Parameters
e.g. 0.001 = 1 m drop per 1000 m.
Results
Wetted area A
0m²
Wetted perimeter P
0m
Hydraulic radius R
0m
Velocity V
0m/s
Flow rate Q
0m³/s
0 L/s
Estimate the flow rate Q in m³/s of a channel or river reach using the Manning formula. Pick the section geometry, enter the dimensions, and you'll get the area, hydraulic radius, velocity, and flow rate.
The equation this calculator uses was published by the Irish engineer Robert Manning in 1889, and it is empirical: it is not derived from fluid mechanics, it was fitted to measurements of real channels and works remarkably well within its range. In SI units, V = (1/n) · R2/3 · S1/2, with velocity in m/s. Worth knowing that in American literature it appears as V = (1.486/n) · R2/3 · S1/2 for feet and seconds: the 1.486 is only the unit conversion, not a different formula.
Choosing n is the only subjective decision in the calculation and the one that weighs most on the result. These are the reference values used in hydraulics handbooks.
| Type of bed | n | Notes |
|---|---|---|
| Well-finished concrete | 0.012 | New irrigation canal, sewer pipe |
| Aged concrete or masonry | 0.017 | With scaling or joints |
| Earth, straight and clean | 0.022 | Maintained ditch, no vegetation |
| Earth with short grass | 0.027 | Roadside gutter |
| Gravel and cobble bed | 0.030 | Mountain river of moderate slope |
| Natural channel with stones and scrub | 0.040 | The commonest case in a Spanish river |
| Channel with dense brush and logs | 0.060 | Unmaintained reach |
| Wooded floodplain | 0.100 | Overbank flow across the valley floor |
The result is not equally sensitive to each input, and knowing that shows where careful measurement pays. Discharge is inversely proportional to n: a 20 % error in roughness is a 20 % error in discharge, and the gap between 0.030 and 0.040 is already 33 %. With slope the error is damped, because it enters under a square root: a 20 % error in S moves discharge by 10 %. And depth governs most of all, because it affects both the area and the hydraulic radius: in a wide channel, discharge grows roughly with the 5/3 power of depth, so 10 % more depth is 17 % more discharge.
Manning assumes steady uniform flow: constant discharge in time, and constant section, slope and roughness along the reach, so that the bed slope can be taken as equal to the energy slope. That rules out four common situations: the passage of a flood wave, where discharge changes hour by hour; reaches with a backwater curve upstream of a weir or a constriction; hydraulic jumps and supercritical flow generally; and very shallow depths over coarse beds, where the stones stop being roughness and become obstacles. For designing a structure, a Manning calculation serves as a first estimate, never as the design itself.