An orifice discharge coefficient Cd relates ideal flow to actual flow through an opening. It is dimensionless, but it is not a material property with one value for every opening. Edge sharpness, bevel or rounding, opening shape, nearby walls, approach velocity, effective head, and whether the opening is submerged all affect the flow pattern. The values below come from three public sources and represent different applications. Keep each coefficient attached to its source condition rather than combining them into a single “recommended” value.

Orifice Discharge Coefficient Reference

Selected published coefficients

USGS FEQ documentation describes a coefficient close to 0.6 for a sharp-edged orifice when its edge is sufficiently far from a boundary, and notes that a rounded edge may call for a value around 0.9. EPA SWMM cites 0.6 as the most commonly used model value and recommends 0.4 for a ragged edge. A USGS report on water-control structures summarizes a 0.5–0.7 range for free orifice flow and lists typical values of 0.6 for submerged vertical-lift gates and 0.7 for submerged radial gates. These are not interchangeable calibrations.

Use the right flow equation

For an incompressible liquid discharged freely under a head, a common model is Q=Cd A sqrt(2gH), where Q is volumetric flow, A is opening area, g is gravitational acceleration, and H is the effective head. For a submerged opening, the relevant head is generally the difference across the opening; use the formulation and head definition in the governing source. The equation’s units must be consistent. With SI units, area in square metres and head in metres produce flow in cubic metres per second when g is in metres per second squared. Gas flow can be compressible and choked, so this liquid equation and table should not be applied to it.

Worked example with stated assumptions

Consider an illustrative circular sharp-edged opening 100 mm in diameter with 0.25 m of effective head, discharging freely to air. Using Cd=0.6 from the sharp-edge source context, area is pi times 0.1 squared divided by four, or about 0.007854 m². With g=9.81 m/s², the ideal velocity term sqrt(2gH) is about 2.214 m/s. The calculated flow is approximately 0.01044 m³/s, or 10.4 L/s. This is a model example, not a field measurement; contraction, boundary spacing, approach flow, and downstream conditions can change the result.

Select a source that matches the installation

A flow-model coefficient may be suitable for routing or planning but not for a calibrated meter. A gate-control coefficient describes a gate opening and flow regime, whereas a sharp-edged plate in a pipe has its own geometry and pressure-tap conventions. Even an edge described as “sharp” may have burrs, wear, or a bevel that changes the contraction. Record the source publication, geometry, head definition, and free or submerged state. If the application has a calibration certificate or governing design standard, use it in preference to this cross-source overview.

Common errors and limits

One common error is to copy Cd=0.6 from a water-control model into a flow-measurement design without checking plate geometry and installation. Another is to substitute upstream water depth for the differential head on a submerged opening. A third is to treat the ragged-edge value or rounded-edge example as an adjustment factor that can be applied to any opening. These values describe specific source cases. For a permanent structure, verify approach conditions, opening dimensions, downstream level, and debris or erosion effects. For high-consequence service, calibrate the installation or use a qualified hydraulic design method.

Sources and verification

Source notes: USGS FEQUTL orifice-flow documentation, the EPA SWMM Hydraulics Reference Manual, and USGS Open-File Report 2022-1011. Their values refer to different geometries and flow conditions.

This table is a reference aid, not a substitute for the governing design code, product specification, qualified engineering review, or measurements from the actual component and service conditions.