How does an orifice plate flow meter work?

An orifice plate creates a constriction in the pipe. The fluid speeds up through the orifice, causing a pressure drop (ΔP). Flow rate is proportional to √(ΔP), calculated using Q=C×ε×A×√(2ΔP/ρ) per ISO 5167.

What is the beta ratio?

Beta (β) = d/D, the ratio of orifice bore diameter to pipe internal diameter. Typical range: 0.2 to 0.75. Higher beta = less pressure loss but lower accuracy.

What is the discharge coefficient C?

The discharge coefficient accounts for real fluid effects (vena contracta, friction). For ISO 5167 corner taps, C is calculated from the Reader-Harris/Gallagher equation and is typically 0.59–0.62 for β = 0.3–0.7.

What is the expansibility factor ε?

ε (epsilon) accounts for gas compressibility. For liquids, ε = 1. For gases, ε < 1 and depends on the pressure ratio and the isentropic exponent (κ). ε ≈ 1 for small ΔP/P ratios.

What are the ISO 5167 requirements for straight pipe?

ISO 5167 requires minimum straight pipe upstream (typically 10–44 D depending on fitting type and β) and 4–8 D downstream. Flow conditioners can reduce upstream requirements.

Free Engineering Tool — #152

Orifice Plate Flow Calculator — ISO 5167

Calculate flow rate through an orifice plate per ISO 5167. Enter orifice and pipe diameters, differential pressure, and fluid density.

ISO 5167Q = C·ε·A·√(2ΔP/ρ)Liquids & Gases

Results

Volume Flow Rate

—

Mass Flow Rate

—

Beta Ratio (β = d/D)

—

Discharge Coefficient C

—

Orifice Velocity

—

Pipe Velocity

—

ISO 5167 Orifice Flow Equation

C — discharge coefficient (Reader-Harris/Gallagher equation)
ε — expansibility factor (1.0 for incompressible liquids)
β — diameter ratio d/D
ΔP — differential pressure across orifice
ρ — upstream fluid density

Simplified Discharge Coefficient

For corner taps, C ≈ 0.5959 + 0.0312β² − 0.184β⁸ (simplified Reader-Harris). For flange taps, add correction terms for pipe diameter.

⚠️ Note: This calculator uses a simplified C estimation. For custody transfer metering, use the full Reader-Harris/Gallagher equation with Reynolds number correction per ISO 5167-2.

Orifice Plate Flow Calculator ISO 5167 | Free Online Tool

Published by Nikolai Shelkovenko on February 15, 2026 February 15, 2026

Results

ISO 5167 Orifice Flow Equation

Simplified Discharge Coefficient