Manning Flow Calculator
Channel velocity from Manning n, radius, slope.
What it does
Open channels move water at the pace set by lining, shape, and slope. Smooth concrete runs fast, weedy earth crawls, and steeper grades pull harder. Manning formula folds the three into velocity with one roughness number.
The tool above solves velocity both ways. With n 0.013, radius 0.5 m, and slope 0.001, water moves at 1.53 m per s, or 5.52 km per h, covering 100 m in 65.3 s. The imperial mirror at 1.6 ft gives 4.94 ft per s with 20.2 s per 100 ft. Multiply by cross area for discharge.
Roughness comes from tables by lining, radius from area over wetted perimeter, and slope as drop over run. Wide channels approach flow depth for radius, while pipes need full versus part full geometry. Small slope errors matter because velocity follows the square root.
This page gives velocity only under uniform flow. It does not compute area, discharge, or backwater. For flow rate, add a surveyed cross section.
How to use
- Pick metric (m) or imperial (ft).
- Enter the Manning n for the lining.
- Enter the hydraulic radius.
- Enter the channel slope as a decimal.
- Read velocity first, then the alternate unit.
- Read seconds per 100 units for travel time.
Formula
- n
- Manning lining value, 0.008 to 0.15.
- R
- Flow area over wetted perimeter, in m or ft.
- S
- Drop over run along the channel, dimensionless.
Steady uniform open channel flow with one n, one radius, one slope. At zero slope there is no drive. US units carry the 1.486 constant; SI uses 1.
Worked example
Example: concrete channel at 0.001 slope
Defaults: metric concrete channel with n 0.013, 0.5 m radius, 0.001 slope. Imperial mirror is 1.6 ft.
- Inputs (metric default): n 0.013, radius 0.5 m, slope 0.001.
- Power: 0.5 to the 2/3 is 0.63, root of 0.001 is 0.0316.
- Velocity: (1/0.013) times 0.63 times 0.0316 is 1.53 m per s.
- Alternate: 1.53 times 3.6 is 5.52 km per h.
- Time: 100 / 1.53 is 65.3 s per 100 m. Imperial mirror gives 4.94 ft per s. Tool shows the same.
Reference table
| Channel | Velocity | Per 100 |
|---|---|---|
| n0.013 R0.5m S0.001 | 1.53 m per s | 65.3 s per 100 m |
| n0.03 R1m S0.002 | 1.49 m per s | 67.1 s per 100 m |
| n0.013 R1.6ft S0.001 | 4.94 ft per s | 20.2 s per 100 ft |
| n0.015 R2ft S0.005 | 11.12 ft per s | 9 s per 100 ft |
| n0.02 R0.3m S0.005 | 1.58 m per s | 63.1 s per 100 m |
Limits
- Uniform flow only. Backwater excluded.
- Full geometry assumed. Part full needs R and A.
- One n per reach. Mixed linings need weighting.
- No discharge. Area times V is separate.
Common mistakes
- Using percent slope as decimal directly.
- Reading diameter as hydraulic radius.
- Mixing SI 1 with US 1.486 constants.
- Applying channel n to pipes without checking.
- Ignoring part full geometry in sewers.
Try it yourself
Quick checks. Answers sit tucked under each question.
n 0.03, radius 1 m, slope 0.002?
Velocity is (1/0.03) times 1 times root 0.002 is 1.49 m per s with 5.37 km per h and 67.1 s per 100 m.
n 0.015, radius 2 ft, slope 0.005?
Velocity is (1.486/0.015) times 2^2/3 times root 0.005 is 11.12 ft per s with 7.58 mi per h and 9 s per 100 ft.
Questions
What is Manning formula?
SI: V = (1/n) R^(2/3) S^1/2. Here 1.53 m per s. Imperial uses 1.486/n.
What is hydraulic radius?
Wetted area over wetted perimeter. Big wide channels approach flow depth.
How is slope entered?
Slope as m per m, dimensionless. Here 0.001.
Which n do I pick?
Concrete near 0.013, earth higher. Tables set n by lining.
How do I get discharge?
Multiply velocity by cross area. This page gives V only.
Does this handle half full pipes?
No. Full flow assumed. Part full needs geometry for R and A.
Sources
- USGS: Roughness Characteristics of Natural Channels (Manning)
- FHWA: Design Charts for Open Channel Flow (Manning)