Open Channel Flow Calculator (Manning Equation)
Compute discharge, normal depth, bed slope, or roughness for rectangular, trapezoidal, triangular, and circular open channels using Manning's equation — with Froude number, critical depth, a Manning's n roughness table, and scouring-velocity checks.
Calculator
Solve for
Channel shape
Results
Manning's n roughness table
Tap any row to load that roughness coefficient into the calculator. Typical values compiled from standard open-channel references (Chow, Open-Channel Hydraulics; US customary tables list the same coefficients — n is dimensionless).
| Surface / lining | Typical n | Common range |
|---|---|---|
| Glass, finished metal | 0.010 | 0.009–0.013 |
| Smooth concrete (steel forms) | 0.012 | 0.011–0.014 |
| Concrete, typical | 0.013 | 0.012–0.016 |
| Vitrified clay / clay tile | 0.013 | 0.012–0.014 |
| Brick masonry | 0.015 | 0.014–0.017 |
| Earth channel, clean | 0.022 | 0.018–0.025 |
| Earth channel, typical | 0.025 | 0.022–0.033 |
| Corrugated metal | 0.024 | 0.021–0.030 |
| Gravel, firm | 0.023 | 0.020–0.030 |
| Gravel / natural stream, typical | 0.030 | 0.025–0.035 |
| Grass / light vegetation | 0.035 | 0.030–0.050 |
| Dense brush / weeds | 0.050 | 0.040–0.080 |
Manning equation formulas
The Manning equation for uniform (steady, constant-depth) open channel flow:
Use k = 1.0 for SI units (meters, m³/s) and k = 1.486 for US customary units (feet, cfs). Rearranged forms used by this calculator's solvers:
Cross-section geometry
| Shape | Flow area A | Wetted perimeter P | Top width T |
|---|---|---|---|
| Rectangular | b·y | b + 2y | b |
| Trapezoidal | (b + z·y)·y | b + 2y·√(1+z²) | b + 2z·y |
| Triangular | z·y² | 2y·√(1+z²) | 2z·y |
| Circular (full) | πD²/4 | πD | — |
Symbols: b = bottom width, y = flow depth, z = side slope (horizontal per 1 vertical), D = diameter. Hydraulic depth Dh = A/T. The Froude number Fr = V/√(g·Dh) classifies the regime: Fr < 1 subcritical (tranquil), Fr = 1 critical, Fr > 1 supercritical (rapid).
How to use this open channel flow calculator
- Choose the unit system — SI (meters, m³/s) or US customary (feet, cfs). The 1.486 conversion is applied automatically.
- Pick what to solve for — discharge Q, normal depth y, bed slope S, or roughness n.
- Select the channel shape and enter its dimensions (bottom width, side slope, or diameter).
- Set Manning's n by typing a value or tapping a row in the roughness table above.
- Press Calculate — you get Q, velocity, hydraulic radius, Froude number, flow regime, critical depth, specific energy, a cross-section sketch, and scouring-velocity checks.
Worked examples
Example 1 — rectangular concrete channel
A rectangular concrete channel 2 m wide carries water 1 m deep. Manning's n = 0.013, bed slope S = 0.001. What is the discharge?
A = 2 × 1 = 2 m², P = 2 + 2×1 = 4 m, R = 2/4 = 0.5 m.
Q = (1/0.013) × 2 × 0.52/3 × 0.0011/2 ≈ 76.92 × 2 × 0.6300 × 0.031623 ≈ 3.065 m³/s.
Velocity V = Q/A ≈ 1.532 m/s. Hydraulic depth Dh = A/T = 1 m, so Fr = 1.532/√(9.81×1) ≈ 0.49 → subcritical flow. The calculator above reproduces these numbers exactly.
Example 2 — normal depth (design problem)
A 3 m wide rectangular channel (n = 0.013, S = 0.005) must carry 12 m³/s. Because Q grows with depth, there is no closed-form solution for y — the calculator bisects the Manning equation and finds normal depth y ≈ 1.024 m. For a trapezoidal channel with the same bottom width and 2H:1V side slopes, the answer is y ≈ 0.749 m (both match textbook iterations).
Scope boundary — what this tool does and does not cover
This calculator covers steady, uniform flow in OPEN channels (free surface exposed to the atmosphere) via the Manning equation. Related but separate:
- Pressurized pipe flow (pipes flowing full under pressure, Darcy–Weisbach head loss, Colebrook friction factor) → Darcy–Weisbach calculator.
- General pipe flow (velocity, flow rate, and diameter relationships in closed conduits) → pipe flow calculator.
- Flow through orifices and weirs (discharge through openings under a head) → orifice flow calculator.
- The circular option here assumes the conduit runs full; partially-full pipe hydraulics is a separate calculation.
