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SimuPipe

Orifice Plate Flow Calculator

Calculate flow rate, pressure drop, or orifice bore size using ISO 5167 with the Reader-Harris/Gallagher discharge coefficient correlation. Supports liquids and gases.

Geometry
Fluid
Density998.2 kg/m³
Viscosity1.002 cP
Results
Volume flow rate19.84
Mass flow rate19803.2
Beta ratio (d/D)0.50000
Discharge coeff. (C)0.60711
Approach factor (E)1.03280
Re_D (pipe)69,917
Pipe velocity0.702m/s
Orifice velocity2.81m/s

C carries the ISO 5167-2 uncertainty: ±0.5% for β ≤ 0.6, ±(1.667·β − 0.5)% above — before your own uncertainties in D, d, ΔP and density.

About Orifice Plate Flow Measurement

An orifice plate is a thin plate with a circular opening (bore) placed in a pipe to create a measurable pressure drop. By measuring the differential pressure across the plate, the flow rate can be calculated using the orifice equation from ISO 5167.

ISO 5167 Orifice Equation

The volumetric flow rate through an orifice plate is:

Q=Cd⋅E⋅ε⋅π4⋅d2⋅2⋅ΔPρQ = C_d \cdot E \cdot \varepsilon \cdot \frac{\pi}{4} \cdot d^2 \cdot \sqrt{\frac{2 \cdot \Delta P}{\rho}}
  • CdC_d — discharge coefficient (Reader-Harris/Gallagher correlation)
  • EE — velocity of approach factor
  • ε\varepsilon — expansibility factor (for compressible fluids)
  • dd — orifice bore diameter
  • ΔP\Delta P — measured differential pressure
  • ρ\rho — fluid density
  • DD — pipe internal diameter (upstream of the plate)
  • β=d/D\beta = d/D — diameter (beta) ratio; ISO 5167-2 covers 0.10–0.75
  • E=1/1−β4E = 1/\sqrt{1-\beta^4} — velocity-of-approach factor; corrects for the kinetic energy the fluid already has in the pipe
  • ReD=ρVD/μRe_D = \rho V D / \mu — pipe Reynolds number, on the pipe diameter D and the mean pipe velocity V, not the bore
  • μ\mu — dynamic viscosity; it enters only through the Reynolds number, which sets C

For gases the expansibility factor from ISO 5167-2 accounts for the density drop between the taps (ε = 1 for liquids). κ is the isentropic exponent — the same quantity the fluid card calls γ:

ε=1−(0.351+0.256β4+0.93β8)[1−(p2/p1)1/κ]\varepsilon = 1 - (0.351 + 0.256\beta^4 + 0.93\beta^8)\left[1 - (p_2/p_1)^{1/\kappa}\right]

Discharge Coefficient

The discharge coefficient C accounts for real-flow effects including contraction of the flow stream and viscous losses. This calculator uses the Reader-Harris/Gallagher (2006) correlation, which is the basis of ISO 5167-2. It depends on the beta ratio (d/D), Reynolds number, pipe diameter, and pressure tap arrangement (corner, flange, or D and D/2 taps).

Pressure Tap Types

  • Flange taps — pressure tappings at 25.4 mm (1 inch) from each face of the orifice plate. Most common in North America.
  • Corner taps — tappings at the orifice plate faces (zero distance). Common in Europe.
  • D and D/2 taps — upstream tap at 1D, downstream at 0.5D from the plate.

For pipe pressure drop calculations, use our friction loss calculator. For pipe network simulation with orifice plates, valves, and other components, try SimuPipe.

