Abstract: The flow capacity coefficient (Cv) is the central parameter in control-valve sizing. For liquid service a de-facto universal FCI equation exists, whereas gas-service equations differ among vendors, and the magnitude and origin of the discrepancy have rarely been quantified. This paper reports a cross-validation between our online Cv calculator and the official Swagelok Cv calculator over six liquid/gas duties covering subcritical and critical flow. The three liquid cases agree to within display rounding; for the three gas cases our results run systematically 11.5%–29.6% lower, with the deviation increasing as the pressure ratio rises. Back-derivation from the Swagelok results shows its subcritical gas constant to be K ≈ 262.5–263.3 (Q: std m³/h, P: bar abs) against our 287 (Q: Nm³/h, P: kgf/cm²); after unit alignment the ratio 1.115 accounts exactly for the measured 11.5%. The critical-flow constants differ further (≈196 vs 254 in bar basis), and the differing subcritical-to-critical constant ratios (≈1.34 vs ≈1.15) indicate a structural difference in choke treatment. The root causes are traced to the standard-flow reference basis, unit-system calibration and the critical-flow model. In engineering practice the gas Cv formula system must be paired with the valve vendor's own Cv tables; cross-system mixing introduces a systematic 10%–30% bias.
Keywords: control valve; flow capacity; flow coefficient; Cv; critical flow; formula comparison; cross-validation
The flow capacity coefficient Cv provides a unified characterization of control-valve capacity and is the central input of valve sizing. For liquid service, the FCI standard equation has become a de-facto universal expression, allowing results from different vendors to be inter-checked exactly after unit conversion. For gas service, compressibility, pressure ratio and the reference basis of standard flow preclude an equally unified formula: vendors publish and use their own gas equations whose constants and applicability conditions differ [1,2].
Although the vendor-to-vendor divergence of gas equations is known in the industry, its quantified magnitude, its evolution with operating conditions and its root causes are rarely documented in open literature. This paper fills that gap with a controlled comparison: our online Cv calculator [3] — which adopts the FCI metric gas form customary in the Chinese industry — and the official Swagelok Cv calculator [4], representing a US vendor's proprietary gas-sizing system, were evaluated on six identical duties, and the measured deviations were attributed at the formula level.
Two publicly available online calculators were compared: (1) the official Swagelok Cv calculator (swagelok.com.cn Chinese site, tested on 2026-10-13), representing the US vendor gas-sizing system; (2) our control-valve Cv calculator (actuators.cn/cv), using the FCI metric form with constants from customary Chinese sizing references. Both are interactive forms; the computation is deterministic and reproducible for identical inputs.
Three principles governed the case design: (1) identical inputs — media present in both tools (water, kerosene, air, nitrogen; specific gravities identical in both libraries), units present in both tools (m³/h-class flow, bar absolute, degrees Celsius); (2) coverage of liquid and gas, subcritical and critical regimes; (3) parameter magnitudes typical of engineering practice. The six cases are listed in Table 1; specific gravities were G = 1.0 (water, air), 0.815 (kerosene), 0.967 (nitrogen), and the temperature was 20 °C throughout.
Note that the Swagelok site states "gas pressure units are absolute, except PSIG"; gas pressures were therefore entered in bar absolute on both sides, consistent with our absolute-pressure basis.
The Cv values from both calculators for the six duties are given in Table 1. Figure 1 shows the L1 case on our calculator.
Table 1 Measured results of the cross-validation
| No. | Fluid | Flow | P₁/P₂ (bar abs) | Regime | Swagelok Cv | Ours Cv | Ours lower by |
|---|---|---|---|---|---|---|---|
| L1 | Water | 2.0 m³/h | 6 / 4.5 | Liquid | 1.887 | 1.88719 | ≈0 |
| L2 | Water | 0.5 m³/h | 4 / 2 | Liquid | 0.409 | 0.40859 | ≈0 |
| L3 | Kerosene | 1.2 m³/h | 5 / 4 | Liquid | 1.252 | 1.25196 | ≈0 |
| G1 | Air | 30 Nm³/h | 6 / 4.5 | Subcritical | 0.493 | 0.44213 | 11.5% |
| G2 | Nitrogen | 50 Nm³/h | 8 / 5 | Subcritical | 0.55 | 0.46049 | 19.4%* |
| G3 | Air | 30 Nm³/h | 10 / 3 | Critical | 0.262 | 0.20224 | 29.6% |
Note: G2 is displayed by Swagelok with two decimals only; the true deviation lies within 19%–21%. The liquid deviations fall inside Swagelok's display rounding and are judged as agreement.
