Guide · Open channels
How to size an irrigation ditch with Manning's equation
A ditch is sized by asking one question: at this slope and roughness, how deep does the water have to run to carry the flow — and does that depth, plus freeboard, fit inside the banks?
Short answer: compute flow with Manning's equation, Q = (1.486 / n) × A × R2/3 × S1/2, where A is the flow area in square feet, R is area divided by wetted perimeter, S is the ditch slope in feet per foot, and n is roughness. Adjust depth until Q matches the flow you need, then check velocity and freeboard.
The equation and its terms
- Q — flow in cubic feet per second (cfs).
- n — Manning's roughness coefficient.
- A — cross-sectional area of the water, in square feet.
- R — hydraulic radius, A divided by the wetted perimeter P.
- S — slope of the ditch bottom, feet of fall per foot of length.
Geometry of a trapezoidal ditch
Most farm ditches are trapezoids: a flat bottom of width b, side slopes of z horizontal to 1 vertical, and water depth y.
Typical roughness values
| Ditch condition | Typical n |
|---|---|
| Concrete lined, good condition | 0.013 – 0.015 |
| Earth, clean and recently shaped | 0.018 – 0.025 |
| Earth, some grass and weeds | 0.025 – 0.035 |
| Earth, heavy weeds or brush | 0.035 – 0.050 and up |
Roughness is the biggest source of error. A ditch that carries its flow easily in April can overtop in August once the weeds come in, because doubling n cuts capacity in half at the same depth.
Worked example
An earth ditch with a 2 ft bottom, 1.5:1 side slopes, a slope of 1 ft per 1,000 ft (S = 0.001), and n = 0.025. How much does it carry running 1.0 ft deep?
That is about 2,160 gpm, moving at V = Q / A = 1.37 ft/s.
Three checks after you have a depth
- Freeboard. Required depth plus freeboard must be less than the bank depth. For small farm ditches, 0.5 ft of freeboard is a common minimum; larger canals need more. In the example, a 1.0 ft flow depth wants banks at least 1.5 ft deep.
- Velocity, high side. Unlined earth starts to scour somewhere around 2 to 3 ft/s in sandy or silty soils, higher in stiff clay. If you are over, flatten the grade with drops or line the ditch.
- Velocity, low side. Below about 1 ft/s, silt settles and weeds take hold. The 1.37 ft/s in the example is in the workable range.
Solving for depth instead of flow
Usually you know the flow you need and want the depth. Manning's equation cannot be rearranged for depth in a trapezoid, so you iterate: guess a depth, compute Q, adjust, repeat. This is the "normal depth" calculation, and it is the part worth handing to software.
What this does not cover
Manning's equation assumes steady, uniform flow in a straight prismatic reach. It does not model backwater behind a check or a plugged culvert, storage, gate transients, or seepage loss. Those need field measurement or a routing model.
Planning estimate, not a stamped design. These are steady-state equations. Real accuracy depends on surveyed elevations, current channel and pipe condition, calibrated gate ratings, and pump curves. Verify in the field and get qualified engineering review before final construction or official operation.
Related guides
- How much water a headgate passes — to check the gate feeding the ditch.
- cfs, gpm, acre-feet, and miner's inches — to convert your water right into a design flow.
- Pipe sizing with Hazen-Williams — if you are piping the ditch instead.
Sources
- USDA NRCS, National Engineering Handbook, open-channel hydraulics.
- U.S. Bureau of Reclamation, Water Measurement Manual.
Let the drawing do the iteration
In FieldFlowCAD, draw the ditch, set its section and roughness, and the app solves normal depth, compares it with bank depth plus freeboard, and flags velocity and grade problems.