What discharge coefficient does an orifice plate use?

For a concentric square-edged plate, ISO 5167-2 uses the Reader–Harris/Gallagher equation C = f(β, Re_D, tap type, D). Because Re_D depends on the flow and the flow depends on C, it is solved iteratively to convergence — not a single pass.

How are eccentric and segmental orifices different?

ISO 5167-2 covers only concentric plates. Eccentric coefficients come from ISO/TR 15377:1998 (corner taps, β-only) or Miller’s Handbook; segmental coefficients exist only in Miller’s Handbook. Both carry larger uncertainty and are flagged accordingly.

When does a gas restriction orifice choke?

When the pressure ratio P₂/P₁ falls to or below the critical ratio rc = [2/(κ+1)]^(κ/(κ−1)) (≈0.528 for air). At that point the flow is sonic at the bore and becomes independent of downstream pressure — size it on the critical-flow equation and stage the drop if needed.

Why use a multi-stage restriction orifice?

A single plate taking a very large pressure drop will choke (gas) or cavitate (liquid). Splitting the drop across N plates with equal pressure ratio keeps each stage within its safe limit; the minimum stage count follows from N_min = ceil(ln(P₂/P₁)/ln(rc)).

Orifice plate sizing per ISO 5167

Differential-pressure flow elements — orifice plates, flow nozzles and venturi tubes — size from one equation: qm = (C/√(1−β⁴))·ε·(π/4)·d²·√(2·ΔP·ρ₁). The art is in the discharge coefficient C and the flow regime. This guide explains both, then hands off to the live calculators.

The C↔Re iteration

For a concentric plate, the Reader–Harris/Gallagher coefficient depends on the pipe Reynolds number, which depends on the very flow you are solving for. A correct ISO 5167 implementation iterates C↔Re_D to convergence (|ΔC| < 1e-8) rather than approximating in one pass — the difference between a right and a wrong answer. Our engine does this and is validated to <0.5% against the standard (reproduced with the open-source fluids library).

Three ways to solve

Solve flow — given a bore and ΔP, find the mass flow.
Solve bore — given a flow and ΔP, size the bore (a nested β-search around the C↔Re loop).
Solve ΔP — given a flow and a bore, find the differential.

Restriction orifices & staging

A restriction orifice deliberately dissipates pressure. For gas, check the critical pressure ratio and stage the drop to avoid choking; for liquid, watch the cavitation index σ. The multi-stage tool sizes a common bore and verifies every stage.

DP Flow calculator →

orifice · nozzle · venturi

Restriction Orifice →

single & multi-stage

Validation →

published V&V cases

FAQ

What discharge coefficient does an orifice plate use?: For a concentric square-edged plate, ISO 5167-2 uses the Reader–Harris/Gallagher equation C = f(β, Re_D, tap type, D). Because Re_D depends on the flow and the flow depends on C, it is solved iteratively to convergence — not a single pass.
How are eccentric and segmental orifices different?: ISO 5167-2 covers only concentric plates. Eccentric coefficients come from ISO/TR 15377:1998 (corner taps, β-only) or Miller’s Handbook; segmental coefficients exist only in Miller’s Handbook. Both carry larger uncertainty and are flagged accordingly.
When does a gas restriction orifice choke?: When the pressure ratio P₂/P₁ falls to or below the critical ratio rc = [2/(κ+1)]^(κ/(κ−1)) (≈0.528 for air). At that point the flow is sonic at the bore and becomes independent of downstream pressure — size it on the critical-flow equation and stage the drop if needed.
Why use a multi-stage restriction orifice?: A single plate taking a very large pressure drop will choke (gas) or cavitate (liquid). Splitting the drop across N plates with equal pressure ratio keeps each stage within its safe limit; the minimum stage count follows from N_min = ceil(ln(P₂/P₁)/ln(rc)).