What this calculator does
This open channel flow calculator uses Manning's equation, the standard formula for estimating how much water moves through an open channel such as a drain, culvert, canal or natural stream: Q = (1/n) × A × R^(2/3) × S^(1/2). Here Q is the flow rate, A is the cross-sectional area of the flow, R is the hydraulic radius, S is the channel slope, and n is Manning's roughness coefficient for the channel material.
The roughness coefficient is what makes this different from a plain pipe-flow calculation: it accounts for friction from the channel surface itself, from smooth finished concrete through to a weedy, irregular natural stream. A rougher channel needs a steeper slope or a larger cross-section to carry the same flow as a smooth one, which is why n is offered as an editable value with common presets rather than a single fixed number.
The formula
Raise the hydraulic radius to the power of two-thirds and the slope to the power of one-half, multiply those together with the cross-sectional area, then divide by Manning's roughness coefficient. The result is the flow rate in cubic metres per second; dividing that by the cross-sectional area gives the average flow velocity.
| Term | Meaning |
|---|---|
| Q | Flow rate through the channel, in cubic metres per second. |
| A | Cross-sectional area of the flowing water, in square metres. |
| R | Hydraulic radius: the flow area divided by the wetted perimeter, a measure of how efficiently the channel shape carries flow. |
| S | Channel slope, expressed as a dimensionless drop per unit length (for example 0.001 for a 1 in 1,000 slope). |
| n | Manning's roughness coefficient, describing friction from the channel surface material. |
The inputs explained
| Field | What to enter |
|---|---|
| Cross-sectional flow area (m²) | The cross-sectional area of the water flowing through the channel. |
| Hydraulic radius (m) | The hydraulic radius, found by dividing the cross-sectional area by the wetted perimeter of the channel. |
| Channel slope | The slope of the channel bed, as a decimal drop per unit length, not a percentage. |
| Manning's roughness coefficient (n) | Manning's roughness coefficient for the channel surface. Pick a preset close to the actual material, or enter a specific value if one is known. |
When to use it
Sizing a drainage channel or culvert
Checking the flow rate a proposed channel size and slope can carry, against the peak flow it needs to handle, is a standard step before a drain or culvert is built.
Estimating flow in a natural stream
Surveying a stream's cross-section, slope and an appropriate roughness value gives a workable flow estimate without needing a flow meter in the water.
Comparing channel materials
Running the same area, radius and slope through different roughness presets shows how much more flow a smooth concrete channel carries than an equivalent earth channel, which matters when choosing a lining material.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How flow rate changes with channel roughness
The same channel geometry and slope, across a range of surface materials.
| Channel material | Flow rate (Q) | Average velocity |
|---|---|---|
| 0.010 | 3.984 m³/s | 1.992 m/s |
| 0.013 | 3.065 m³/s | 1.532 m/s |
| 0.025 | 1.594 m³/s | 0.797 m/s |
| 0.060 | 0.664 m³/s | 0.332 m/s |
How flow rate changes with channel slope
The same channel and material, at a range of bed slopes.
| Channel slope | Flow rate (Q) | Average velocity |
|---|---|---|
| 0.0005 | 2.167 m³/s | 1.084 m/s |
| 0.001 | 3.065 m³/s | 1.532 m/s |
| 0.002 | 4.334 m³/s | 2.167 m/s |
| 0.005 | 6.853 m³/s | 3.427 m/s |
Questions
What is Manning's equation used for?
It estimates the flow rate of water moving through an open channel under gravity, such as a stream, drain, canal or culvert, using the channel's geometry, slope and surface roughness rather than requiring a direct flow measurement.
How do I find the hydraulic radius for my channel?
Hydraulic radius is the cross-sectional flow area divided by the wetted perimeter, the length of the channel boundary actually in contact with the water. For simple shapes like a rectangle or trapezoid this can be worked out geometrically from the channel dimensions and water depth.
How sensitive is the result to Manning's roughness coefficient?
Quite sensitive: flow rate is inversely proportional to n, so doubling the roughness coefficient halves the estimated flow for the same geometry and slope. Choosing a realistic n for the actual channel surface matters more than precision in the other inputs.
Is this the same as the hydraulic conductivity calculator?
No. The hydraulic conductivity calculator uses Darcy's Law to describe how easily water moves through a porous material such as soil. This calculator uses Manning's equation to find the flow rate of water moving openly along a channel, which is a different physical situation.
For the geometric step of finding the hydraulic radius used above, see the hydraulic radius calculator. For flow through porous ground rather than an open channel, see the hydraulic conductivity calculator.