ISO 5167 / ASME MFC-3M Intermediate Flow Measurement & Metering

Differential Pressure Orifice Plate Flowmeter

Calculate volumetric flow through concentric thin-plate square-edge orifices and tap dP.

Solves Bernoulli continuity through orifice restrictions with discharge coefficient Cd calibration. Demonstrates dP square-root extraction, vena contracta expansion, and Reynolds number influences.

Governing Physical Law & Equations

q_m = \frac{C_d}{\sqrt{1 - \beta^4}} \epsilon \frac{\pi}{4} d^2 \sqrt{2 \rho \Delta P}, \quad \beta = \frac{d}{D}

ISO 5167 mass flow equation with beta ratio and discharge coefficient.

Law: Bernoulli Conservation of Fluid Energy & Continuity | Standard Reference: ISO 5167-2:2003 / ASME MFC-3M / AGA Report No. 3 (Measurement of Fluid Flow by Orifice Plates)

Adjustable System Parameters

Parameter	Nominal Value	Dynamic Range	Physical Role
Orifice Bore Diameter d (d)	60 mm	30 to 80 mm	Internal throat restriction diameter (pipe is 100mm)
Volumetric Flow Rate (Q)	45 m³/h	5 to 80 m³/h	Actual fluid flow rate through pipeline
Fluid Density ρ (ρ)	1000 kg/m³	700 to 1100 kg/m³	Density of flowing medium (water = 1000 kg/m³)
Process Temperature (T)	25 °C	10 to 90 °C	Operating temperature of process fluid

Analytical Proof & Derivation

Applying Bernoulli’s equation and continuity for incompressible fluid through pipe diameter D and orifice bore diameter d: p₁/ρ + v₁²/2 = p₂/ρ + v₂²/2. Continuity requires v₁ (π D²/4) = v₂ (π d²/4), giving v₁ = β² v₂ where β = d/D. Solving for theoretical flow and introducing discharge coefficient C_d to account for boundary layer friction and vena contracta contraction gives mass flow rate: q_m = [C_d / √(1 - β⁴)] ε (π d²/4) √(2 ρ ΔP). For liquid flows, expansibility factor ε = 1.000.

Verification Benchmark

ISO 5167 benchmark: D = 100 mm, d = 60 mm (β = 0.60), water density ρ = 1000 kg/m³, Q = 45 m³/h (12.5 kg/s). Stolz equation C_d = 0.605. Measured differential pressure ΔP = 186.4 mbar; permanent pressure loss ΔP_loss = ΔP (1 - β^1.9) = 186.4 × (1 - 0.378) = 115.9 mbar, matching ISO 5167 calibration data.

Field Engineering Insights

ISO 5167 enforces strict installation requirements: beta ratio must lie between 0.10 ≤ β ≤ 0.75 (optimal 0.20 to 0.70). Upstream straight pipe run must be at least 20D to 44D (or equipped with a 19-tube bundle flow conditioner) to eliminate swirl before the orifice plate.