🌊 Manning's Equation Calculator
Calculate the flow velocity and discharge rate in an open channel using Manning's Equation.
Inputs
e.g., Concrete ~0.013, Earth channel ~0.022
Results
Open Channel Flow Cross-section
Calculator Description
Manning's equation is the most widely used empirical relation for finding the average velocity and discharge of a liquid flowing by gravity in an open channel. It is the standard tool for analyzing rivers, canals, drainage ditches, storm sewers, and free-surface flow in rectangular, trapezoidal or circular cross-sections.
What this calculator finds
From the channel geometry (area and wetted perimeter), the roughness coefficient n, and the bed (or water-surface) slope S, it computes the average velocity V [m/s (ft/s)] and the total discharge Q [m³/s (ft³/s)]. It is also used in reverse to size a channel or pick a slope for a target flow.
Why it matters
- Checking that rivers and storm drains can carry design flood flows without overtopping
- Sizing sewer pipes and irrigation channels to the right diameter or cross-section
- Comparing how lining material (concrete, stone, vegetation) changes velocity through roughness
- Confirming a minimum velocity (scour/self-cleansing) to avoid sediment deposition
Formula
Manning's Equation
For uniform flow, the average velocity is proportional to the hydraulic radius R raised to the 2/3 power and the slope S to the 1/2 power, and inversely proportional to the roughness coefficient n. It is an empirical relation valid in the fully-developed turbulent regime.
- V — Cross-sectional average velocity [m/s (ft/s)]
- Q — Discharge / flow rate [m³/s (ft³/s)]
- k — Conversion factor (1.0 for SI, 1.486 for US customary)
- n — Manning roughness coefficient (dimensionless, typically 0.01–0.04)
- R — Hydraulic radius (A/P) [m (ft)]
- S — Slope of water surface or channel bed (m/m or ft/ft)
- A — Flow (wetted) cross-sectional area [m² (ft²)]
How the formula works
- A larger roughness n (rougher walls) slows the flow — velocity is inversely proportional to n.
- A larger hydraulic radius R reduces wall-friction influence, increasing velocity — proportional to R^(2/3).
- A steeper slope S increases the gravity driving force, speeding flow — proportional to √S.
- For circular pipes, the hydraulic radius peaks at roughly half-full, so velocity is highest at partial fill, not at full bore.
Worked example
Consider a rectangular channel 2 m wide with 1 m depth. Area A = 2 m², wetted perimeter P = 2 + 1 + 1 = 4 m, so hydraulic radius R = A/P = 0.5 m. With a concrete lining roughness n = 0.013 and slope S = 0.001 (0.1%), using SI factor k = 1.0: V = (1/0.013) × 0.5^(2/3) × 0.001^(1/2) ≈ 0.85 m/s, giving Q = V × A ≈ 1.70 m³/s.
Useful Tips
Practical tips
- Roughness n varies strongly with wall condition: smooth concrete ≈ 0.012, vegetated stream ≈ 0.03–0.04. Be conservative.
- Slope S assumes uniform flow where water-surface and bed slopes are equal; it is only approximate where the section changes rapidly.
- When using US customary units (ft), you must use k = 1.486 for dimensional consistency.
Limitations & cautions
- Strictly valid only for uniform, fully-developed turbulent flow; inaccurate near sudden expansions, contractions or bends.
- Manning is for free-surface flow, not pressurized pipe flow — use Darcy-Weisbach for pressurized pipes.
- At very low velocities a laminar correction is needed, and ice or sediment effects are not captured.