A pressure main is full by definition; a gravity sewer almost never is. Everything about checking a sewer — capacity, velocity, self-cleansing shear, Froude number — depends on how deep the flow actually runs in the pipe, expressed as the proportional depth d/D. The relationships between depth and the other hydraulic quantities were catalogued for designers by T.R. Camp in 1946, and his chart still appears in every sewer-design manual.
Why sewers run part-full
Air space above the water surface is functional, not waste: it ventilates the sewer (managing odour and corrosive sulphide gas), provides headroom for flows above the design estimate, and keeps the hydraulics in the stable free-surface regime. That is why authorities set depth limits well below full — Yarra Valley Water, for example, caps ultimate peak wet weather flow at d/D ≤ 0.70 for reticulation and branch sewers, explicitly preserving 30% air space, relaxing to 0.82 for main sewers whose attenuated flows are more predictable (YVWCD-2-4853 §4.3.1–4.3.3).
The geometry of a circular segment
θ — wetted central angle (radians)A — flow area · P — wetted perimeter · R — hydraulic radiusFeed these through Manning's equation at each depth and divide by the full-pipe values, and you get the two dimensionless curves of the hydraulic-elements chart: Q/Qfull and V/Vfull against d/D.
Reading the hydraulic-elements chart
Three results to know by heart (all assume constant Manning n with depth — the classical convention):
- Maximum discharge occurs at d/D ≈ 0.938, carrying about 1.076 × the full-pipe flow. A "full" pipe is not the pipe at its most productive.
- Maximum velocity occurs at d/D ≈ 0.81, about 1.14 × the full-pipe velocity.
- At exactly half depth, velocity equals full-pipe velocity — because the hydraulic radius at d/D = 0.5 equals the full-pipe value of D/4 — and discharge is therefore exactly half the full-pipe flow.
Between half depth and full, velocity is always higher than the full-pipe value, which is why a part-full check can never be replaced by a simple full-pipe calculation when velocity or shear criteria are in play.
Why capacity peaks below full
Near the crown, each increment of depth adds almost no flow area (the segment is closing) but adds wetted perimeter rapidly as the water touches more of the curved crown. Hydraulic radius — area over perimeter — therefore falls, and with it the Manning conveyance. From d/D ≈ 0.938 to 1.0, added friction outweighs added area and the discharge drops back to the full-pipe value. In practice the region above ~0.94 is also unstable (slugs of air, intermittent surcharge), which is one more reason design depth limits sit far below it.
Design depth limits in practice
| Authority | Limit | Basis |
|---|---|---|
| Yarra Valley Water | d/D ≤ 0.70 (reticulation, branch, road crossings) · ≤ 0.82 (main sewers) | 30% / 18% air space (YVWCD-2-4853 §4.3.1–4.3.3) |
| Water Corporation DS50 | depth ≤ ½ D (DN150) · ≤ ⅔ D (DN225–600) | Table 4.4 |
| Icon Water | design flow without surcharge | STD-SPE-G-011 |
The Gravity Sewer Design Checker draws the hydraulic-elements diagram from its own Manning engine — the peaks land at 0.938D/1.076× and 0.81D/1.14× because the maths produces them, not because they were drawn in — and plots your actual operating points on the curves as you change grade.
Summary
- d/D — proportional depth — is the master variable of part-full pipe hydraulics.
- Peak capacity ≈ 1.076 × Qfull at 0.938D; peak velocity ≈ 1.14 × Vfull at 0.81D; half-depth flow runs at exactly full-pipe velocity.
- Authorities cap design depth well below the capacity peak — ventilation, headroom and stability all want air space.
- Velocity and shear criteria must be checked at the actual part-full depth, never approximated from full-pipe values.
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