Manning Equation Calculator Formula
Understand the math behind the manning equation calculator. Each variable explained with a worked example.
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
| Variable | Description | Default |
|---|---|---|
n_coeff | Manning's Roughness (n) | 0.013 |
hyd_radius | Hydraulic Radius (R)(m) | 0.5 |
slope | Channel Slope (S)(m/m) | 0.002 |
area | Flow 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.
- 01R^(2/3) = 0.5^0.667 = 0.630
- 02S^(1/2) = 0.002^0.5 = 0.04472
- 03V = (1/0.013) x 0.630 x 0.04472 = 76.92 x 0.02817 = 2.168 m/s
- 04Q = 1.5 x 2.168 = 3.252 m^3/s
Frequently Asked Questions
What are typical Manning's n values?
Smooth concrete: 0.012-0.014. Corrugated metal: 0.022-0.026. Earth channel (clean): 0.022-0.025. Natural streams: 0.030-0.050. Floodplain with brush: 0.050-0.120.
What is the hydraulic radius?
Hydraulic radius R = flow area / wetted perimeter. For a full circular pipe of diameter D, R = D/4. For a wide shallow channel, R approximates the depth.
Is the Manning equation metric or imperial?
The formula V = (1/n) R^(2/3) S^(1/2) is for SI (metric) units. For US customary (feet), use V = (1.486/n) R^(2/3) S^(1/2) to account for unit conversion.
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