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Open-Channel Flow (Manning Equation) — result sheet
Estimate uniform flow velocity and discharge in a rectangular open channel from geometry, slope, and Manning roughness.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: A = by; P = b + 2y; R = A/P; V = (1/n)R^(2/3)S^(1/2); Q = AV.
For a rectangular channel, the flow area and wetted perimeter determine the hydraulic radius. The metric Manning equation then estimates mean uniform-flow velocity from hydraulic radius, slope, and roughness, and discharge follows from Q = A V.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Channel width — m; minimum 1.0E-6; maximum 1000000
- Flow depth — m; minimum 1.0E-6; maximum 1000000
- Friction slope — m/m; minimum 1.0E-12; maximum 1
- Manning roughness n — relative; minimum 1.0E-6; maximum 10
Worked example
| Input | Value |
|---|---|
| Channel width | 3 |
| Flow depth | 1 |
| Friction slope | 0.001 |
| Manning roughness n | 0.03 |
The example channel has area 3 m², hydraulic radius 0.6 m, mean velocity about 0.750 m/s, and discharge about 2.25 m³/s.
Assumptions and limits
- The channel is rectangular, prismatic, and approximately uniform over the reach.
- The entered slope is the friction or energy slope and is positive; Manning n represents the combined boundary resistance.
- This is a uniform-flow estimate and does not solve backwater profiles, contractions, sediment transport, freeboard, flooding, or design safety.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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