Orifice Discharge Coefficients (Cd) — Reference
For outlet structures, detention risers, and tank drains: Q = Cd·A·√(2gh), with A the orifice area and h the head on the centroid (free) or the head difference (submerged). Cd = Cc·Cv (contraction × velocity).
Discharge Coefficient by Orifice Type
| Orifice / outlet type | Cd |
|---|---|
| Sharp-edged (thin plate) orifice | 0.61–0.62 |
| Standard stormwater orifice outlet (design value) | 0.60 |
| Rounded / bell-mouth entrance | 0.95–0.98 |
| Short tube (L ≈ 2–3 diameters), flowing full | 0.80–0.82 |
| Borda re-entrant tube, running full | ~0.72 |
| Submerged orifice (use head difference) | ~0.61 |
| Pipe/culvert entrance treated as orifice | 0.60–0.62 |
Component Coefficients (Sharp-Edged)
| Coefficient | Value | Meaning |
|---|---|---|
| Contraction Cc | ~0.62 | vena-contracta area / orifice area |
| Velocity Cv | ~0.98 | actual / ideal jet velocity |
| Discharge Cd | ~0.61 | Cc × Cv |
Sources: Brater & King, Handbook of Hydraulics. ASCE/WEF MOP-77. Standard stormwater outlet-structure practice (Cd = 0.6 for orifice plates).
Worked example: detention pond low-flow orifice
6-in sharp-edged orifice plate, 4.0 ft of head on the centroid, free discharge
The coefficient is the biggest lever in the calculation. A field-fabricated hole cut in a riser wall, with a rough or chamfered edge, is not the 0.61 thin plate that the textbook value describes. The release rate of a detention pond is often a regulatory limit, so pick Cd to match what will actually be built, show it on the plans, and inspect it at construction.
Common mistakes
- Measuring head to the orifice invert instead of the centroid. At high head the error is small. At the low heads that set water-quality and channel-protection releases, it is not.
- Using the free-discharge equation when the outlet is submerged. Once tailwater rises above the orifice, the driving head is the difference between the headwater and tailwater surfaces.
- Applying the orifice equation at heads below the top of the opening. Until the opening is submerged it acts as a weir. Calculate both and take the lower discharge at each stage.
- Forgetting the trash rack. A clogged rack is the usual reason a small orifice under-performs. Many manuals set a minimum orifice size (often 2–3 in) for this reason.
When this card doesn’t apply
The tabulated coefficients assume a fully contracted jet. That needs the orifice well away from the floor and walls, about two diameters is a common rule, with low approach velocity. Orifices near a boundary suppress the contraction and discharge more. Large gates, partly open sluices and orifices in thick walls have their own coefficients: see the sluice gate tool and the minor-loss tables. Calibrated metering orifices follow ISO 5167 or ASME MFC-3M, not these design values.
Related cheat sheets and tools
Pair Cd with the orifice tool and the weir coefficient card for the weir-controlled stages of the same riser. For sizing the detention volume that the outlet drains, start from NRCS runoff. For a full stage-storage-discharge outlet design and pond routing, see HydroComplete.