Formula Used
The open channel Froude number compares flow inertia to gravity waves: Fr = V / √(g·Dh). Here, V is mean velocity and g is gravity.
The hydraulic depth is Dh = A/T, where A is flow area and T is top width. Many sections compute A and T from geometry to obtain Dh.
Regime meaning: Fr < 1 subcritical, Fr ≈ 1 critical, and Fr > 1 supercritical.
How to Use This Calculator
- Select the calculation type: Fr, velocity, depth, or critical velocity.
- Choose geometry input: direct Dh, rectangular, trapezoidal, or triangular.
- Select velocity source: enter V directly or compute it from discharge Q.
- Set units, then enter the required values with realistic signs.
- Press Calculate to view results above the form.
- Use CSV or PDF to save a clean copy.
Example Data Table
| Section | Inputs | Computed Dh (m) | Velocity (m/s) | Froude Number | Regime |
|---|---|---|---|---|---|
| Rectangular | b=2.0 m, y=0.6 m | 0.600 | 1.50 | 0.619 | Subcritical |
| Trapezoidal | b=1.5 m, y=0.7 m, z=1.0 | 0.420 | 2.00 | 0.982 | Near critical |
| Triangular | y=0.8 m, z=1.0 | 0.400 | 2.60 | 1.311 | Supercritical |
Values above are illustrative and assume g = 9.80665 m/s².
Open Channel Froude Number Guide
1) What this calculator evaluates
This tool calculates the open channel Froude number, a dimensionless indicator of whether surface waves can move upstream. It combines mean velocity, gravity, and hydraulic depth. The result helps classify flow as subcritical, critical, or supercritical.
2) Why the Froude number matters in practice
Froude-based classification supports decisions about control sections, energy dissipation, and hydraulic jumps. Subcritical flow is typically deeper and slower, while supercritical flow is shallower and faster. Knowing the regime improves safety for transitions, drops, and channel constrictions.
3) Typical regime thresholds and interpretation
For open channels, Fr < 1 indicates tranquil flow, where gravity waves travel upstream. Fr ≈ 1 marks critical behavior, often near control points. Fr > 1 suggests rapid flow and possible jump formation downstream of disturbances.
4) Hydraulic depth links geometry to wave speed
Hydraulic depth is Dh = A/T, where area A depends on the wetted shape, and top width T represents the free-surface span. For a rectangular section, Dh equals the flow depth. For a triangular section, Dh equals half the depth, reflecting the narrowing surface.
5) Velocity options support field and design workflows
You can enter velocity directly, or compute it from discharge using V = Q/A. This is useful when discharge comes from a flow meter, weir rating, or pump curve. When using discharge, accurate geometry is essential because area strongly influences velocity.
6) Data-rich outputs for quick verification
The result panel reports Fr, regime label, Dh, and √(g·Dh), which represents the characteristic wave celerity scale. For example, with Dh = 0.50 m and standard gravity, √(g·Dh) is about 2.21 m/s. If velocity is 1.10 m/s, the flow is comfortably subcritical. If velocity rises to 2.40 m/s at the same depth, Fr exceeds one, and rapid behavior becomes more likely at transitions.
7) Design insights from regime classification
Subcritical reaches often require backwater considerations, while supercritical reaches demand careful transition design. Near-critical conditions may indicate a controlling section, so small geometry changes can shift the regime. Use the classification to guide where to place stilling basins, drop structures, or expansions.
8) Common uncertainty sources and good measurement habits
Errors usually come from depth readings, surface width estimation, and roughness-driven velocity variation across the section. Measure depth at multiple points, average intelligently, and use consistent units. When possible, pair discharge estimates with cross-section surveys to stabilize computed area and hydraulic depth.
FAQs
1) What does a Froude number of 0.5 mean?
It indicates subcritical flow. Surface disturbances can travel upstream, and the flow is typically deeper and more stable than rapid flow in the same channel.
2) When should I use hydraulic depth instead of flow depth?
Use hydraulic depth for non-rectangular sections. It accounts for free-surface width through Dh = A/T, making wave-speed scaling consistent across shapes.
3) Can I compute velocity from discharge in this tool?
Yes. Select the discharge option and provide a geometry that computes area. The calculator uses V = Q/A, then evaluates Fr.
4) What is “critical velocity” in open channels?
It is the velocity at Fr = 1. The calculator returns V = √(g·Dh), which is the boundary between tranquil and rapid regimes.
5) Why is the regime label important?
Regime affects how water surfaces respond to controls and transitions. Supercritical flow may form hydraulic jumps, while subcritical flow may show backwater effects upstream.
6) Which gravity value should I enter?
Standard gravity 9.80665 m/s² is appropriate for most cases. If you need local adjustment, enter a positive value and keep lengths and velocities consistent.
7) How accurate are results with real channels?
Accuracy depends on your measured inputs. Use averaged depths, reliable cross-section dimensions, and consistent discharge or velocity measurements. The calculator’s math is direct, so input quality dominates.