Drawing No. EH–FM–013 // Fluid Mechanics & Piping
Orifice Flow Calculator
Reviewed August 2026
Estimate incompressible liquid flow through a sharp-edged orifice plate from measured differential pressure, pipe/orifice geometry, fluid density and an appropriate discharge coefficient.
What problem does this solve?
Orifice plates create a measurable pressure drop that can be related to flow. This tool applies the standard incompressible energy relationship with the velocity-of-approach correction, but requires you to supply the discharge coefficient rather than pretending it is known from beta ratio alone.
Inputs
Results
Background
Q = Cd·E·A·√(2ΔP/ρ), where Cd is the discharge coefficient, E = 1/√(1−β⁴) is the velocity-of-approach factor, A is orifice area, ΔP is differential pressure, and ρ is upstream liquid density. This is the incompressible differential-pressure relationship used as the basis of orifice-meter calculations; standards-grade metering adds validated Cd correlations, installation limits, Reynolds-number effects and—when applicable—compressibility corrections.
β = d/D, the orifice bore diameter divided by the pipe's internal diameter. A small beta (tight orifice) produces a larger, more easily measured differential pressure but also a larger permanent pressure loss and higher uncertainty at low flow; a large beta produces a gentler differential pressure with less permanent loss but is more sensitive to installation and measurement errors. ISO 5167 recommends keeping beta between about 0.1 and 0.75 for reliable measurement.
The discharge coefficient Cd accounts for contraction, viscous effects and non-ideal velocity distribution. It is not a universal function of beta alone. Standards-grade metering determines Cd from validated correlations using Reynolds number, pressure-tap configuration and geometry, or from calibration. This calculator therefore asks you to supply Cd explicitly.
E = 1/√(1−β⁴) corrects for the fact that fluid already has significant velocity in the pipe before reaching the orifice, so the pressure drop reflects the flow more efficiently than a simple orifice-in-a-wall would. This correction is small at low beta (E≈1.004 at β=0.3) but becomes significant at high beta (E≈1.228 at β=0.7, a 23% correction) — which is one reason very high beta ratios trade measurement simplicity for greater sensitivity to this correction.
ISO 5167 and similar standards require substantial straight, unobstructed pipe upstream (typically 10–40 pipe diameters, depending on beta and the upstream fitting) and some straight pipe downstream of the orifice plate. Elbows, valves, tees or other fittings too close to the plate distort the velocity profile the discharge coefficient was calibrated against, introducing errors that a differential-pressure reading alone can't reveal.
Frequently asked questions
Practical questions about inputs, assumptions and interpretation.
A smaller bore (lower beta) forces the fluid through a smaller area at the same volumetric flow rate, so its velocity — and therefore the pressure drop, which scales with velocity squared — increases. This is the whole principle behind orifice metering, but it comes with a tradeoff: a smaller bore also causes a larger permanent (non-recoverable) pressure loss in the system.
No. This calculator intentionally does not implement the full Reynolds-number- and tap-dependent discharge-coefficient procedure, plate tolerances, installation requirements, uncertainty calculation or compressible-flow treatment required for standards-grade metering. Use the applicable standard and calibrated/traceable hardware for custody transfer, billing or regulatory reporting.
Without it, the equation would assume the fluid starts from rest before the orifice — but it's already moving at the pipe's own velocity. The velocity of approach factor accounts for the kinetic energy the fluid already has, which becomes an increasingly important correction as the orifice bore approaches the pipe diameter (high beta).
Do not use this incompressible form for gases when density changes materially through the meter. Compressible orifice metering requires an expansibility factor plus upstream thermodynamic properties and the applicable discharge-coefficient correlation.