Engineering calculators · Drainage
Sewer and drain pipe capacity calculator
Find the capacity and velocity of a circular gravity sewer or drain, running full or part-full, from its diameter, gradient and roughness. The calculator uses the Colebrook-White equation that UK sewer design is based on, finds the depth and velocity at your design flow, and checks the result against the Water UK Design and Construction Guidance for adoptable foul and surface water sewers.
Inputs
Choosing a sewer type fills in the DCG roughness. Gradient is entered as 1 in X, so 1:150 is 150.
Results
- Runs at 44% of pipe depth at design flow: within the DCG limit that foul sewers run no more than 75% of pipe full.
- Velocity at one-third design flow is 0.49 m/s, under the DCG self-cleansing minimum of 0.75 m/s. The DCG also accepts 150 mm laid no flatter than 1:150 (at least ten dwellings), or 100 mm no flatter than 1:80 with a WC connected.
Part-full flow
| Depth, % of diameter | Depth, mm | Flow, L/s | Velocity, m/s | Flow, % of full |
|---|---|---|---|---|
| 10% | 15 | 0.251 | 0.273 | 2% |
| 20% | 30 | 1.09 | 0.432 | 9% |
| 25% | 38 | 1.71 | 0.495 | 14% |
| 30% | 45 | 2.46 | 0.551 | 19% |
| 40% | 60 | 4.24 | 0.643 | 34% |
| 50% | 75 | 6.30 | 0.713 | 50% |
| 60% | 90 | 8.47 | 0.766 | 67% |
| 70% | 105 | 10.6 | 0.799 | 84% |
| 75% | 113 | 11.5 | 0.809 | 91% |
| 80% | 120 | 12.3 | 0.814 | 98% |
| 90% | 135 | 13.4 | 0.803 | 107% |
| 100% | 150 | 12.6 | 0.713 | 100% |
A circular pipe carries its greatest flow a little below the crown, where the wetted perimeter grows faster than the flow area. Velocity is also highest at part depth. Design to full-bore capacity, not to this peak, because a pipe that fills completely falls back to full-bore flow.
How the calculation works
- Geometry. At depth y in a pipe of radius R, the flow area is the circular segment R² arccos(1 − y/R) − (R − y)√(y(2R − y)) [seg], the wetted perimeter is the arc Rθ, and the hydraulic radius is area ÷ wetted perimeter.
- Velocity comes from Colebrook-White combined with the Darcy-Weisbach friction slope [dff]: v = −2√(8gRS) log₁₀(ks/14.8R + 2.51ν/(4R√(8gRS))). Here S is the gradient and ν is the kinematic viscosity of water at the chosen temperature [NIST]. For a full pipe 4R = D, which gives the familiar full-bore form. Part-full flow uses the same equation with the part-full hydraulic radius.
- Depth at a given flow is found by searching the rising part of the depth–flow curve.
- Roughness. The DCG sets ks = 1.5 mm for foul gravity sewers "for all sewer material types", and 0.6 mm for surface water sewers and lateral drains [DCG].
- Checks [DCG]:
- Foul sewers should run no more than 75% of pipe full. The calculator checks this as the depth at design flow.
- Foul sewers need a velocity of at least 0.75 m/s at one-third of design flow.
- Surface water sewers need at least 1 m/s at pipe-full flow.
- Where a velocity cannot be met, the DCG accepts minimum gradients instead: 1:150 for 150 mm, and 1:80 (or 1:40 without a WC) for 100 mm foul drains.
What this cannot tell you. It covers one straight pipe with steady, uniform flow. It does not model backwater from downstream, surcharge, manhole losses, or the time-varying flows of a storm event. It does not work out design flows either: peak foul flow and design rainfall come from the DCG and your sewerage company. For a network, use a hydraulic model.
Sources
- Water UK (2023) Design and Construction Guidance for foul and surface water sewers, v2.3 (Sewerage Sector Guidance Appendix C)
- Wikipedia: Circular segment (area from radius and height)
- Wikipedia: Darcy friction factor formulae (Colebrook-White, Swamee-Jain, flow regimes)
- NIST Chemistry WebBook: Isobaric properties of water at 0.101325 MPa (density and viscosity, 0–100 °C)