entered in metric units. Several depth and length results are also displayed in feet for convenience.
How the Hydraulic Jump Calculation Works
The calculator first converts the total flow rate into discharge per unit width. It then determines upstream velocity and the upstream Froude number using gravitational acceleration of 9.81 m/s².
Here, Q is flow rate in m³/s, b is channel width in meters, q is flow per unit width, y₁ is upstream depth, v₁ is upstream velocity, g is 9.81 m/s², and Fr₁ is the upstream Froude number.
The calculator also displays the critical depth in the note beside the Froude number:
If Fr₁ is below 1, the calculator identifies the approach flow as subcritical and reports that a hydraulic jump cannot form. If Fr₁ equals 1, it identifies critical flow and reports that no jump forms. The remaining jump calculations are performed only when Fr₁ is greater than 1.
Jump Classification
| Upstream Froude Number | Classification | Calculator Description |
|---|---|---|
| 1 < Fr₁ < 1.7 | Undular jump | Smooth standing waves and negligible energy loss under 5% |
| 1.7 ≤ Fr₁ < 2.5 | Weak jump | Small surface rollers and 5–15% energy loss |
| 2.5 ≤ Fr₁ < 4.5 | Oscillating jump | Unstable flow with waves traveling downstream and 15–45% energy loss |
| 4.5 ≤ Fr₁ ≤ 9 | Steady jump | Stable, well-balanced jump with 45–70% energy loss |
| Fr₁ > 9 | Strong jump | Violent, rough flow with 70–85% energy loss |
For supercritical approach flow, the calculator uses the Bélanger sequent-depth relationship to calculate the conjugate downstream depth:
It then calculates downstream velocity and the downstream Froude number from the new depth.
The jump height is the difference between the sequent depth and upstream depth. The calculator uses that height to determine the specific-energy loss across the jump.
Upstream specific energy and the percentage dissipated are calculated as:
Finally, jump length is estimated as 6.9 times the calculated jump height.
Worked Example
Suppose Q = 2.5 m³/s, channel width = 1.2 m, and upstream depth = 0.35 m. These values give q = 2.083 m²/s, upstream velocity of about 5.95 m/s, and Fr₁ = 3.21. Because 3.21 falls between 2.5 and 4.5, the calculator classifies the result as an oscillating jump.
The calculated sequent depth is 1.425 m, the jump height is 1.075 m, and the specific-energy loss is 0.622 m. Upstream specific energy is 2.156 m, so the displayed energy loss is 28.9%. The estimated jump length is 7.41 m, or about 24.3 ft.
If the optional tailwater depth is set to 1.8 m in this example, it exceeds 1.1 times the calculated sequent depth. The calculator therefore reports the jump as drowned and notes that energy dissipation is reduced.
How to Use the Hydraulic Jump Calculator
- Enter the Flow Rate, Q in cubic meters per second.
- Enter the rectangular Channel Width, b in meters.
- Enter the Upstream Depth, y₁ in meters.
- If available, enter the Actual Downstream (Tailwater) Depth in meters. This field is optional.
- Click Calculate to display the hydraulic jump analysis.
- Use Reset to clear all four input fields and hide the current results.
Flow rate, width, and upstream depth must all be greater than zero. A blank optional tailwater field is treated as zero and does not produce a tailwater warning. Negative values and nonnumeric values are treated as invalid.
The main Froude number is shown to two decimal places. Sequent depth and jump height are shown to three decimal places in meters, with feet also displayed. Energy loss is shown in meters plus a percentage of upstream specific energy. Estimated jump length is shown in both meters and feet.
How to Read Your Hydraulic Jump Results
Froude Number and Critical Depth
The first result is Fr₁. The calculator also shows the calculated critical depth and labels the upstream flow as subcritical, critical, or supercritical. Only supercritical approach flow, where Fr₁ is greater than 1, proceeds to a hydraulic jump calculation.
Sequent Depth and Jump Height
The conjugate or sequent depth, y₂, is the calculated downstream depth associated with the jump. The calculator also reports downstream velocity and Fr₂. Jump height is y₂ minus y₁ and represents the calculated rise in the water surface.
Energy Loss and Jump Length
Energy loss is displayed as a head loss in meters and as a percentage of the calculated upstream specific energy. Jump length is an empirical estimate equal to 6.9 times the jump height. The calculator specifically notes that this length estimate is most reliable for steady jumps with Fr₁ from 4.5 through 9.
Optional Tailwater Check
If you provide an actual tailwater depth, the calculator compares it with the calculated sequent depth. Tailwater below y₂ produces a warning that the jump cannot hold and will be swept downstream. Tailwater from y₂ up to less than 1.1y₂ indicates that the jump forms and holds its position. Tailwater at or above 1.1y₂ is classified as a drowned jump.
The results are estimates based on the calculator’s stated channel assumptions and equations. Its jump-length result is empirical. The calculator itself advises verifying critical designs with a physical or CFD model rather than treating the result as a final design determination.
Frequently Asked Questions
What inputs does the hydraulic jump calculator require?
The required inputs are flow rate Q in m³/s, rectangular channel width b in meters, and upstream depth y₁ in meters. All three must be greater than zero. An actual downstream or tailwater depth can also be entered, but it is optional.
What does the upstream Froude number mean in this calculator?
Fr₁ determines the upstream flow regime and whether the calculator continues with a jump analysis. Values below 1 are treated as subcritical, a value of 1 as critical, and values above 1 as supercritical. The supercritical range is then divided into the calculator’s five hydraulic jump classifications.
What happens if Fr₁ is 1 or less?
If Fr₁ is below 1, the calculator states that the approach flow is subcritical and a hydraulic jump cannot form. If Fr₁ equals 1, it reports critical approach flow and no jump. In either case, the sequent depth, jump height, energy loss, and jump length outputs are replaced with dashes.
How is hydraulic jump length calculated?
The calculator estimates jump length by multiplying the calculated jump height by 6.9. For example, a jump height of 1 meter gives an estimated length of 6.9 meters. The result is displayed in meters and feet, and the calculator identifies it as an empirical estimate.
What does the optional tailwater depth change?
The optional tailwater depth does not change the calculated sequent depth, energy loss, or jump length. It is used only for the tailwater warning. The calculator compares the entered value with y₂ and 1.1y₂ to indicate whether the jump is swept downstream, holds its position, or is drowned.
Can I enter feet or cubic feet per second?
No unit selector is included. The calculator inputs are defined in metric units: flow rate in m³/s and channel dimensions in meters. It does provide supplementary feet values for the calculated sequent depth, jump height, and jump length, using a conversion factor of 3.28084 feet per meter.
Is the result suitable for final hydraulic design?
The calculator describes its results as estimates. It assumes a horizontal, rectangular, prismatic channel with hydrostatic pressure distribution, and its jump-length calculation is empirical. For critical designs, the calculator’s own limitation statement recommends verification with a physical or CFD model.