Open channel flow calculator (Manning)
Work out the discharge and mean velocity of water in an open channel from its geometry, bed slope and roughness — using the standard Q = (1/n)·A·R^(2/3)·S^(1/2) relation.
Handles rectangular and trapezoidal sections, with roughness presets for concrete, brick, earthen and natural channels. A design-aid for irrigation canals, drains and headrace channels, computed in your browser.
Channel geometry
Width of the channel bed.
Depth of water above the bed.
Horizontal run per 1 unit vertical rise. Trapezoid only.
Longitudinal slope of the channel bed, e.g. 0.001 = 1 in 1000.
Surface roughness coefficient.
Discharge (Q)
11.935 m³/s
Flow rate carried at this depth.
Mean velocity
2.072 m/s
Flow area (A)
5.760 m²
Wetted perimeter (P)
7.327 m
Hydraulic radius (R)
0.786 m
Top width (T)
6.600 m
| Manning equation | Q = (1/n) · A · R^(2/3) · S^(1/2) |
| Flow area (A) | (3.00 + 1.50 × 1.20) × 1.20 = 5.760 m² |
| Wetted perimeter (P) | 3.00 + 2 × 1.20 × √(1 + 1.50²) = 7.327 m |
| Hydraulic radius (R) | 5.760 ÷ 7.327 = 0.786 m |
| Velocity (V) | (1 ÷ 0.013) × 0.786^(2/3) × 0.0010^(1/2) = 2.072 m/s |
| Discharge (Q) | 2.072 × 5.760 = 11.935 m³/s |
A uniform (steady, normal-flow) estimate using Manning's formula in SI units. It assumes a straight prismatic channel and a single representative roughness; real channels vary in section, vegetation and slope along their length. Pick the roughness coefficient (n) for your lining carefully — it dominates the result.
From channel shape to flow rate
The flow depends on the channel's cross-sectional shape (area and wetted perimeter), how steeply it falls (bed slope) and how rough its surface is (Manning's n).
Geometry
From the bottom width, depth and side slope, compute the flow area A and wetted perimeter P, then the hydraulic radius R = A ÷ P.
Velocity
Apply Manning's formula V = (1/n)·R^(2/3)·S^(1/2) — faster on steeper slopes and smoother (lower-n) surfaces.
Discharge
Multiply velocity by the flow area: Q = V·A = (1/n)·A·R^(2/3)·S^(1/2), the volume of water passing per second.
Open channel flow, answered
What is the Manning equation?+
Manning's formula gives the mean velocity of uniform flow in an open channel: V = (1/n) · R^(2/3) · S^(1/2), where n is the roughness coefficient, R is the hydraulic radius (flow area ÷ wetted perimeter) and S is the bed slope. Multiplying by the flow area A gives the discharge: Q = (1/n) · A · R^(2/3) · S^(1/2). These are the SI-unit forms used by this calculator.
What is the hydraulic radius?+
The hydraulic radius R is the flow area A divided by the wetted perimeter P — the length of channel boundary in contact with the water. For a rectangular channel A = b·y and P = b + 2y. For a trapezoid A = (b + z·y)·y and P = b + 2·y·√(1 + z²), where b is the bottom width, y the flow depth and z the side slope.
What Manning's n value should I use?+
Manning's n captures surface roughness. Typical values are about 0.013 for smooth concrete, 0.015 for brickwork, 0.022 for a clean earthen channel and 0.035 for a natural stream with stones and weeds. The coefficient dominates the answer, so choose the value that best matches your lining and condition, and check a standard reference for your case.
What does the side slope z mean?+
For a trapezoidal channel, z is the horizontal run per unit of vertical rise (H:V). A side slope of z = 1.5 means the bank rises 1 m vertically for every 1.5 m horizontally. For a rectangular channel z is zero (vertical walls), so the side-slope input is disabled.
Is this calculation valid for any channel?+
Manning's equation assumes steady, uniform (normal) flow in a straight prismatic channel with a single representative roughness. Natural rivers vary in cross-section, slope and roughness along their length, and flow may be non-uniform, so real designs use it as a starting estimate alongside detailed hydraulic analysis.
What units does this tool use?+
All inputs and outputs are in SI units: widths and depths in metres, bed slope as a dimensionless ratio (m/m), discharge in cubic metres per second (m³/s) and velocity in metres per second (m/s). Manning's n is dimensionless in this SI form of the equation.
Sources & data note
Based on Manning's formula for uniform open-channel flow, Q = (1/n)·A·R^(2/3)·S^(1/2), in SI units. Roughness presets (concrete 0.013, brick 0.015, clean earth 0.022, natural channel 0.035) are typical reference values — the actual n depends on lining, condition and vegetation, so verify the coefficient for your case. This is a planning estimate assuming steady, uniform flow, not a substitute for detailed hydraulic design.