Inputs and outputs explained
  • Calculate modes. “Flow rate (from ΔP)” solves Q from a measured differential; “Pressure drop (from Q)” inverts the same equation for ΔP at a known flow; “Orifice size (from Q + ΔP)” finds the bore d that gives the target differential at the design flow, iterating β because C itself depends on β and Re_D.
  • Pressure tap type. Where the two pressure tappings sit relative to the plate. It changes the C correlation constants (and slightly the reading), so pick the arrangement actually installed — see the tap-type list above.
  • Upstream pressure P₁ (gases). The absolute static pressure at the upstream tap. It fixes the gas density (ideal-gas law at P₁ and the stated temperature) and, with ΔP, the pressure ratio p₂/p₁ used by the expansibility factor.
  • Isentropic exponent γ (gases). The ratio of specific heats cₚ/cᵥ (κ in ISO 5167), used only in the expansibility factor. Typical values: air, N₂, O₂ 1.40; methane 1.31; natural gas 1.27–1.32; CO₂ 1.29; steam ≈ 1.3; propane 1.13. The fluid preset fills it in.
  • Re_D (pipe). Reynolds number on the pipe diameter and mean pipe velocity, ρ·V·D/μ. The discharge coefficient falls slowly as Re_D rises, so C and Q are solved together; ISO 5167-2 needs Re_D ≥ 5,000.
  • Pipe velocity / orifice velocity. Q divided by the pipe area and by the bore area respectively. The bore velocity is the one to watch: high values mean flashing or cavitation risk in liquids and compressibility effects in gases.
  • Normal flow rate (gases). The volumetric flow converted to normal conditions, 0 °C and 101.325 kPa absolute (Nm³/h), so it can be compared with meter specifications and process data quoted at normal conditions.
Worked example

Water at 20 °C (ρ = 998.2 kg/m³, μ = 1.002 mPa·s, i.e. cP) in a 100 mm pipe with a 50 mm concentric orifice, flange taps, measured differential 10 kPa — the calculator's default inputs, so it shows exactly these figures when you open the page (properties from the same water correlation).

  1. Diameter ratio β = d/D = 0.50, velocity-of-approach factor E = 1/√(1 − β⁴) = 1.03280.
  2. Bore area A_d = π·d²/4 = 1.9635e-3 m²; √(2·ΔP/ρ) = 4.4762 m/s. For a liquid the expansibility ε = 1.
  3. The discharge coefficient depends on the pipe Reynolds number, which depends on the flow — so C and Q are iterated together. Converged after 4 passes at Re_D = 69,917 (the exact converged value), C = 0.60711 (Reader-Harris/Gallagher, flange taps).
  4. Q = C·E·ε·A_d·√(2·ΔP/ρ) = 19.84 m³/h (mass flow 19803.2 kg/h).
  5. Mean velocity 0.702 m/s in the pipe and 2.81 m/s through the bore.
  6. Permanent pressure loss (ISO 5167-2, exact form) ω = ΔP·(√(1 − β⁴(1 − C²)) − C·β²)/(√(1 − β⁴(1 − C²)) + C·β²) = 7.32 kPa — about 73% of the tap differential.

Because C is iterated with Re_D to convergence (tolerance 10⁻¹⁰ on Q) rather than read once from a chart, the result matches a hand calculation done to ISO 5167-2 to the last significant figure.

Assumptions and limits
  • Concentric, thin, square-edged orifice plate in a full circular pipe, with fully developed single-phase flow upstream. ISO 5167-2 requires straight lengths upstream and downstream (Table 3 of the standard) that this page assumes are met.
  • Validity of the Reader-Harris/Gallagher equation: 0.10 ≤ β ≤ 0.75, D ≥ 50 mm, d ≥ 12.5 mm, and Re_D ≥ 5,000 (≥ 170·β²·D/mm for corner or D–D/2 taps above β = 0.56). Outside this band the calculator still returns a number but flags it; treat it as indicative only.
  • Gases: density is evaluated at the upstream tap conditions, as ISO 5167 requires, from the ideal-gas law at the stated pressure and temperature (no compressibility factor Z). The ISO 5167-2 expansibility factor ε is applied with the fluid's isentropic exponent; the standard limits it to p₂/p₁ ≥ 0.75.
  • ΔP is the differential between the taps (what the transmitter reads), not the permanent pressure loss. The permanent loss is smaller — ISO 5167-2 gives ω = ΔP·(√(1 − β⁴(1 − C²)) − C·β²)/(√(1 − β⁴(1 − C²)) + C·β²), about 73% of the reading at β = 0.5; the common shortcut ΔP·(1 − β^1.9) is an approximation of this.
  • Uncertainty: ISO 5167-2 quotes ±0.5% on C for β ≤ 0.6 (±(1.667·β − 0.5)% above), before adding your own uncertainties in D, d, ΔP and density.
  • Wet gas, pulsating flow, eccentric or segmental plates, and plates with edge wear or upstream swirl are outside the method.

