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Flow rate calculation with an orifice plate to ISO 5167-2

From the differential pressure to the flow rate of a liquid, with the Reader-Harris/Gallagher discharge coefficient and the permanent pressure loss.

Orifice plateISO 5167-2Flow measurementDischarge coefficientLiquids
Free tool. For a real project the numbers must be checked on the specific case: if you need help, request a consultation.
CalculatorThe result updates as you type
Pipe and orifice plate
mm
mm
Fluid and measurement
mbar
kg/m³
mPa·s
Water at 20 °C: 1.0 mPa·s

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Indicative results, provided for preliminary estimation. They do not replace the design and verification of the real case by a qualified professional.

How to use it

Enter the inside diameter of the pipe, the bore diameter, the tapping position, the differential pressure read and the properties of the liquid. The tool calculates by iteration the discharge coefficient, which depends on the Reynolds number, and returns flow rate, velocity in the pipe and the pressure loss that remains downstream of the orifice plate.

Formulas used

Mass flow rate qm = C / √(1 − β⁴) · π/4 · d² · √(2 · Δp · ρ) Diameter ratio β = d / D Reynolds number ReD = 4 · qm / (π · μ · D) Coefficient C Reader-Harris/Gallagher equation (ISO 5167-2), a function of β, ReD and the tappings Permanent loss Δω = [√(1 − β⁴(1 − C²)) − C·β²] / [√(1 − β⁴(1 − C²)) + C·β²] · Δp

Limits

The calculation applies to liquids, that is, with an expansibility factor equal to 1: for gases and steam the expansibility factor is also needed. The standard applies with a bore of at least 12.5 mm, a pipe between 50 and 1000 mm, β between 0.10 and 0.75 and turbulent flow, and requires straight lengths upstream and downstream that depend on the fittings present. For sizing the meter and calculating the uncertainty there is the service orifice plate flow meter.

FAQ

What is the discharge coefficient?

It is the ratio between the real flow rate and the theoretical one without losses. For a sharp-edged orifice plate it is about 0.60 and changes little with β and with the Reynolds number: the standard gives it by a formula, with no need for calibration.

How much pressure is lost?

Part of the differential pressure is recovered downstream, the rest is lost. With β = 0.6 the permanent loss is about 60% of the differential pressure; it decreases as β increases.

Which tapping position should I choose?

Flange tappings are the most common because they are machined in the orifice flanges. Corner tappings are used on small pipes. The formula changes little, but the value of C must be calculated for the real configuration.

Technical consulting

From rough calculation to verified design

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