When to use: Manning's equation estimates the uniform (steady, normal-depth) flow velocity and discharge in an open channel or partially-full pipe. V = (1.49/n)·R^⅔·S^½ (US units), where n is the Manning roughness coefficient, R = A/P is the hydraulic radius, and S is the longitudinal channel slope. Discharge is Q = V·A. Choose the channel cross-section, enter the flow depth and geometry, and the calculator solves the wetted geometry for you.
This calculator applies Manning's equation to compute uniform flow velocity and discharge in trapezoidal, rectangular, and circular (partially full) open channel cross-sections — the foundational tool for sizing drainage channels, roadside ditches, culverts, and irrigation canals.
Manning's equation in US customary units is V = (1.49/n) · R^(2/3) · S^(1/2), where n is the dimensionless Manning's roughness coefficient, R = A/P is the hydraulic radius (ft), A is the flow area (ft²), P is the wetted perimeter (ft), and S is the longitudinal channel slope (ft/ft). Discharge is Q = V · A (cfs). In SI units the constant becomes 1.0 instead of 1.49.
For a given depth y, this calculator computes the wetted geometry analytically: rectangular (A = b·y, P = b + 2y), trapezoidal (A = (b + z·y)·y, P = b + 2y·sqrt(1 + z²)), and circular partial-full (A = D²/8 · (θ − sin θ), P = Dθ/2, where θ = 2·acos(1 − 2y/D)). Note that a circular pipe flowing full has R = D/4 and reaches maximum discharge at about 94% full depth, a counterintuitive result important for storm drain design.
ASCE Manuals of Engineering Practice No. 36 and FHWA HDS-5 (Hydraulic Design of Highway Culverts) both reference Manning's equation as the standard for open channel and partially full pipe flow. FHWA Urban Drainage Design Manual (HEC-22) uses Manning's equation for roadway gutter, inlet, and storm drain capacity. The USDA NRCS National Engineering Handbook (NEH) Part 650 provides Manning's n values for agricultural channels and waterways. HEC-RAS computes water surface profiles by solving Manning's equation iteratively between cross-sections.
Minimum velocity to prevent sediment deposition is typically 2.0 ft/s for sand-bearing flow and 2.5 ft/s for silt. Maximum non-erosive velocity depends on the lining: bare earth 3–4 ft/s, grass-lined 4–6 ft/s, riprap 8–12 ft/s, concrete 15–20 ft/s. Channels should be designed with 1–2 ft of freeboard above the design water surface.
Manning's n values by material: smooth concrete 0.012–0.013; corrugated metal 0.022–0.025; clean earth 0.020–0.025; stony earth 0.030–0.035; natural stream with dense riparian vegetation 0.070–0.150. A 10% error in n produces approximately a 10% error in discharge, so field verification of roughness on critical channels is recommended.
Select the channel shape and enter Manning's n, longitudinal slope S (ft/ft), and flow depth y. For trapezoidal and rectangular sections, enter bottom width b and (for trapezoidal) side slope z. For circular, enter the pipe diameter D. Results show flow area A, wetted perimeter P, hydraulic radius R, velocity V, and discharge Q in both cfs and m³/s. Iterate on depth to find the depth that carries a target discharge (normal depth), or adjust channel geometry to achieve minimum or maximum allowable velocities.
Use n = 0.012–0.013 for smooth formed concrete, 0.013–0.015 for unfinished concrete or concrete with joints, and 0.015–0.017 for rough concrete or concrete with significant deterioration. ASCE and FHWA tables provide n values as a function of surface texture and age.
As depth increases in a circular pipe, the wetted perimeter grows faster than the area above about 82% full depth, reducing the hydraulic radius R. Since V is proportional to R^(2/3), velocity actually decreases above 82% full. Discharge Q = V·A peaks at about 94% full depth and decreases slightly before reaching full-pipe flow. This means a pipe at 94% full carries more flow than a full pipe — an important consideration in storm drain hydraulic grade line analysis.
Normal depth is the depth at which Manning's equation gives exactly the target Q for given n, S, and geometry. It must be solved iteratively (bisection or Newton-Raphson). The Channel Flow Profile Simulator on this site solves normal depth by bisection. Design software like HEC-RAS, SWMM, and Civil 3D also compute normal depth automatically.
For a full circular pipe: R = D/4. For a wide rectangular channel where b >> y: R ≈ y. For a trapezoidal channel R increases with depth and increases with both b and z. The hydraulic radius is always between y/2 and y for typical well-proportioned channels, and it is the key geometric parameter controlling conveyance.
Yes. Manning's equation with the partial-flow geometry equations (theta method) gives accurate results for circular pipes at any depth y ≤ D. However, at very low depths (y/D < 0.1) the equation can underestimate friction due to wave action and surface tension effects. For design of low-flow gutters and sub-inlets, these effects are typically ignored in practice.