Manning Equation Calculator Formula

Understand the math behind the manning equation calculator. Each variable explained with a worked example.

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Formulas Used

Flow Velocity

velocity = (1 / n_coeff) * pow(hyd_radius, 2/3) * pow(slope, 0.5)

Discharge (Q)

discharge = area * (1 / n_coeff) * pow(hyd_radius, 2/3) * pow(slope, 0.5)

Variables

VariableDescriptionDefault
n_coeffManning's Roughness (n)0.013
hyd_radiusHydraulic Radius (R)(m)0.5
slopeChannel Slope (S)(m/m)0.002
areaFlow Cross-Section Area(m^2)1.5

How It Works

Manning's Equation for Open Channels

The Manning equation is the most widely used formula for computing uniform open-channel flow.

Formula

V = (1/n) R^(2/3) S^(1/2)

Q = A V

where n is Manning's roughness coefficient, R is the hydraulic radius (A/P, area divided by wetted perimeter), and S is the slope of the energy grade line (equal to channel slope for uniform flow).

Worked Example

A concrete-lined channel with n=0.013, R=0.5 m, slope 0.2%, area 1.5 m^2.

n_coeff = 0.013hyd_radius = 0.5slope = 0.002area = 1.5
  1. 01R^(2/3) = 0.5^0.667 = 0.630
  2. 02S^(1/2) = 0.002^0.5 = 0.04472
  3. 03V = (1/0.013) x 0.630 x 0.04472 = 76.92 x 0.02817 = 2.168 m/s
  4. 04Q = 1.5 x 2.168 = 3.252 m^3/s

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