Calculator Inputs
Example Data Table
| Case | Shape | Depth | Width / z | Input | Hydraulic Depth | Froude Number | Regime |
|---|---|---|---|---|---|---|---|
| 1 | Rectangular | 1.20 m | b = 4.00 m | V = 2.50 m/s | 1.2000 m | 0.7290 | Subcritical |
| 2 | Trapezoidal | 1.10 m | b = 3.00 m, z = 1.00 | V = 3.80 m/s | 0.8673 m | 1.3030 | Supercritical |
| 3 | Triangular | 0.90 m | z = 1.50 | Q = 2.10 m³/s | 0.4500 m | 0.8230 | Subcritical |
Formula Used
The open-channel Froude number is: Fr = V / √(gDh)
V is mean velocity, g is gravitational acceleration, and Dh is hydraulic depth.
Hydraulic depth is: Dh = A / T
A is flow area and T is water-surface top width.
Geometry relations used
- Rectangular: A = by, T = b
- Trapezoidal: A = y(b + zy), T = b + 2zy
- Triangular: A = zy², T = 2zy
Additional outputs
- Wave celerity: c = √(gDh)
- Specific energy: E = y + V²/(2g)
- Discharge: Q = AV
Interpretation: Fr < 1 indicates subcritical flow, Fr ≈ 1 indicates critical flow, and Fr > 1 indicates supercritical flow.
How to Use This Calculator
- Select SI or US customary units.
- Choose the open-channel shape.
- Choose whether velocity or discharge is known.
- Enter flow depth and geometry values.
- Enter gravity, or keep the default.
- Define the depth range for the Plotly graph.
- Press the calculate button.
- Review Froude number, regime class, hydraulic properties, and graph.
- Use the export buttons to save results as CSV or PDF.
Frequently Asked Questions
1. What does the Froude number tell me?
It compares flow inertia with gravity-wave influence. The value helps identify whether disturbances move upstream easily, remain near critical, or are swept downstream rapidly.
2. Why is hydraulic depth used instead of flow depth?
Hydraulic depth accounts for the actual cross-section and surface width. That makes it more appropriate for non-rectangular open channels, especially trapezoidal and triangular sections.
3. What is subcritical flow?
Subcritical flow occurs when Fr is below one. Gravity effects dominate, waves can travel upstream, and the flow is usually deeper and slower.
4. What is supercritical flow?
Supercritical flow occurs when Fr exceeds one. Inertia dominates, the stream is relatively shallow and fast, and disturbances generally move downstream only.
5. Why does this calculator support discharge mode?
Sometimes flow rate is measured directly while velocity is not. In discharge mode, the calculator derives average velocity from area and discharge before computing the Froude number.
6. What happens near Fr = 1?
The flow is close to critical. Small changes in depth or velocity can produce notable hydraulic changes, so design checks and transitions deserve extra attention.
7. Can I use US customary units?
Yes. Switch the unit system to US customary, then enter consistent values in feet, feet per second, cubic feet per second, and feet per second squared.
8. Why is the graph useful?
The graph shows how Froude number changes as depth varies. It helps you see where the flow may cross the critical threshold for the chosen geometry and inputs.