The size of an open channel follows from Manning’s equation: a 30 cm bottom width with 1:1 side slopes and 20 cm of water carries about 42 L/s at a 0.2% slope in an earth channel, many times the 2-5 L/s it is quoted for, and at 5 L/s the same channel runs only about 6 cm deep at 0.23 m/s. Dig the section for what you can build and maintain, add 10-15 cm of freeboard above the design water level, and work out the depth the real flow will take.
Part of Aqueducts and Channels
The cross section of a channel is the shape of the cut across it: bottom width, side slope and depth. It decides how much water the channel carries at a given slope, and how deep and how fast that water runs.
Flow Is Area Times Speed, And Speed Comes From Manning
Manning’s equation for an open channel in SI units:
V = (1 ÷ n) × R^(2/3) × S^(1/2), and then Q = A × V
V is the mean speed in m/s, n the roughness, R the hydraulic radius (A ÷ P), S the slope (0.002 for 0.2%), Q the flow in m³/s (multiply by 1,000 for L/s). For a trapezoid with bottom width b, depth y and side slope z (horizontal run per unit of rise): A = (b + z·y)·y and P = b + 2y·√(1 + z²).
Roughness n (Chow, Open-Channel Hydraulics, 1959; ranges for the surfaces described on this page):
| Surface | n |
|---|---|
| Earth, clean, after weathering | 0.018-0.025 |
| Earth with short grass and few weeds | 0.022-0.033 |
| Cemented rubble masonry | 0.017-0.030 |
| Concrete, trowel finish | 0.011-0.015 |
What The Standard Section Actually Carries
The aqueducts page recommends, for 2-5 L/s: bottom width 30 cm, side slopes 1:1 in firm soil (2:1 in sandy soil), water depth 15-20 cm and freeboard 10-15 cm. Check it with Manning at 0.2% slope, n = 0.025:
- Depth 0.20 m: A = (0.30 + 0.20) × 0.20 = 0.100 m²; P = 0.30 + 2 × 0.20 × √2 = 0.866 m; R = 0.1155 m; R^(2/3) = 0.2371; V = 0.2371 × √0.002 ÷ 0.025 = 0.2371 × 0.04472 ÷ 0.025 = 0.424 m/s; Q = 0.100 × 0.424 = 0.0424 m³/s = 42 L/s.
- Depth 0.15 m: A = 0.0675 m²; P = 0.724 m; R = 0.0932 m; V = 0.368 m/s; Q = 25 L/s.
Across slopes of 0.1-0.5% and n of 0.022-0.025, depths of 15-20 cm carry between 18 and 76 L/s. So the standard section is not sized for 2-5 L/s. It is a generous section that is easy to dig and clean, and it leaves a large reserve for storm inflow.
Working Backwards For A Real Flow
Find the depth for 5 L/s at 0.2% by trial. At y = 0.06 m: A = (0.30 + 0.06) × 0.06 = 0.0216 m²; P = 0.30 + 2 × 0.06 × 1.414 = 0.4697 m; R = 0.04599 m; R^(2/3) = 0.1283; V = 0.1283 × 0.04472 ÷ 0.025 = 0.230 m/s; Q = 0.0216 × 0.230 = 0.00496 m³/s = 5.0 L/s. So 5 L/s runs 6.0 cm deep, about 6 cm, at 0.23 m/s. For 2 L/s the depth is 3.5 cm and the speed 0.17 m/s.
The reserve is a benefit and a cost: shallow, slow flow in a wide bed silts up and grows weeds (Sediment Management). The 30 cm bottom is a practical width for digging and cleaning, not a hydraulic need.
Other Sections
- Sandy soil, 2:1 sides (z = 2), 0.30 m bottom, 0.20 m depth, 0.2%, n = 0.025: A = 0.140 m²; P = 1.194 m; R = 0.1172 m; V = 0.428 m/s; Q = 60 L/s.
- Lined channel, 0.30 m bottom, 1:1, 0.15 m depth, 0.5% slope, n = 0.015: A = 0.0675 m²; R = 0.0932 m; V = 0.97 m/s; Q = 65 L/s.
What You Need
- The design flow, measured or estimated
- The slope from the survey, and the surface (n)
- A calculator, or a notebook for the trial method
- Marked stakes or a template cut to the section, to check the dug shape
Method: Choose, Compute, Add Freeboard
Step 1: Pick a trial bottom width and side slope that you can dig and clean.
Step 2: Choose n for the surface.
Step 3: Try a depth, compute A, P, R, V and Q.
Step 4: Adjust the depth until Q matches the design flow, then check the speed against the soil limit (Optimal Gradient).
Step 5: Dig to the design depth plus 10-15 cm of freeboard.
Common Mistakes
- Reading depth as a sign of flow. A deep channel can carry very little.
- Using the wrong n. Weeds change n from 0.022 to 0.033 and cut the flow at the same depth by a third (0.022 ÷ 0.033 = 0.67).
- Forgetting freeboard. Storms and partial blockages overtop it.
- Choosing the section before the slope is known. Speed depends on both.
What’s Next
- Learn next: Earth Channels — digging the section
- Combine with: Lined Channels — what changes with a smooth lining