Flow rate through a sharp-edged orifice plate from measured differential pressure (ISO 5167 form, incompressible).
qm = Cd / √(1 − β⁴) · (π/4) d² · √(2 ΔP ρ)
How it works
A sharp-edged plate forces the flow through a bore smaller than the pipe, and the resulting pressure drop across the plate is a direct measure of flow. The tool applies the ISO 5167 orifice equation with your discharge coefficient to convert the measured ΔP into mass and volumetric flow.
Worked example
Water through a 50 mm bore in a 100 mm line (β = 0.5) reading 25 kPa of differential. ≈ 31.5 m³/h — a convenient way to infer flow from two pressure taps.
Inputs
Pipe inside diameter (mm)
Orifice bore (mm)
Differential pressure (kPa)
Fluid density ρ (kg/m³)
Discharge coefficient — ≈ 0.60–0.61 for a sharp-edged plate with corner taps at high Re.
Frequently asked questions
What discharge coefficient should I use?
A sharp-edged concentric plate runs at Cd ≈ 0.60–0.61 over a wide Reynolds range. For custody-transfer accuracy, compute Cd from the Reader-Harris/Gallagher equation in ISO 5167 for your exact tap arrangement and Reynolds number.
Does this work for gases?
Approximately, if the differential is small (below roughly 10% of the upstream absolute pressure). Beyond that, gas expansion through the bore matters and the expansibility factor ε must be included — this tool assumes ε = 1.
What is the beta ratio and why does it matter?
β is bore diameter divided by pipe inside diameter. ISO 5167 correlations are valid for about 0.2–0.75; a higher β gives less permanent pressure loss but a weaker, noisier signal.
Assumptions
Incompressible flow (ε = 1). For gases keep ΔP below ~10% of the absolute upstream pressure.
Sharp-edged concentric plate, fully developed turbulent flow upstream.
Cd is user-supplied — for custody transfer use the full Reader-Harris/Gallagher equation with your tap geometry.
References
ISO 5167-2 — Measurement of fluid flow by means of orifice plates.
Reader-Harris, M. (2015), Orifice Plates and Venturi Tubes, Springer.
Related Fluid Mechanics tools
Pipe Pressure Drop — Frictional ΔP and head loss for single-phase flow in a circular pipe (Darcy–Weisbach, Swamee–Jain friction factor).
Fittings Pressure Drop (K-factors) — Minor losses through elbows, tees, and valves by the ΣK excess-head method — the companion to straight-pipe friction.
Pipe Velocity & Reynolds — Line velocity, Reynolds number, and flow regime from flow rate and pipe inside diameter.
Friction Factor (Moody) — Darcy (and Fanning) friction factor from Reynolds number and relative roughness — Colebrook–White solved exactly, with the Swamee–Jain explicit fit for comparison.