Restriction orifice sizing
Bore of a restriction orifice for a given pressure drop — liquids by ISO 5167-2 with a cavitation check and plates in series, gases with choked flow.
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The Orifice Plate Sizing Excel tool does everything here and more: orifice bore for a flow and transmitter range, the flow from a measured differential, or the differential for a flow, by ISO 5167-2 — with β, C, ε, permanent loss, limit checks and straight lengths. Print-ready report, any units, visible formulas, no macros.
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How this calculator works
A restriction orifice is a plate with a small bore that takes a fixed pressure drop or limits the flow — on pump minimum-flow bypasses, purge and sample lines, drains and depressuring lines. Unlike a metering orifice, it is sized on the permanent pressure loss, from upstream to the point downstream where the pressure has recovered. For liquids the plate follows ISO 5167-2: the Reader-Harris/Gallagher discharge coefficient (flange taps) and the ISO relation between the differential at the taps and the permanent loss, solved for the bore that passes your flow with your pressure drop. For gases the bore comes from isentropic flow with a discharge coefficient, held at the critical pressure ratio when the flow chokes.
Example — water: 30,000 kg/h of water at 30 °C dropping from 10 to 2 bar g in a 3-inch Schedule 40 line needs a 20.6 mm bore (β = 0.265, C = 0.598); the differential at the taps is 8.7 bar. The cavitation index σ = (P1 − Pv)/(P1 − P2) is only 1.37, so a single plate would cavitate — the calculator suggests 5 plates in series to keep σ at or above 2.5 on each. Example — gas: 5,000 Nm³/h of natural gas (M = 17.4, Z = 0.95, γ = 1.30) at 30 °C from 30 to 5 bar g in a 4-inch line needs a 20.1 mm bore with Cd = 0.61; the flow is choked, so any downstream pressure below 15.9 bar g gives the same flow.
The liquid method was checked against the discharge coefficient and pressure-loss functions of the open-source fluids library for five plates (bores within 0.01 %); the gas method against an independent coding of the choked and subcritical equations. Limits: single-hole, sharp-edged plates. The ISO coefficient is extrapolated below β = 0.1 and above 0.75, and gases at high pressure ratios pass more than Cd = 0.61 suggests — have the plate maker confirm the bore where the flow limit matters. Flashing liquids need a two-phase method. References: ISO 5167-2:2022; Crane, Flow of Fluids (TP-410); J. P. Tullis, Hydraulics of Pipelines (1989); Perry's Chemical Engineers' Handbook §6.