Orifice Flow Calculator

An orifice plate infers flow rate from a pressure drop. Forcing fluid through a restriction accelerates it, and by Bernoulli's principle the static pressure falls; combining the energy equation with continuity gives velocity proportional to the square root of the differential pressure. The working equation, Q equals Cd times orifice area times the velocity-of-approach factor times the square root of 2 dP over density, contains two corrections to the ideal result. The velocity-of-approach factor, 1 over the square root of 1 minus beta to the fourth, accounts for the fact that the upstream fluid is already moving rather than at rest. The discharge coefficient Cd absorbs everything the ideal derivation omits: the vena contracta forming downstream of the plate so the true minimum flow area is smaller than the bore, plus viscous losses and velocity profile effects. For a sharp-edged concentric plate Cd sits between about 0.58 and 0.65, near 0.61 at typical Reynolds numbers. Beta, the bore-to-pipe diameter ratio, is the main design variable. ISO 5167 restricts standard plates to beta between 0.20 and 0.75, and most installations use 0.50 to 0.65 as a compromise: low beta produces a strong differential signal but wastes energy, high beta recovers pressure but yields a weak signal that is hard to measure accurately. Permanent pressure loss, the portion never recovered downstream, is approximately 1 minus beta squared times the measured differential, so a beta of 0.50 permanently loses about 75 percent of the dP as heat. Practical constraints follow from the physics. Because flow varies with the square root of dP, usable turndown is limited to roughly 4 to 1. Straight-run requirements are substantial, from about 10 to more than 40 pipe diameters upstream depending on beta and the disturbance, with 4 to 8 diameters downstream. The equation as implemented assumes incompressible flow; gas and steam service requires the expansion factor from ISO 5167, and a rounded or eroded upstream edge shifts Cd by several percent.

The physics dates to the beginning of fluid mechanics. Evangelista Torricelli established in 1643 that efflux velocity through an opening varies with the square root of the head above it, and Daniel Bernoulli's Hydrodynamica of 1738 gave the general energy relation from which the orifice equation is derived. Applying it to metering required an empirical correction, since the theoretical discharge consistently overpredicted reality; measurement of the contracted jet downstream of a sharp-edged opening supplied the discharge coefficient that reconciles the two, and the same reasoning underlies Giovanni Battista Venturi's converging-diverging tube and the later Herschel venturi meter. The orifice plate became an industrial instrument through the natural gas business. Early twentieth-century gas sales required a cheap, robust way to meter large volumes in pipelines, and the thin plate between flanges met that need better than positive displacement meters could at scale. The American Gas Association organized systematic testing and issued the first of its orifice metering reports around 1930, work later carried forward jointly with the American Petroleum Institute as AGA Report No. 3 and API MPMS Chapter 14.3, the documents that still govern custody transfer measurement in North America. International standardization followed a parallel path, with ISO 5167 consolidating European and global practice on the geometry of plates, tap arrangements, and installation requirements. The most significant modern revision came from the Reader-Harris and Gallagher equation, developed in the 1990s from a large combined European and American database, which replaced the older Stolz equation for discharge coefficient and was adopted in the 2003 revision of ISO 5167-2.