Water Resources HubWater topic 16 of 18 — free theory
Wastewater Collection Systems
Gravity sewer design with Manning's equation, self-cleansing velocity, lift stations, force mains, and infiltration & inflow.
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Gravity sewer design with Manning's equation
Sewers are designed to flow partly full under gravity, so Manning's equation is applied to the wetted cross-section at the design depth — not the full pipe.
V = (1/n) · R2/3 · S1/2 Q = AV (SI; use 1.486/n for US units)
| R = A/P | hydraulic radius of the wetted portion at depth d (not D/4, unless the pipe is full) |
| n | Manning's roughness (≈ 0.013 for concrete/clay pipe) |
| d/D | flow depth ratio; design practice limits peak flow to d/D ≈ 0.75–0.8 |
For a circular pipe at depth ratio d/D, the wetted angle is θ = 2 arccos(1 − 2d/D); then A = (D²/8)(θ − sin θ) and P = Dθ/2. Useful landmarks: at d/D = 0.8, Q/Qfull ≈ 0.98; at d/D = 0.75, Q/Qfull ≈ 0.91.
Self-cleansing velocity — both limits matter
Sewers must run fast enough to keep solids moving, but not so fast that the pipe scours.
Vmin ≈ 0.6 m/s (2 ft/s) Vmax ≈ 3 m/s (10 ft/s)
| Vmin | self-cleansing velocity, checked at the design (usually peak) flow — and ideally at minimum flow too |
| Vmax | upper limit to avoid abrasion of the pipe wall, checked on steep slopes |
Because velocity at partial depth exceeds full-flow velocity over much of the range (peak V/Vfull ≈ 1.14 near d/D = 0.8), checking only the full-pipe velocity can understate the real one.
Minimum slopes and cover
Slope and diameter are traded against each other: a steeper slope carries more flow in a smaller pipe, but trench depth costs money. Design standards therefore set minimum slopes per diameter — smaller pipes need steeper minimum slopes to hold 0.6 m/s at design flow (for example, an 8-inch sewer typically needs about 0.4% minimum). Minimum cover of roughly 0.9–1.0 m (3 ft) protects the pipe from surface loads and frost; where cover cannot be provided, the pipe is encased or the alignment changes.
Lift stations and force mains
When gravity can no longer do the job — the trench gets too deep or the route must climb — a lift station pumps the flow up, and a force main carries it under pressure to a higher gravity sewer. The moment a conduit flows full under pressure, gravity-sewer geometry stops applying:
Force main: use Darcy-Weisbach or Hazen-Williams (full circular area A = πD²/4, no d/D)
| hf = 10.67 L Q1.852 / (C1.852D4.87) | Hazen-Williams head loss, SI units (Q in m³/s, D in m) |
| Pump head = static lift + hf + minor losses | total dynamic head the lift-station pump must develop |
Design velocity in a force main is typically kept between 0.6 and about 2.5 m/s — fast enough to resuspend solids, slow enough to limit surge pressures.
Infiltration & inflow (I/I) and peaking
Design flow is not just the sanitary component. Infiltration is groundwater seeping in through pipe defects and bad joints; inflow is stormwater entering through direct connections — roof drains, foundation drains, manhole covers. Both ride on top of the sanitary flow and both respond to rain, so design peaking factors fold them in: peak flow = (per-capita sanitary flow × peaking factor) + I/I allowance. That is why the design d/D limit matters — the pipe must swallow the wet-weather peak without surcharging.
PE depth: wet wells, minimum slopes, and the d/D = 1.0 trap
Lift-station wet wells are sized from the pump cycle: with steady inflow Qin and pump rate Qp, a usable volume Vu fills in Vu/Qin and empties in Vu/(Qp − Qin). The cycle time is the sum, and the number of starts per hour must stay within the motor's rating — short-cycling burns out pumps.
Minimum-slope tables exist because velocity, not slope, is the real requirement: the slope that produces 0.6 m/s at design flow in a 200 mm pipe is steeper than for a 600 mm pipe. If a question gives you a slope flatter than the standard minimum for that diameter, either the diameter grows or a lift station appears.
PE trap: designing a gravity sewer to run at d/D = 1.0 leaves zero margin — any flow above design surcharges the pipe, and there is no air space for ventilation of sewer gases. The 0.75–0.8 limit is a capacity reserve, not a hydraulics correction.
Worked example Size a gravity sewer at minimum slope
Given:
- Peak design flow Q = 0.35 m³/s; concrete pipe, n = 0.013; slope S = 0.005.
- Design limit d/D ≤ 0.8; self-cleansing minimum 0.6 m/s.
Solution:
- At d/D = 0.8, Q/Qfull ≈ 0.977, so the pipe must carry Qfull ≥ 0.35/0.977 = 0.358 m³/s flowing full.
- Full-flow Manning: Qfull = (1/0.013)(πD²/4)(D/4)2/3(0.005)1/2 = 1.695 D8/3. Setting 1.695 D8/3 = 0.358 gives D ≥ 0.558 m — try D = 600 mm.
- Check: Qfull = 1.695 × 0.68/3 = 0.434 m³/s; Vfull = 0.434/0.2827 = 1.54 m/s. Operating ratio Q/Qfull = 0.35/0.434 = 0.807, so d/D ≈ 0.68 ≤ 0.8. ✓
- Velocity at d/D ≈ 0.68: V/Vfull ≈ 1.11, so V ≈ 1.71 m/s ≥ 0.6 m/s. ✓
Answer: A 600 mm pipe at S = 0.005 works — operating d/D ≈ 0.68 and V ≈ 1.71 m/s satisfy both checks.