Drainage
Pipe full-bore capacity (Manning)
- where
- internal diameter (m)
- internal diameter (mm)
- hydraulic radius, D/4 for a full pipe (m)
- full-bore velocity (m/s)
- Manning’s roughness coefficient
- gradient, 1 in G
- full-bore capacity (l/s)
Explain this equation
This is a quick check of a circular pipe’s full-bore velocity and capacity using Manning’s equation.
D is the bore (Dm in metres) and R the hydraulic radius, flow area divided by wetted perimeter, which is D/4 for a full circle. n is Manning’s roughness, G the gradient as 1 in G, V the velocity and Q the flow in l/s.
Velocity rises with the slope’s square root and with R to the power 2/3, because bigger pipes lose proportionally less to wall friction. Multiplying by the area π Dm²/4 gives the flow, and ×1000 converts m³/s to l/s.
Sense check: a 100 mm PVC pipe at 1 in 80 with n = 0.009 runs about 1.06 m/s and 8.3 l/s full; with n = 0.013 it drops to about 5.8 l/s.
Watch out: n changes the answer directly, so choose it carefully; UK designs normally use Colebrook–White.
A quick full-bore capacity check for a circular drain using Manning’s equation Q = (1/n)·A·R^(2/3)·S^(1/2).
Enter your values to see the result.
Good to know
For a circular pipe running full the hydraulic radius R is D/4. Manning’s n: 0.009 for PVC gravity sewer pipe (Uni-Bell), 0.012–0.014 vitrified clay and 0.011–0.013 concrete (Innovyze closed-conduit table). Many designers use 0.013 for any material as an allowance for ageing and slime. UK sewer design uses Colebrook–White; Manning is a simpler cross-check.
Common mistake
Using n for a new pipe in lab conditions on a drain that will carry sewage for decades. Be conservative.
Limits
Full-bore, steady, uniform flow. n is treated as constant, which is less accurate than Colebrook–White for small, smooth pipes.
Sources
- Uni-Bell PVC Pipe Association, Manning’s n for PVC gravity sewer pipe (design n = 0.009)
- Innovyze XPS help, Manning’s n roughness coefficients for closed conduits (vitrified clay 0.012–0.014; concrete 0.011–0.013)
- BS EN 752:2017 Drain and sewer systems outside buildings. Sewer system management (hydraulic design basis)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow BS 8500, BS EN 206, BS EN 752, Building Regulations Part H, manufacturers’ data and your engineer’s design. Structural concrete and foundations need a competent designer.