Manning's Equation Calculator

Calculate uniform flow in open channels. Supports rectangular, trapezoidal, triangular and circular sections. Includes roughness coefficient reference.

Manning's formula: \( Q = \frac{1}{n} A R^{2/3} S^{1/2} \)     (metric units: Q in m³/s, A in m², R in m, S in m/m)

\( V = \frac{1}{n} R^{2/3} S^{1/2} \) (mean velocity, m/s)

Flow Results
Discharge Q
-- m³/s
Flow velocity V
-- m/s
Hydraulic radius R
-- m
A = 0 m²   |   P = 0 m   |   R = A/P = 0 m
Froude number = -- (--)

Understanding Manning's Equation

Manning's equation is the most widely used empirical formula for uniform flow in open channels. It relates flow rate to channel geometry, roughness, and slope.

Manning's equation (metric): \( Q = \frac{1}{n} A R^{2/3} S^{1/2} \)

Velocity: \( V = \frac{1}{n} R^{2/3} S^{1/2} \)

Key Parameters

  • n – Manning's roughness coefficient (dimensionless). Higher n means more resistance (e.g., natural streams).
  • A – Cross-sectional area of flow (m²).
  • R – Hydraulic radius = A / P (m), where P is wetted perimeter.
  • S – Channel slope (m/m), usually the energy grade line for uniform flow equals bottom slope.

Typical Manning's n values

Channel type n range Common design value
Smooth concrete 0.011–0.013 0.012
Earth channel, clean 0.018–0.025 0.020
Earth channel with weeds 0.025–0.040 0.030
Natural stream (clean, straight) 0.025–0.035 0.030
Natural stream with stones/weeds 0.035–0.050 0.040
Riprap (rock lining) 0.035–0.050 0.045

Geometric relationships

  • Rectangle: A = b·y, P = b + 2y
  • Trapezoid: A = (b + z·y)·y, P = b + 2y√(1+z²)
  • Triangle: A = z·y², P = 2y√(1+z²)
  • Circle (full): A = πD²/4, P = πD, R = D/4

Flow regime (Froude number)

Fr = V / √(g·D_h) where D_h = A / T (hydraulic depth), T = top width.

  • Fr < 1 : subcritical (tranquil) – downstream control
  • Fr = 1 : critical – minimum specific energy
  • Fr > 1 : supercritical (rapid) – upstream control

Applications & Limitations

Applications: Design of drainage channels, sewers, irrigation canals, floodplain analysis, culverts.

Limitations: Assumes steady, uniform flow; prismatic channel; constant roughness; fully turbulent flow (Re > 10⁵). Not accurate for very steep slopes, rapidly varied flow, or non‑prismatic channels.

Frequently Asked Questions (5)

Normal depth is the depth of flow in a prismatic channel under uniform flow conditions, where the energy slope equals the bed slope. Manning's equation is used to compute normal depth by solving for y such that Q = (1/n) A(y) R(y)^(2/3) S^(1/2).

Selection depends on channel material, vegetation, alignment, and condition. Published tables (e.g., Chow, 1959) provide ranges. For natural channels, consider also channel irregularities, obstructions, and seasonal changes. When in doubt, use a higher n for conservative design.

Yes, but geometry becomes more complex (A and P are functions of flow depth). This calculator currently assumes full flow for circular sections. For partially full pipe flow, specialized culvert calculators or nomographs are recommended.

Both are empirical resistance factors. Chezy's C is related to n by C = (1/n) R^(1/6). Manning's n is more commonly used because it is relatively constant for a given channel type, while C varies with R.

In imperial units (feet), the formula is Q = (1.486/n) A R^(2/3) S^(1/2). The constant 1.486 (actually 1.4859) accounts for unit conversion. The n values remain the same as in metric.