The Calculation, Explained
From Bernoulli to the working equation
An orifice plate squeezes the flow through a smaller hole. Continuity says the fluid must speed up; Bernoulli says the pressure must fall. Measuring that pressure fall gives the flow. Combining the two, and folding the real-world losses and the jet's vena contracta into a discharge coefficient C, gives the standard equation of ISO 5167:
The 1/√(1−β⁴) term is the velocity-of-approach factor: the fluid arrives at the plate already moving. For gases and steam, ε (expansibility) corrects for the density drop as the gas expands through the plate; for liquids ε = 1. ISO 5167 gives ε for orifice plates as:
Assumptions and applicability
- Discharge coefficient. C is not a constant of nature: rigorously it comes from the Reader-Harris/Gallagher equation in ISO 5167-2, varying with β, Reynolds number and tapping arrangement. The default 0.61 is representative for a sharp-edged plate at high Reynolds number; a test-grade calculation should evaluate C properly and iterate, since C itself depends on the flow.
- Validity envelope: 0.2 ≤ β ≤ 0.75, pipe Reynolds number above about 5,000 (higher for large β), fully developed flow — which in practice means the straight upstream/downstream lengths of ISO 5167 for the fittings actually installed. A DP meter behind an elbow, without its straight length, is a random number generator with good documentation.
- Density is the upstream density at the actual pressure and temperature of the run.
- For gases, the expansibility formula holds while p2/p1 ≥ 0.75.
Worked example (the defaults above)
A 180 mm orifice in a 300 mm line (β = 0.60), water at 998 kg/m³, Δp = 25 kPa, C = 0.61: approach factor 1/√(1−0.1296) = 1.072; bore area 0.02545 m²; √(2 × 25,000 × 998) = 7,064. Flow = 0.61 × 1.072 × 0.02545 × 7,064 = 117.5 kg/s — 423 t/h (424 m³/h), at a pipe Reynolds number of about 5.0 × 10⁵, comfortably inside the valid range.
References
ISO 5167-1/-2 — Measurement of fluid flow by means of pressure differential devices; ASME MFC-3M.
Frequently Asked Questions
How does an orifice plate measure flow?
The plate restricts the pipe, the flow speeds up through the bore and the static pressure falls. That differential pressure is proportional to the square of the flow, so flow is calculated from the square root of the differential pressure, the bore and pipe diameters, and the upstream density, following ISO 5167.
What beta ratio should an orifice plate have?
Beta, the bore-to-pipe diameter ratio, should normally sit between 0.4 and 0.7, inside the ISO 5167 validity range of 0.2 to 0.75. Higher beta means lower permanent pressure loss but a weaker signal; lower beta gives a stronger signal at the cost of pumping energy.
Why is a DP flow meter inaccurate at low flow?
Because differential pressure falls with the square of flow: at 30% flow the DP is only 9% of its full-scale value, where transmitter error and noise dominate. A DP meter ranged for full flow cannot be trusted in the bottom quarter of its range.
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