Trapezoidal Channel Flow Calculator — Manning Open Channel

Calculate flow capacity (cfs) and velocity (ft/s) of a trapezoidal open channel using Manning’s equation. Enter bottom width, flow depth, side slope, channel slope, and lining material.

By TradeCalc, Plumber Calculators — Code-Referenced — FHWA HEC-22 (Urban Drainage Design Manual), ASPE PDH Vol. 2, Chow Open-Channel Hydraulics (1959), USDA NRCS Engineering Field Manual

Related Calculators

How to Calculate Trapezoidal Channel Flow (Manning)

Trapezoidal Open-Channel Flow

A trapezoidal channel is the standard cross-section for roadside ditches, drainage swales, and man-made canals — flatter side slopes than a rectangular channel (for stability) but narrower than a triangular swale (for capacity). Manning’s equation, the same formula used for pipe flow, calculates the gravity-driven capacity. FHWA HEC-22 (Urban Drainage Design Manual) and ASPE PDH Vol. 2 reference it for stormwater channel design.

The Manning Equation for Trapezoids

Q = (1.486 / n) × A × R^(2/3) × S^(1/2)

A = (b + z·y) · y P = b + 2·y·√(1 + z²) R = A / P

Q = flow rate (cfs)
n = Manning roughness coefficient (0.015 concrete, 0.035 grass)
b = bottom width (ft), y = flow depth (ft)
z = side slope (horizontal ft per 1 ft vertical); z=0 is rectangular
A = flow area (ft²), P = wetted perimeter (ft)
R = hydraulic radius (ft), S = channel slope (ft/ft)

Side Slopes and Lining Materials

Side slope z depends on soil stability: 1:1 (z=1) for hard rock or concrete, 2:1 (z=2) for stable earth, 3:1 (z=3) for grass-lined ditches (also the safe slope for mowing), 4:1 (z=4) for loose sandy soils. Manning n by lining: concrete 0.015, grouted rock 0.025, smooth earth 0.022, grass 0.030–0.040, riprap 0.045, weedy earth 0.040. Smoother linings carry 2–3× more flow at the same geometry because of the lower n.

Worked Example

Scenario: A grass-lined roadside drainage ditch has a 4 ft bottom width, 1.5 ft flow depth, 3:1 side slopes, and 1% longitudinal slope. Find the capacity and check the velocity against the grass-lining erosion limit.

b = 4 ft, y = 1.5 ft, z = 3, S = 0.01, n (grass) = 0.035
A = (4 + 3·1.5) · 1.5 = (4 + 4.5) · 1.5 = 8.5 · 1.5 = 12.75 ft²
P = 4 + 2·1.5·√(1+9) = 4 + 3·√10 = 4 + 9.487 = 13.49 ft
R = A/P = 12.75 / 13.49 = 0.945 ft
Q = (1.486/0.035) × 12.75 × 0.945^(2/3) × √0.01 = 42.46 × 12.75 × 0.964 × 0.1 = 52.1 cfs
v = Q/A = 52.1 / 12.75 = 4.09 ft/s

Velocity of 4.09 ft/s is right at the upper limit for grass lining (3–5 ft/s, depending on grass species and maturity). A well-established Bermuda or fescue sod holds to 5–6 ft/s; a new seeding erodes above 3 ft/s. If the velocity had exceeded 5 ft/s, the fix would be a heavier lining (riprap, gabion, or concrete) or a wider/flatter channel to slow the flow.

Practical Tips

Velocity drives lining selection. Grass lining holds 3–5 ft/s (species-dependent); bare earth erodes above 2 ft/s; riprap handles 6–10 ft/s; concrete handles 15+ ft/s. Always check velocity before picking a lining — a channel sized for capacity alone may erode at design flow.
Side slope z = 3 is the mowing limit. A 3:1 slope is the steepest that a riding mower can safely traverse. Steeper (z=2) requires hand trimming or specialized equipment; flatter (z=4) eats more right-of-way. Most roadside ditches use z=3 for maintenance access.
Freeboard is required. The channel should run at design depth with 0.5–1.0 ft of freeboard (extra depth) above the design water surface to contain surges. For the 1.5 ft design depth in the example, the actual ditch depth should be 2.0–2.5 ft.
Grass n varies with depth. A shallow grass-lined channel (y < 0.5 ft) has n ≈ 0.060 because the grass dominates the flow; at y > 1 ft the grass bends flat and n drops to 0.030. HEC-22 and Chow give depth-adjusted n curves for grass. Use the conservative (higher) n for shallow flow.
Steep slopes cause supercritical flow. Above ~5% slope, open-channel flow goes supercritical (Froude number > 1), which causes hydraulic jumps, wave action, and erosion at any discontinuity. If your channel needs >5% slope, use a drop structure or energy dissipater rather than a continuous steep run.

Code References

FHWA HEC-22 (Urban Drainage Design Manual), ASPE PDH Vol. 2, Chow Open-Channel Hydraulics (1959), USDA NRCS Engineering Field Manual

Frequently Asked Questions

What is the Manning equation for a trapezoidal channel?

Q = (1.486/n) × A × R^(2/3) × S^(1/2), where A = (b + z·y)·y, P = b + 2·y·√(1+z²), and R = A/P. b is bottom width, y is flow depth, z is side slope (horizontal per 1 vertical), n is the Manning roughness coefficient, and S is the channel slope (ft/ft). A grass-lined 4 ft × 1.5 ft deep ditch at 3:1 sides and 1% slope carries 52 cfs at 4.1 ft/s.

What side slope should I use for a drainage ditch?

z = 3 (3:1) is standard for grass-lined roadside ditches — it is stable for most soils and the steepest slope a riding mower can safely handle. Use z = 2 for concrete or grouted-rock lined channels in tight right-of-way. Use z = 4 for loose sandy soils that slump. Use z = 1 only for hard rock or vertical concrete walls. Flatter slopes are safer but consume more land.

What is the maximum velocity for a grass-lined channel?

3–5 ft/s for established sod (Bermuda, fescue) at design flow; 2–3 ft/s for new seedings until the grass matures. Above 5 ft/s, switch to riprap, gabion, or concrete lining. The velocity is checked at the design storm flow (typically 10-year for residential ditches, 100-year for major channels). HEC-22 Table 4.1 gives permissible velocities by lining type and soil.

How does Manning n vary between grass, concrete, and earth?

Concrete n = 0.013–0.015, smooth earth n = 0.020–0.025, grass n = 0.030–0.040, riprap n = 0.040–0.050, natural streams n = 0.035–0.070. A concrete-lined channel carries 2–3× more flow than a grass-lined channel of the same geometry because the lower n reduces friction. Grass n also varies with depth — shallow flow (y < 0.5 ft) has n ≈ 0.060 because grass dominates; deep flow (y > 1 ft) bends the grass flat and n drops to 0.030.