The measurement and the equation
An orifice plate restricts the flow, converting pressure into velocity; the resulting differential pressure is measured across the plate and related back to flow by the ISO 5167 equation:
with β = d/D the beta ratio, C the discharge coefficient, and ε the expansibility factor (1.0 for liquids). The awkward part is that C is not a constant — it depends on β, on the Reynolds number, on pipe diameter and on where the pressure taps sit. ISO 5167-2 specifies the Reader-Harris/Gallagher equation for it, which this calculator implements in full rather than assuming C ≈ 0.61. When solving for the bore, β and C are mutually dependent, so the solution iterates to convergence.
Worked example
Water, 100 m³/h, 100 mm pipe, 50 kPa design differential, flange taps:
- Pipe velocity 3.54 m/s → ReD ≈ 353,700 (firmly turbulent)
- Iterating β against the RG coefficient converges to β = 0.709, C = 0.608
- Bore = 0.709 × 100 = 70.9 mm
- Permanent pressure loss ≈ 0.47 × 50 ≈ 23 kPa lost for good
Design rules that matter more than the arithmetic
- Keep β between 0.4 and 0.6 if you can. ISO 5167 permits 0.10–0.75, but low β wastes pumping energy while high β raises uncertainty and gets sensitive to upstream disturbance.
- Respect the Reynolds minimum. The RG coefficient is only valid above ReD ≈ 5,000 (and higher for small β). Below that, the plate does not obey the equation — check with the Reynolds calculator at your minimum flow, not just design flow.
- Straight run is not optional. Typically 10–44 pipe diameters upstream depending on β and the fitting; short runs are the leading cause of orifice metering error in the field.
- DP is square-law: the transmitter output must have square root extraction applied exactly once — see the square root extraction calculator. Turndown suffers accordingly: at 25% flow the DP is only 6.25% of range.
- Use the true pipe bore, from the pipe schedule lookup — nominal diameter will size the plate wrong.
Frequently asked questions
What is the beta ratio of an orifice plate?
Beta is the orifice bore divided by the pipe internal diameter (β = d/D). ISO 5167 validates concentric orifice plates between β = 0.10 and 0.75; most designs target 0.4 to 0.6, where accuracy and permanent pressure loss are best balanced.
How do I calculate orifice plate size?
Solve the ISO 5167 mass flow equation for the bore: qm = (C ÷ √(1−β⁴)) × ε × (π/4)d² × √(2ΔPρ). Because the discharge coefficient C depends on β and Reynolds number, the solution is iterative — this calculator converges it for you.
What is a typical discharge coefficient for an orifice plate?
For concentric plates in turbulent flow it sits near 0.60 to 0.62. The Reader-Harris/Gallagher equation in ISO 5167-2 computes it from beta, Reynolds number, pipe diameter and tapping type rather than assuming a constant.
How much permanent pressure loss does an orifice plate cause?
Roughly (1 − β¹·⁹) times the measured differential — about 70% of the DP at β = 0.5 and around 45% at β = 0.7. That loss is pumping energy spent permanently, which is why very low beta ratios are expensive to run.
Implements the ISO 5167-2 concentric orifice equations for incompressible flow, for reference and education. Final metering design must follow the full standard including installation, uncertainty and expansibility requirements. See our disclaimer.