The equation
Q = (1/n) · A · R2/3 · S1/2 — where Q is discharge (m³/s), n is Manning's roughness, A is flow area (m²), R is hydraulic radius A/P (m), and S is the energy slope (m/m), taken as the bed slope for uniform flow. For partial circular flow the calculator uses the exact circular-segment geometry: θ = 2·cos⁻¹(1 − 2y/D), A = (D²/8)(θ − sin θ), P = θD/2.
Manning's n — typical values
| Surface | n |
|---|---|
| PVC / HDPE pipe | 0.009 – 0.011 |
| Concrete pipe (good condition) | 0.012 – 0.014 |
| Concrete-lined channel | 0.013 – 0.017 |
| Earth channel, clean | 0.022 – 0.030 |
| Earth channel, weedy / wadi bed | 0.030 – 0.050 |
| Riprap lining | 0.030 – 0.040 |
Limits worth respecting
Manning's equation assumes steady, uniform, fully rough turbulent flow. It does not see backwater, surcharge, junction losses or unsteady storm behaviour — exactly the effects that govern real drainage networks at design storms. For those, a hydraulic model is the honest tool; our note on HEC-RAS 2D vs InfoWorks ICM covers choosing one. Peak flows feeding this check usually come from the Rational Method calculator with time of concentration from Kirpich or FAA.