In short: this calculator uses Manning's equation to estimate the steady flow rate in an open channel — a ditch, canal or flume with a free water surface — from its shape, depth, slope and lining. For the default trapezoidal channel above, it returns about 12.3 ft³/s (~5,530 GPM). Change the shape, dimensions, slope or material to match your own channel.
These are planning-aid estimates for steady, uniform flow. For channel design affecting drainage capacity, erosion control or regulatory compliance, confirm with a licensed engineer.
How to calculate open-channel flow (Manning's equation)
Open-channel flow — water moving with a free surface exposed to the atmosphere, as opposed to pressurized flow in a full pipe — is almost always estimated with Manning's equation. It combines the channel's cross-sectional shape, how rough its surface is, and how steeply it slopes:
This calculator works out A, the wetted perimeter and R from your chosen shape (rectangular, trapezoidal or triangular) and depth, then applies the formula directly. It also reports velocity (V = Q ÷ A) and the Froude number, which tells you whether the flow is calm (subcritical) or fast and shallow (supercritical).
Worked example. Take a rectangular concrete flume 3 ft wide, flowing 2 ft deep, with Manning's n = 0.013 and a slope of 0.2% (S = 0.002). Area A = 3 × 2 = 6 ft². Wetted perimeter P = 3 + (2 × 2) = 7 ft. Hydraulic radius R = 6 ÷ 7 = 0.857 ft, and R^(2/3) ≈ 0.902. Putting it together: Q = (1.486 ÷ 0.013) × 6 × 0.902 × √0.002 ≈ 27.7 ft³/s (about 12,400 GPM), at a velocity of roughly 4.6 ft/s.
Uniform flow, one more assumption. Manning's equation assumes the channel's slope, shape and roughness stay constant over the reach you're checking, so the water depth is steady rather than rising or falling. Real channels often have bends, transitions or a downstream control that change the depth locally — this calculator gives the normal-depth flow the channel would settle into if it ran that way for a good distance.
Why slope, roughness and shape change the answer
Slope is the driving force — it's gravity pulling the water downhill. But it enters the equation as a square root, so doubling the slope only increases flow by about 41%, not 100%. Small slope surveying errors can still shift a result noticeably, which is why accurate slope measurement matters more than most people expect.
Roughness (Manning's n) represents everything that drags on the moving water: the surface texture of the lining, vegetation, sediment and bends. A smooth concrete flume (n ≈ 0.013) carries far more water than an earth ditch of the same size and slope (n ≈ 0.022–0.030), because friction against the rough banks slows the flow.
Shape matters because it controls the hydraulic radius — the ratio of flow area to the wetted perimeter that touches the channel. A wide, shallow channel has more wetted perimeter per unit of area than a deep, narrow one, so it experiences relatively more friction and carries less flow for the same cross-sectional area. This is also why the Pipe Flow Rate Calculator gives a different-looking formula for full pipes — it's the same physics, just a different geometry.
Manning's roughness coefficient (n) by material
Typical values, matching the presets in the calculator above. Actual roughness varies with maintenance, sediment and vegetation, so treat these as a starting point rather than a precise measurement.
| Material | Manning's n |
|---|---|
| PVC / smooth plastic pipe | 0.009 |
| Concrete, trowel-finished | 0.013 |
| Brick or masonry | 0.015 |
| Concrete, unfinished/rough | 0.017 |
| Earth channel, clean & straight (default) | 0.022 |
| Corrugated metal | 0.024 |
| Gravel bed, straight | 0.025 |
| Earth channel, weedy or stony | 0.030 |
| Natural stream, clean & straight | 0.030 |
| Riprap / rock-lined | 0.035 |
| Natural stream, weedy with pools | 0.045 |
Worked examples
Concrete-lined irrigation channel
20.8 cfs
Trapezoidal, 2 ft bottom width, 1.5 ft deep, side slope 1.5H:1V, n = 0.013, slope 0.1%. Carries about 20.8 ft³/s (~9,360 GPM) at 3.27 ft/s — Froude ≈ 0.58, comfortably subcritical.
Concrete flume, 3 ft wide
27.7 cfs
Rectangular, 3 ft wide, 2 ft deep, n = 0.013, slope 0.2%. Flows at about 27.7 ft³/s (~12,400 GPM) and 4.61 ft/s — fast enough that a lining is worth keeping in good repair.