Frequently asked questions
What is the Manning equation for open channel flow?
The Manning equation relates discharge to channel roughness, geometry, and slope: Q = (k/n)·A·R2/3·S1/2, where Q is discharge, n is Manning's roughness coefficient, A is flow area, R = A/P is the hydraulic radius, S is the bed slope, and k = 1.0 for SI units or 1.486 for US customary units. It applies to steady, uniform flow — the depth does not change along the channel.
What is normal depth and how is it calculated?
Normal depth is the flow depth at which gravity and friction balance so the depth stays constant along a uniform channel. Because depth appears inside both A and R, the Manning equation cannot be rearranged to isolate y — it must be solved iteratively. This calculator uses bisection on Q(y) to find the depth that produces your target discharge.
What is the difference between open channel flow and pipe flow?
Open channel flow has a free surface exposed to the atmosphere (rivers, canals, ditches, sewers flowing partly full) and is driven by the bed slope. Pressurized pipe flow fills the conduit completely and is driven by the pressure gradient, analyzed with the Darcy–Weisbach equation instead. Use this tool for the first case and the Darcy–Weisbach calculator for the second.
What are typical Manning's n values?
Common values: finished concrete 0.012–0.013, brick 0.015, earth channels 0.022–0.025, gravel 0.023–0.030, grass 0.035, dense brush 0.050. The full clickable table above lists typical values and ranges. n is dimensionless and identical in SI and US units.
How do I calculate flow in a trapezoidal channel?
Select "Trapezoidal", enter bottom width b, side slope z (horizontal per 1 vertical), flow depth y, Manning's n, and slope S. The calculator uses A = (b+z·y)·y and P = b+2y·√(1+z²), then applies Manning's equation. Trapezoidal sections are popular because sloped banks are stable in earth and the shape is close to the hydraulically efficient section.
What is the Froude number in open channel flow?
The Froude number Fr = V/√(g·Dh) compares flow velocity to wave speed, where Dh = A/T is the hydraulic depth. Fr < 1 means subcritical (tranquil) flow, Fr = 1 is critical flow, and Fr > 1 is supercritical (rapid) flow. The regime matters because it controls how disturbances travel and which boundary condition governs the water surface profile.
What is critical depth?
Critical depth is the depth at which the Froude number equals 1 for a given discharge — the depth of minimum specific energy. If your normal depth is greater than critical depth, flow is subcritical; if smaller, it is supercritical. The calculator reports critical depth and compares it with your depth automatically.
How do I use the Manning equation in feet and cfs?
Switch the unit system to "US customary". The calculator applies the 1.486 conversion factor: Q = (1.486/n)·A·R2/3·S1/2 with A in ft², R in ft, and Q in cfs (ft³/s). The roughness coefficient n is the same number in both systems.
What is the difference between hydraulic radius and hydraulic depth?
Hydraulic radius R = A/P (area over wetted perimeter) measures friction efficiency and goes into Manning's equation. Hydraulic depth Dh = A/T (area over top width) measures the average depth and goes into the Froude number. They are equal only for very wide rectangular channels.
What causes supercritical flow?
Supercritical flow (Fr > 1) occurs on steep slopes, in smooth channels, or at shallow depths for a given discharge. It is fast and shallow, and any transition back to subcritical flow happens through a hydraulic jump, which dissipates energy and can cause scour — one reason the calculator flags supercritical results.
What flow velocity is safe against scouring and sedimentation?
As design guidance: keep velocity above about 0.6 m/s (2 ft/s) to avoid sediment deposition, and below roughly 1.2 m/s for earth, 2.0 m/s for gravel, 1.5 m/s for grass, and 3.0 m/s for concrete lining to avoid erosion. The calculator checks your result against these limits and warns when they are exceeded. Always confirm with local design standards.
Can this replace an open channel flow calculator in Excel?
Yes — it performs the same Manning calculations as the common spreadsheet templates (discharge from depth, normal depth by iteration) without installing anything, works offline after loading, and adds Froude number, critical depth, a roughness table, and scouring checks that most spreadsheet versions lack.
What is uniform flow?
Uniform flow means the depth, velocity, and discharge are constant along the channel — the energy grade line, water surface, and channel bed are all parallel. The Manning equation in the form used here assumes uniform flow. Real channels are rarely perfectly uniform, but the equation is the standard first approximation in channel design.
Does this calculator handle partially full circular pipes?
No — the circular option assumes the conduit flows full (A = πD²/4, P = πD). For partially full pipes the wetted area and perimeter change with depth and need a separate partial-flow calculation. For full-pressure pipe analysis, use the Darcy–Weisbach calculator.
Free tool by NRTechStudio