Manning's Equation
Discharge and velocity in steady uniform flow.
Manning's equation relates discharge to geometry, roughness and hydraulic gradient in steady, uniform flow. It is the standard sizing tool for gravity sewers in Australia and underpins most capacity checks.
The equation is empirical. Its accuracy depends on the roughness value chosen and on the assumption that the pipe runs at normal depth, meaning the friction slope equals the pipe grade.
Key design considerations
- n is a property of the pipe and its condition, not only of its material; aged and slimed sewers are rougher.
- S is the hydraulic gradient. Where the pipe is submerged or under backwater, S is not the bed grade.
- Use the same equation with part-full area and wetted perimeter for part-full flow.
- Work in SI units throughout, and use the actual internal diameter rather than a nominal label.
- Where the authority nominates design roughness values, those values govern.
Equations
Q = (1/n) · A · R^(2/3) · S^(1/2)
SI form, with Q in m³/s, A the flow area in m², R the hydraulic radius in m and S the friction slope in m/m.
V = (1/n) · R^(2/3) · S^(1/2)
Mean velocity; also V = Q/A.
R = A / P
Full circular pipe: A = πD²/4, P = πD, therefore R = D/4.
Design checks
- Roughness value justified and referenced.
- Gradient consistent with the invert levels actually used.
- Capacity recomputed at the true internal diameter.
Standards and authority references
- WSA 02 Gravity Sewerage Code of Australia (current edition), Water Services Association of Australia
- Authority design roughness values
Confirm the current edition, amendment and any local supplement before applying any of the above.
Limitations and assumptions
- Assumes steady, uniform, turbulent flow with a fixed roughness.
- Not valid for surcharged networks or rapidly varied flow without additional analysis.
Related calculators
This reference is general engineering information. Confirm requirements against WSA 02, the current Australian Standards and the local water authority's supplement before use in design, and obtain project-specific advice for the conditions at hand.