Roadside earth ditch
9.0 cfs
Triangular, side slope 3H:1V, 1 ft deep, n = 0.030, slope 1%. Carries about 9.0 ft³/s (~4,060 GPM) at 3.0 ft/s — Froude ≈ 0.75, still subcritical but worth checking against erosion limits for bare earth.
What else affects the result
Non-uniform and gradually varied flow. Manning's equation gives the "normal depth" a channel settles into over a long, unchanging reach. Near bends, culvert entrances, weirs or a downstream dam, the actual depth can differ — for a flow-over-a-weir or spillway situation, see the Weir Flow Calculator instead.
Changing roughness over time. Vegetation growth, sediment deposits and debris raise n as a season progresses, which lowers a channel's real capacity even though its geometry hasn't changed. Maintained channels should be checked with a range of n values, not just the freshly-built figure.
Freeboard. This calculator reports the flow at the depth you enter — it doesn't add a safety margin above that for wave action, debris or an unusually large storm. Most design guidance adds freeboard of 6 inches to a foot (or more for larger channels) above the calculated depth.
Enclosed pipes and culverts. A pipe or culvert flowing completely full is pressurized, not open-channel, flow. Use the Pipe Flow Rate Calculator for a full pipe, or the Culvert Flow Calculator for a culvert that may flow partly full under inlet control. For a natural stream measured directly rather than modeled, the Streamflow Calculator uses the velocity-area method instead.
Frequently asked questions
What is Manning's equation for open-channel flow?
Manning's equation, Q = (k/n)·A·R2/3·S1/2, estimates the steady flow rate in an open channel from its cross-sectional area (A), hydraulic radius (R, area divided by wetted perimeter), the channel's roughness (n) and its longitudinal slope (S). The constant k is 1.486 for U.S. customary units (feet, cfs) or 1.0 for SI units (meters, m³/s).
How do I choose Manning's roughness coefficient n?
Manning's n depends on the channel lining: smooth materials like trowel-finished concrete or PVC have low n (0.009–0.013), while earth, gravel or vegetated channels have higher n (0.022–0.045) because rougher surfaces and plant growth slow the water more. Use the calculator's material presets, or a site-specific value from a hydraulics reference if you have one, since n can vary with maintenance and season.
What is the Froude number and why does it matter?
The Froude number compares flow velocity to the speed of a small surface wave. Fr less than 1 is subcritical flow (calmer, deeper, controlled from downstream); Fr greater than 1 is supercritical (fast, shallow, controlled from upstream); Fr equal to 1 is critical flow. Channels are usually designed to stay subcritical to avoid standing waves and an unstable water surface.
Does this calculator work for pipes flowing full?
No. This tool models open-channel flow with a free water surface exposed to atmospheric pressure. A pipe flowing completely full is pressurized flow, which follows a different set of equations — use the Pipe Flow Rate Calculator for that case instead.
What's a typical slope for a drainage ditch or swale?
Most roadside and yard drainage channels use slopes between about 0.5% and 2% — enough to keep water moving without causing erosion. Slopes flatter than about 0.2% can allow sediment and debris to settle, while slopes steeper than 3–4% may need erosion protection such as riprap.
Why doesn't doubling the slope double the flow rate?
Manning's equation uses the square root of slope, so flow rate scales with the square root of S, not S itself. Doubling the slope increases flow by a factor of about 1.41, or roughly 41 percent, not 100 percent. Flow is more sensitive to depth and cross-sectional area, which enter the equation through A and R2/3.
Sources & references
- Manning, R. (1891). On the flow of water in open channels and pipes. Transactions of the Institution of Civil Engineers of Ireland, 20, 161–207.
- Chow, V. T. (1959). Open-Channel Hydraulics. McGraw-Hill.
- U.S. Federal Highway Administration. Hydraulic Engineering Circular No. 15 (HEC-15), Design of Roadside Channels with Flexible Linings.
John Mac, PE
Water Systems Specialist · Austin, Texas
Texas-licensed Professional Engineer with 13+ years in residential water systems and 180+ completed projects. Writes and reviews the calculators on watercalculator.us. Read full bio
Texas PE (2016) · BS Civil Engineering, Hydraulics (2013)