Calculator Inputs
Example Data Table
| Shape | Sample Inputs | Approx. Critical Depth | Notes |
|---|---|---|---|
| Rectangular | Q = 2.50 m^3/s, b = 3.20 m, g = 9.81 m/s^2 | 0.396251 m | Useful for wide channels with constant bottom width. |
| Triangular | Q = 5.40 m^3/s, z = 1.50, g = 9.81 m/s^2 | 1.214488 m | Common when sidewalls meet at the channel invert. |
| Trapezoidal | Q = 7.80 m^3/s, b = 2.40 m, z = 1.00 | 0.898473 m | Useful for earth channels and lined conveyance sections. |
| Circular | Q = 1.80 m^3/s, D = 1.60 m, g = 9.81 m/s^2 | 0.674360 m | Applies to partially full conduits and stormwater pipes. |
Formula Used
The calculator uses the general critical-flow condition for open channels. At critical depth, the Froude number is approximately one, and specific energy is minimized for the given discharge.
Critical condition: Q²T / (gA³) = 1 Specific energy: E = y + V² / (2g) Velocity: V = Q / A Hydraulic depth: Dₕ = A / TGeometry relations used
- Rectangular: A = by, T = b
- Triangular: A = zy², T = 2zy
- Trapezoidal: A = by + zy², T = b + 2zy
- Circular: Segment area and surface width are evaluated from the wetted angle.
For shapes without a closed-form shortcut, the page solves the critical-depth equation numerically by bisection, which is stable and accurate for engineering work.
How to Use This Calculator
- Select the unit system and the channel shape.
- Enter the discharge and gravitational acceleration.
- Fill only the geometry fields required for that shape.
- Press the calculate button to show the result above the form.
- Review critical depth, energy, velocity, hydraulic properties, and the graph.
- Use the CSV or PDF buttons to export the computed summary.
FAQs
1) What is critical depth?
Critical depth is the water depth where specific energy is minimum for a given discharge. At that point, the flow sits exactly at the transition between subcritical and supercritical behavior.
2) Why is the Froude number important here?
The Froude number compares inertial effects with gravity effects. Near critical depth, it is approximately one, which confirms the transition condition used by this calculator.
3) Can I use this for rectangular channels only?
No. This version supports rectangular, triangular, trapezoidal, and circular channel sections, making it useful for several open-channel and conduit design checks.
4) Why does the circular case use a numerical solver?
Partially full circular sections rely on segment geometry, which creates a nonlinear equation. A numerical method solves it accurately without requiring manual iteration.
5) What should I enter for side slope?
Enter the horizontal-to-vertical value for each side, written as z in H:1V. For example, a 1.5H:1V side slope means z = 1.5.
6) Does this calculator work in SI and US units?
Yes. The equations are dimensionally consistent, so the calculator works in either system as long as discharge, geometry, and gravity are entered in matching units.
7) Why is specific energy plotted against depth?
That curve makes the minimum-energy point easy to see. The lowest point on the graph corresponds to the critical condition for the selected flow and geometry.
8) When would engineers use critical depth?
It is commonly used in channel transitions, flumes, spillways, culverts, stormwater systems, and energy-based flow checks where control sections matter.