The calculator and the SimuPipe solver share the same Reader-Harris/Gallagher and expansibility code; the solver applies the plate as K = (1 − β⁴)/(C²·β⁴), which reproduces the tap differential. Its accuracy is documented case by case on the validation page (53 published cases, including the GPSA Ex 3-2 gas orifice and an ISO 5167-2 compressible meter).

References

None of these methods are ours — check them at the source.

  • ISO 5167-1:2022 and ISO 5167-2:2022. Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full — Part 1: General principles; Part 2: Orifice plates. — the discharge-coefficient equation, expansibility factor, validity limits and uncertainties used here.
  • Reader-Harris, M. (2015). Orifice Plates and Venturi Tubes. Springer. doi:10.1007/978-3-319-16880-7 — derivation and data behind the Reader-Harris/Gallagher equation.
  • Reader-Harris, M. J. and Sattary, J. A. (1990). "The orifice plate discharge coefficient equation." Flow Measurement and Instrumentation, 1(2), 67–76. doi:10.1016/0955-5986(90)90031-2
  • Miller, R. W. (1996). Flow Measurement Engineering Handbook, 3rd ed., McGraw-Hill — practical design and installation guidance.
  • GPSA Engineering Data Book, Section 3 (Measurement) — worked gas-orifice examples (one is a published SimuPipe validation case).

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Frequently Asked Questions

What is the beta ratio and why does it matter?
The beta ratio is the orifice bore diameter divided by the pipe internal diameter (d/D). It determines the restriction severity and affects the discharge coefficient. ISO 5167 is valid for beta ratios between 0.1 and 0.75. Higher beta ratios produce less pressure drop but lower differential pressure signals, making flow measurement less sensitive. Typical flow measurement plates use beta 0.3-0.7.
What is the discharge coefficient (Cd)?
The discharge coefficient accounts for the difference between actual flow and theoretical flow through the orifice. For a sharp-edged orifice plate, Cd is typically 0.59-0.65 depending on beta ratio, Reynolds number, and tap type. This calculator uses the ISO 5167 Reader-Harris/Gallagher (RHG) correlation to compute Cd accurately. Cd is not constant — it varies with flow rate through the Reynolds number dependency.
What are the different orifice tap types?
ISO 5167 defines three standard pressure tap locations: corner taps (at the orifice plate face), flange taps (1 inch from the plate on each side), and D-D/2 taps (one pipe diameter upstream, half a diameter downstream). Flange taps are most common in process industries. The tap location affects the measured differential pressure and the Cd calculation. All three are supported by this calculator.
Can I use an orifice plate for gas flow measurement?
Yes, orifice plates work for both liquids and gases. For gases, the expansibility factor (epsilon) accounts for the density change across the plate. This factor depends on the pressure ratio, beta ratio, and the gas's isentropic exponent (ratio of specific heats). This calculator automatically applies the expansibility correction when gas mode is selected.
What is the permanent pressure loss through an orifice plate?
The permanent pressure loss is always less than the measured differential because part of the pressure recovers downstream of the plate. ISO 5167-2 gives it as ω = ΔP·(√(1 − β⁴(1 − C²)) − C·β²)/(√(1 − β⁴(1 − C²)) + C·β²): at β = 0.5 about 73% of the differential is permanently lost (the worked example shows the exact figure); at β = 0.7 about half. This non-recovered loss is the energy cost of an orifice plate compared with a venturi tube, which recovers most of the differential.

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