Size a ditch by computing how much water its cross-section carries at the chosen gradient with Manning’s equation, V = (1/n) x R^(2/3) x S^(1/2), then check the water speed against what the bed can resist. A 50 cm by 40 cm trapezoidal ditch with an assumed 1:1 side slope carries about 0.42 m3/s brim-full at 0.5 percent but runs at 2.35 m/s at 2 percent, fast enough to scour most soils, so steeper or looser ground needs a stone or concrete lining.
Part of Flood Control and Drainage
Ditch construction covers sizing, grading and lining: choosing a cross-section that carries the flow, a gradient that keeps water moving without eroding the bed, and a lining where the soil cannot resist.
Gradient And Section Set Speed, And Speed Sets Whether The Bed Survives
A ditch fails in two ways. Too flat, and it silts and overflows. Too steep, and the water cuts the ditch into a gully. The parent article’s limits, 0.5 percent minimum and up to 2 percent unlined, bracket the safe range, and Manning’s equation shows what lies inside them.
The parent article gives the interceptor as 50 cm wide and 40 cm deep, trapezoidal, without stating the side slope or which dimension is the bottom width. This page assumes a 0.5 m bottom width, a 0.4 m depth and 1:1 side slopes (one metre out for each metre up), giving a top width of 1.3 m. A different reading of the dimensions gives different numbers; the method is the same.
What You Need
- A level and pegs — to hold the gradient.
- A cord and a measuring stick — to check width and depth.
- Digging tools.
- Flat stones — for the lining.
- A roughness value — Manning’s n is about 0.022 for a clean, weathered earth ditch. A grassed ditch is rougher, with an assumed n of about 0.035 used below. These are typical textbook values, written down without access to the books, so check them against a hydraulics reference.
Method: Size And Check The Ditch
Step 1: Compute the flow area and wetted perimeter. For a trapezoid with bottom width b, depth y and side slope z (z horizontal per 1 vertical), area = (b + z x y) x y and wetted perimeter = b + 2 x y x sqrt(1 + z^2).
Step 2: Compute the hydraulic radius. R = area / wetted perimeter.
Step 3: Apply Manning. V = (1 / n) x R^(2/3) x S^(1/2), where S is the slope as a fraction. Then Q = area x V.
Step 4: Check the velocity against the bed. Compare V with the speed the soil can withstand. A table of maximum permissible velocities for unlined channels, compiled by Fortier and Scobey, lists roughly 0.5 m/s for fine sand, 0.6 m/s for silt loam, 0.75 m/s for firm loam, 1.1 m/s for stiff clay and 1.8 m/s for hard shale, from memory of the textbook table, so confirm against it before trusting these figures.
Step 5: Line where it exceeds the limit. Flat stones set on the bed and lower banks raise the limit sharply. Use them for all sandy or loose soil, and for any ditch steeper than 2 percent.
Worked Example: The Parent Article’s Interceptor Ditch
- Area at y = 0.4 m: (0.5 + 1 x 0.4) x 0.4 = 0.36 m2.
- Wetted perimeter: 0.5 + 2 x 0.4 x sqrt(2) = 0.5 + 1.131 = 1.631 m.
- R = 0.36 / 1.631 = 0.2207 m; R^(2/3) = 0.365.
- At 0.5 percent (S = 0.005, S^(1/2) = 0.0707): V = (1 / 0.022) x 0.365 x 0.0707 = 1.17 m/s; Q = 0.36 x 1.17 = 0.42 m3/s.
- At 2 percent (S = 0.02, S^(1/2) = 0.1414): V = 45.45 x 0.365 x 0.1414 = 2.35 m/s; Q = 0.36 x 2.35 = 0.85 m3/s.
Ditches rarely run brim-full, so check the depth you expect. At a flow depth of 0.2 m: area = 0.7 x 0.2 = 0.14 m2; perimeter = 0.5 + 0.4 x 1.414 = 1.066 m; R = 0.131 m; R^(2/3) = 0.258.
| Gradient | V at 0.2 m depth | V at 0.4 m depth |
|---|---|---|
| 0.5 percent | 0.83 m/s | 1.17 m/s |
| 1 percent | 1.17 m/s | 1.66 m/s |
| 2 percent | 1.66 m/s | 2.35 m/s |
If the Fortier and Scobey limits recalled above are right, the 2 percent unlined ditch in loam or sand scours even at a 0.2 m depth, and only hard ground survives it. This is a reason to read the parent article’s 2 percent as an upper limit for firm ground, and to line anything looser.
Effect of grass. Raising n from 0.022 to 0.035 cuts the brim-full flow at 0.5 percent from 0.42 to 0.27 m3/s, a loss of about 37 percent. A grassed ditch resists scour better but carries less, so cut grass short and make the section bigger.
Common Mistakes
- Sizing on area alone — a big ditch at a steep gradient is still a scour channel.
- Checking only brim-full flow — the common flow is a fraction of it, but check the speed at that depth too.
- Leaving out the lining at the junctions — the speed rises where branches meet and where the slope breaks.
- Spoil heaped at the lip — dug earth piled at the edge slumps back and narrows the ditch. Spread or remove it.
- Treating one n as certain — roughness changes with weeds, silt and wear. Build in margin.
Safety
Fast water and unstable banks
Water at 1.7 to 2.4 m/s in a ditch moves faster than a walk, and about 15 cm of fast-flowing water can knock an adult off their feet. Never stand in a running ditch. Dig new ditches to a safe slope and keep spoil back from the edge; even a shallow trench wall can collapse onto someone working at the bottom.
What’s Next
- Learn next: Safe Outlets — the end of the ditch
- Combine with: Culvert Sizing — the same arithmetic applied to a pipe
- Combine with: Vegetation Cover — grass-lined ditches and their trade-off