Manning’s Equation for Partially Filled Pipes and Sewers
Gravity sewers are open channels inside a circle. A and R from y/D, why peak Q is not at full, self-cleansing velocity, and the rational method.
Key takeaways
- Part-full circular geometry uses θ = 2 arccos(1 − 2y/D).
- Maximum discharge is slightly below the soffit, not at y = D.
- n is a lining coefficient; do not drop it into Darcy-Weisbach.
- Storm peaks come from the rational method, then Manning checks the pipe.
A sanitary or storm sewer that is not surcharged is not a pressure pipe. Darcy-Weisbach still exists in the background, but design practice uses Manning with the hydraulic radius of the wetted circular segment.
The formula
Why you do not design just-full
Discharge in a circular pipe peaks a little below the soffit, around 0.94 D, because the extra wetted perimeter near the crown costs more than the extra area. Just-full is also unstable: a little extra Q fills the pipe and you jump to pressurized flow. Typical design is 0.5–0.8 full at peak, with a self-cleansing velocity (often 0.6–0.9 m/s) at average dry-weather flow.
| Lining | Design n | Use |
|---|---|---|
| PVC / HDPE, new | 0.009–0.011 | Laterals and small sewers |
| Concrete, good joints | 0.012–0.013 | Municipal trunks |
| Concrete, poor / slimy | 0.015–0.017 | Aged linings |
| Corrugated metal | 0.022–0.026 | Culverts more than sewers |
From rainfall to diameter
Example: C = 0.7, i = 80 mm/h, A = 2.5 ha → Q = 0.7×80×2.5/360 = 0.389 m³/s. A 600 mm pipe at S = 0.005 and n = 0.013 has a just-full Manning capacity of about 0.43 m³/s — tight but OK as a screen. Culverts on the same drain need a separate inlet/outlet-control check.
Open solver: Storm sewer / rational methodOpen solver: Culvert inlet vs outlet controlFrequently asked questions
Once the pipe surcharges and flows full under pressure, switch to Darcy-Weisbach. Manning assumes a free surface and uniform gravity flow.