Orifice plate flow
Flow from differential pressure for a square-edged orifice plate, by ISO 5167-2 — liquids, gases and steam.
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How this calculator works
Mass flow qm = C/√(1 − β⁴) · ε · (π/4)·d² · √(2·ΔP·ρ1). The discharge coefficient C comes from the Reader-Harris/Gallagher equation of ISO 5167-2 for your tap type, and depends on the Reynolds number — so the calculator iterates until flow and C agree. For gases the expansibility factor ε is included. The permanent pressure loss is also shown, because it costs pumping or compression energy.
The example is water at 20 °C in a 4" Schedule 40 line (102.26 mm) with a 51.13 mm bore (β = 0.5) and flange taps, at 25 kPa differential: C = 0.6059, flow 32,680 kg/h (32.7 m³/h), about 18 kPa permanent loss.
Limits: square-edged concentric orifice plates within the ISO 5167-2 limits (β 0.10–0.75, D 50–1,000 mm, d ≥ 12.5 mm, Reynolds number above the minimum); the calculator warns outside them. Straight upstream and downstream lengths as in the standard. References: ISO 5167-1 and 5167-2 (equations as published); Perry's §10; Miller, Flow Measurement Engineering Handbook.