Orifice Flow Calculator

A sharp-edged orifice typically has a discharge coefficient (Cd) between 0.60 and 0.65, with 0.61 being the most commonly cited value. The coefficient can vary based on the Reynolds number, orifice geometry, and the ratio of orifice diameter to pipe diameter (beta ratio). Rounded or beveled edges generally yield higher Cd values closer to 0.8.

The standard formula is Q = Cd × A × √(2ΔP/ρ), where Q is the volumetric flow rate, Cd is the discharge coefficient, A is the orifice cross-sectional area (π × d²/4), ΔP is the pressure drop across the orifice, and ρ is the fluid density. This equation is derived from Bernoulli's principle combined with a continuity correction.

The discharge coefficient is primarily influenced by the orifice edge sharpness, the Reynolds number of the flow, the beta ratio (orifice diameter to pipe diameter), fluid viscosity, and surface roughness. At higher Reynolds numbers, Cd tends to stabilize. Sharp-edged orifices generally follow well-established Cd standards, while worn or rounded edges require empirical calibration.

Temperature affects the fluid's density and viscosity. As temperature increases, most liquids become less dense and less viscous, which changes both the flow rate calculation and the discharge coefficient. For accurate results, always use the fluid density at the actual operating temperature rather than at standard conditions. For gases, temperature also affects compressibility.

A minimum pressure drop of around 250–500 Pa is generally recommended to ensure the orifice is operating in a turbulent flow regime (high Reynolds number) where Cd is stable and predictable. Very low pressure drops can result in laminar or transitional flow conditions, where the discharge coefficient varies significantly and measurement accuracy decreases.

This calculator uses the incompressible flow equation, which is suitable for liquids and for gases where the pressure drop is small relative to the absolute inlet pressure (typically less than 10–15%). For high pressure-drop gas applications, an expansion factor (Y) correction must be applied to account for compressibility effects. Always verify that ΔP/P₁ is small before using incompressible equations for gas flows.

Start with your required flow rate and available pressure drop, then rearrange the orifice equation to solve for area: A = Q / (Cd × √(2ΔP/ρ)), and from that derive the diameter. Ensure the resulting beta ratio (orifice diameter / pipe diameter) stays between 0.2 and 0.75 for standard orifice meter accuracy. Oversized orifices reduce pressure sensitivity, while undersized ones create excessive permanent pressure loss.

Common causes of deviation include worn or damaged orifice edges, upstream flow disturbances (bends, valves, pumps) that create non-uniform velocity profiles, entrained gases in liquids (or liquid droplets in gases), fouling or deposits on the orifice plate, incorrect pressure tap locations, and using a Cd value that doesn't match the actual orifice geometry or flow regime. Adequate straight-pipe runs upstream (typically 10–20 pipe diameters) help minimize installation effects.