อัปเดต 2026-09-07

Orifice / Nozzle / Venturi Meter

ISO 5167-1..4:2022

Sizes and rates differential-pressure primary flow elements (orifice plates, ISA-1932/long-radius nozzles, Venturi tubes) from geometry, fluid state, and measured ΔP.

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Fixed-point iteration couples the discharge coefficient C to the pipe Reynolds number Re_D (C seeded at the device's high-Re asymptote, 50/50-relaxed to convergence in ~3–5 steps); expansibility ε is evaluated once per solve for gas service. Inverse sizing bisects β against a target mass flow. ISO 5167-1 §8 RSS uncertainty is combined from C, ε, β, ΔP, and ρ sensitivities.

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Master flow equation (ISO 5167-1 Eq 5.1)

q_{m} = \frac{C ε}{1 - β ^{4}} \cdot \frac{π}{4} d^{2} 2 Δ P ρ_{1}

Mass flow through the primary element; β = d/D diameter ratio, C the discharge coefficient, ε the expansibility factor (≡1 for liquids).

Discharge coefficient (Reader–Harris/Gallagher, 8-term)

C = 0.5961 + 0.0261 β^{2} - 0.216 β^{8} + 0.000521 (\frac{1 0 ^{6} β}{R e _{D}})^{0.7} + (0.0188 + 0.0063 A) β^{3.5} (\frac{1 0 ^{6}}{R e _{D}})^{0.3} + (0.043 + 0.080 e^{- 10 L_{1}} - 0.123 e^{- 7 L_{1}}) (1 - 0.11 A) \frac{β ^{4}}{1 - β ^{4}} - 0.031 (M_{2}^{'} - 0.8 M_{2}^{'}^{1.1}) β^{1.3}

ISO 5167-2:2022 §5.3.2 orifice-plate C; A=(19000β/Re_D)^0.8, L₁/L₂' encode tap position (flange taps: L₁ = 25.4/D_mm).

Expansibility factor ε (gas, orifice)

ε = 1 - (0.351 + 0.256 β^{4} + 0.93 β^{8}) (1 - τ^{1/ κ})

τ = p₂/p₁, κ = Cp/Cv. ISO 5167-2 §5.4 Eq 9; nozzles/Venturis use a different closed-form expression.

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