อัปเดต 2026-09-07

Gas Control Valve Cv/Kv

ANSI/ISA-75.01.01-2012 (IEC 60534-2-1), compressible flow

Required Cv/Kv for a gas or vapor control valve from the ISA-75.01.01 §6 compressible mass-flow equation, including the expansion factor Y, the specific-heat-ratio factor Fγ, and choked (sonic) flow detection.

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The mass equation is solved directly (closed form, no iteration) for Cv. Once the pressure-drop ratio x reaches the choke boundary Fγ·xT, x is clamped and Y is set to its analytic choked limit (0.667) per §6.3.

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Pressure-drop ratio & choke boundary

x = \frac{p _{1} - p _{2}}{p _{1}}, F_{γ} = \frac{γ}{1.40}, x_{c h o k e d} = F_{γ} x_{T}

γ=Cp/Cv (specific-heat ratio); xT = ISA-75.05 critical-flow factor for the valve trim (preset by valve type). Flow is sonic at the vena contracta once x ≥ x_choked (ISA-75.01.01 §6.3).

Expansion factor Y

Y = 1 - \frac{x}{3 F _{γ} x _{T}} (x < x_{c h o k e d}), Y = 0.667 (choked)

The analytic limit of the Y formula at x=x_choked is 1−1/3=0.667, matching the ISA-prescribed choked value exactly (no discontinuity at the clamp).

Compressible mass-flow Cv equation

W = N_{6} F_{p} C_{v} Y x p_{1} ρ_{1}, ρ_{1} = \frac{p _{1} M W}{Z R ˉ T}

N6=27.3 with W in kg/h, p1 in kPa, ρ1 in kg/m³ (ISA-75.01.01 Table 1 unit set); Fp = piping-geometry factor (reducers). Solved directly for Cv; Kv=0.865·Cv (IEC 60534-2-1). Validation anchor (self-derived, no copyrighted numbers): air, W=1 kg/s, p1=1000 kPa, p2=700 kPa, T=320 K, xT=0.72, Fp=1.0 → x=0.300, Fγ=1.000, Y=0.8611, Cv=2.68, Kv=2.32 (exact hand-derivation match).

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