# Open Channel Flow Calculator (Manning)

URL: https://speedycalculator.com/calculators/physics/open-channel-flow/
Last updated: 2026-10-30

> The open channel flow calculator applies Manning's equation to find the velocity and discharge of uniform flow in a rectangular, trapezoidal or triangular channel from its geometry, slope and surface roughness.

## Inputs

- Channel shape
- Bottom width b (m, cm, mm, km, in, ft, yd, mi)
- Flow depth y (m, cm, mm, km, in, ft, yd, mi)
- Side slope z (H:1V)
- Channel surface (Manning n)
- Manning n
- Bed slope S (m/m)

## Results

- Flow area
- Wetted perimeter
- Hydraulic radius
- Velocity
- Discharge Q
- Froude number

## Formula

```
V = (1/n)·R_h^{2/3}·S^{1/2} (SI),  Q = V·A,  R_h = A/P
```

## Explanation

Manning's equation is the standard tool for designing canals, ditches, culverts and storm drains. Rougher channels (higher n) and flatter slopes carry less water at the same depth.

### How to use the Open Channel Flow Calculator

- **Channel shape**
- **Bottom width b**
- **Flow depth y**
- **Side slope z (H:1V)**
- **Channel surface (Manning n)**
- **Manning n**
- **Bed slope S (m/m)**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the channel shape and surface, enter the dimensions and the bed slope.

### Inputs explained

FieldWhat to enterChannel shapeChoose one: Rectangular, Trapezoidal, TriangularBottom width bUnits: m, cm, mm, km, in, ft …Flow depth yUnits: m, cm, mm, km, in, ft …Side slope z (H:1V)A numberChannel surface (Manning n)Choose one: PVC / plastic, Smooth steel, Concrete (finished), Cast iron …Manning nA numberBed slope S (m/m)A number

### What each result means

- **Hydraulic radius** = [Flow area]÷[Wetted perimeter]
- **Discharge Q** = [Velocity]×[Flow area]

### Example values

How the main result changes when **Bottom width b** changes and everything else stays at the example values above:

Bottom width b (m)Discharge Q (m³/s)11.49241.51.936722.3922.52.855233.324144.2739

## Worked example

Inputs — Channel shape: Trapezoidal; Bottom width b: 2 m; Flow depth y: 0.8 m; Side slope z (H:1V): 1.5; Channel surface (Manning n): Earth channel, clean; Bed slope S (m/m): 0.001.

Results — Flow area = 2.56 m²; Wetted perimeter = 4.88444 m; Hydraulic radius = 0.52411 m; Velocity = 0.93439 m/s; **Discharge Q = 2.39203 m³/s**; Froude number = 0.3912.

## Key terms

- **Uniform flow**: Depth and velocity constant along the channel.

## FAQ

**What is Manning's n?**
An empirical roughness coefficient for the channel surface.

**Is the formula valid for any flow?**
For steady, uniform, turbulent flow.

**How do I get more capacity?**
Increase depth, width or slope, or use a smoother lining.

**What is the most efficient trapezoid?**
Half of a regular hexagon (z = 1/√3).


## Sources

- [Fluid Mechanics (F. M. White) – reference text](https://www.mheducation.com/highered/product/fluid-mechanics-white-chul/M9781260258318.html)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)