Orifice β-Ratio Sizing (ISO 5167)
Size a concentric square-edged orifice plate for a target flow — solves bore diameter, β, and differential pressure.
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The engineering
The β-ratio is the single most important number on an orifice plate: it is the bore-to-pipe diameter ratio d/D, and it sets both the differential pressure you'll read and the permanent head you'll lose. This card ties together the ISO 5167 mass-flow equation and the Reader-Harris/Gallagher discharge-coefficient correlation (corner taps here) so you can size a plate to hit a target ΔP transmitter span, or predict ΔP from an existing bore.
Keep β between 0.20 and 0.75 — ISO 5167 does not certify plates outside that band, and low β wastes permanent pressure while high β makes C sensitive to edge sharpness and installation. A good starting target is β ≈ 0.5, which gives a discharge coefficient near 0.606 and a comfortable ΔP. If your solver pins against the 0.75 limit, the pipe is too big for the flow; step down a size.
Everything assumes fully developed turbulent flow with adequate straight run upstream and a knife-sharp square edge. The expansibility factor ε is 1.0 for liquids; drop it below 1 only for compressible service where ΔP is a meaningful fraction of line pressure.
Where this math comes from
Orifice metering is old plumbing wisdom made rigorous. Giovanni Poleni and later Weisbach studied flow through sharp-edged holes in the 1700s–1800s, but industrial gas and water metering in the early 20th century demanded repeatable coefficients. The American Gas Association and ASME ran thousands of calibration tests through the 1920s–1930s to pin the discharge coefficient of the concentric square-edged plate.
Michael Reader-Harris and J.A. Gallagher distilled decades of European and American data into the correlation that now anchors ISO 5167, replacing the older Stolz equation. The result is a plate that any shop can machine to a drawing and trust to a fraction of a percent — no on-site calibration required, which is exactly why the square-edged orifice still dominates custody-transfer and process flow.
- 1738Daniel BernoulliHydrodynamica establishes the pressure–velocity trade that orifice metering exploits.
- 1930AGA / ASMELarge calibration campaigns fix discharge coefficients for square-edged plates.
- 1991M. Reader-Harris & J. GallagherPublish the RG discharge-coefficient equation adopted by the standard.
- 2003ISO 5167Revised into four parts; orifice plates in Part 2 use the Reader-Harris/Gallagher C.
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