Drainage
Pipe full-bore capacity (Colebrook–White)
- where
- internal diameter (m)
- internal diameter (mm)
- √(2gD/G), a velocity scale (m/s)
- gradient, 1 in G
- full-bore velocity (m/s)
- roughness (mm)
- kinematic viscosity of water (mm²/s)
- full-bore capacity (l/s)
Explain this equation
This works out how much water a circular pipe carries when running just full, and how fast, using the Colebrook–White equation behind UK sewer design tables.
D is the bore (Dm in metres), G the gradient as 1 in G, ks the roughness of the pipe wall and ν the kinematic viscosity of water. a = √(2gDm/G) is a velocity scale set by gravity, size and slope. V is the velocity and Q the flow in litres per second.
The log term blends two effects: wall roughness (ks/3.7D), which dominates in rough or large pipes, and the viscous film (2.51ν/(D·a)), which matters in small smooth ones. The 10⁻⁶ converts mm²/s to m²/s and the final ×1000 turns m³/s into l/s.
Sense check: a 100 mm drain at 1 in 80 carries about 6 l/s full at around 0.75 m/s with ks = 1.5 mm. Doubling the slope raises the flow by about √2.
Watch out: this is for full-bore flow; real drains run part full and the velocity at low flow can be much less.
Flow capacity and velocity of a circular pipe running just full, using the Colebrook–White equation that UK sewer design tables are based on.
Enter your values to see the result.
Good to know
Colebrook–White is the basis of the HR Wallingford design tables and is the method used for adoptable sewers. Roughness ks: 1.5 mm for foul sewers and 0.6 mm for surface water sewers (Sewers for Adoption / BS EN 16933-2, as quoted by MPA Precast). Kinematic viscosity of water is about 1.14 mm²/s at 15 °C (1.0 at 20 °C). As a check, Approved Document H Table 6 gives about 6.3 l/s for a 100 mm drain at 1:80 and 9.2 l/s at 1:40; this calculator gives 5.8–6.8 and 8.3–9.6 l/s for ks between 1.5 and 0.6 mm. Foul sewers should reach about 0.75 m/s to self-cleanse.
Common mistake
Using the nominal size instead of the internal diameter. A DN 100 plastic pipe is about 100–104 mm bore; concrete and clay pipes vary.
Limits
Full-bore, steady, uniform flow of clean water. Part-full flow, surcharge and losses at bends and manholes need a full hydraulic design to BS EN 752.
Sources
- MPA Precast / British Precast, Drainage hydraulic design (Colebrook–White adopted by HR Wallingford; ks 1.5 mm foul, 0.6 mm storm per Sewers for Adoption; 0.75 m/s self-cleansing)
- Innovyze InfoDrainage help, Colebrook–White formula (D = 4R, ν = 1×10⁻⁶ m²/s; ks 0.6 mm storm, 1.5 mm foul)
- HR Wallingford & Barr, Tables for the hydraulic design of pipes, sewers and channels (Colebrook–White full-bore relation)
- BS EN 752:2017 Drain and sewer systems outside buildings. Sewer system management (hydraulic design basis)
- Approved Document H: Drainage and waste disposal, 2015 edition (Table 6 minimum gradients for foul drains; Tables 11 and 12 access fittings, inspection chambers and manholes; para 3.15 rainwater drain gradients; paras 3.27–3.30 soakaways)
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.