Orifice Plate Flow Calculator (ISO 5167)
Calculate flow through a concentric square edged orifice plate from the measured differential pressure. The discharge coefficient is calculated with the Reader Harris/Gallagher equation from ISO 5167-2, iterated on Reynolds number.
- β = d ÷ D = 51.13 ÷ 102.26 = 0.5000
- C from the Reader Harris/Gallagher equation, iterated with Re = 112,800: 0.6059
- qm = C ÷ √(1 − β⁴) × ε × π/4 × d² × √(2 ΔP ρ) = 9.0777 kg/s
The ISO 5167 Orifice Equation
ISO 5167-2 gives the mass flow through an orifice plate from the measured differential pressure and the geometry of the plate and pipe:
Where qm is mass flow (kg/s), C is the discharge coefficient, β = d/D is the diameter ratio, ε is the expansibility factor (1 for liquids), d is the bore (m), ΔP is the differential pressure (Pa) and ρ1 is the upstream density (kg/m³).
C depends on β, the tapping arrangement and the Reynolds number, which itself depends on the flow. The calculator solves this loop by iteration, exactly as flow computers do.
Worked example
Water at 20 °C (998.2 kg/m³, 1.002 cP) flows in a 4 inch Sch 40 pipe (ID 102.26 mm) through a 51.13 mm bore (β = 0.5) with flange taps. At 250 mbar the calculator gives C = 0.606, a mass flow of about 32,700 kg/h and a volume flow of 32.7 m³/h (1.1 m/s in the pipe).
Frequently Asked Questions
What is a typical orifice discharge coefficient?
For a sharp edged concentric orifice in turbulent flow C is close to 0.6, typically 0.598 to 0.61 depending on β, tappings and Reynolds number.
What beta ratio should I use?
ISO 5167-2 allows 0.1 to 0.75. Values of 0.4 to 0.65 are a good compromise between permanent pressure loss and required straight pipe length.
Does this calculator work for gas and steam?
Yes. Select Gas or steam and enter the absolute upstream pressure and isentropic exponent; the expansibility factor ε is then applied. Use density at flowing conditions.
How accurate is an orifice flow measurement?
With ISO 5167 geometry and installation, the uncertainty of C is about 0.5 % for most β ratios. Total installed uncertainty, including the DP transmitter and density, is typically 1 to 2 % of rate.
Learn more on the blog
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