Fig. 1 Case L1 on our calculator (water 2.0 m³/h at 6/4.5 bar): C = 1.61713, Cv = 1.88719, matching Swagelok's displayed 1.887
Both calculators implement the FCI liquid equation:
Cv = Q·√(G/ΔP) (1)
Swagelok evaluates it with Q in gpm and ΔP in psi; we evaluate with Q in m³/h and ΔP in kgf/cm² and report Cv = 1.167·C. A unit-closure check gives 1 m³/h = 4.40287 gpm and 1 bar = 14.5038 psi, so the gpm/√psi coefficient is 4.40287/√14.5038 = 1.1557 — within 1% of 1.167 (rounding in the gpm definition); the two unit systems express the same physical relation. The liquid agreement is therefore expected, and the digit-for-digit match simultaneously verifies the correctness of our unit-conversion chain.
Our subcritical gas equation is:
Cv = (Q/287)·√( G·T / (ΔP·(P₁+P₂)) ) (2)
with Q in Nm³/h (0 °C basis), T in K, and P in kgf/cm² abs. Assuming Swagelok uses the same structure,
Cv = (Q/K)·√( G·T / (ΔP·(P₁+P₂)) ) (3)
with Q in std m³/h and P in bar abs, K can be back-derived from the two measured subcritical results. For G1: K = 30×√(293.15/15.75)/0.493 = 262.5. For G2: K = 50×√(283.48/39)/0.55 = 263.3. The two independent derivations agree within 0.3% (inside Swagelok's display rounding), establishing Swagelok's subcritical constant as K ≈ 262.5–263.3.
Our constant 287 converts to ≈292.7 in the bar basis (287×1.0197, since pressure enters the radical linearly in the squared term). The ratio 292.7/262.5 = 1.115 corresponds exactly to the measured 11.5% deviation of G1 — the entire subcritical deviation is explained by the constant, with no structural divergence.
Our critical equation is:
Cv = Q·√(G·T) / (249·P₁) (4)
with the transition at ΔP = P₁/2. For G3 (ΔP/P₁ = 0.7, within the critical region) Swagelok gives 0.262 versus our 0.202. Back-derivation yields Swagelok's critical constant K = 30×√(293.15)/0.262/10 = 196.0 in the bar basis (our 249 kgf/cm² ≡ 253.9), a ratio of 1.295, matching the measurement. Significantly, the subcritical-to-critical constant ratio differs between the two systems: Swagelok 262.5/196.0 ≈ 1.34 versus ours 287/249 ≈ 1.15. The mismatch means the critical-flow deviation cannot be explained as a simple scaling of the subcritical constant — the choke criterion and the critical expression themselves differ structurally. The exact critical constants are published in Swagelok's valve-sizing technical bulletin [2].
Combining the derivations above, the gas-formula differences stem from three causes:
(1) Different standard-flow references. Our flow basis is 0 °C / 101.325 kPa (Nm³, the Chinese industry convention); Swagelok's "std" flow follows the US convention of 60 °F / 14.7 psia. The same numeric standard volume represents different actual gas quantities, and each constant is calibrated against its own reference. (2) Different unit-system calibrations. Our constants 287/249 are calibrated in the kgf/cm² basis and Swagelok's 262.5/196 in the bar/psi basis; the calibrations embed unit-specific empirical corrections and do not close by simple conversion. (3) Different critical-flow models, as evidenced by the differing subcritical/critical constant ratios (Section 3.3).
(1) No single cross-vendor gas Cv formula exists. A vendor's gas equation is calibrated consistently with its own valve Cv tables; sizing calculations should pair the formula system with the Cv table of the same system — Swagelok's equation with Swagelok tables, or the metric equation with Chinese valve tables. (2) Cross-system mixing introduces the systematic 10%–30% bias measured here, growing with the pressure ratio and thus most consequential in high-differential and critical-flow service. (3) Regarding direction of bias: our metric equation yields the smaller Cv for identical duties — the conservative side; selecting a Swagelok valve directly on our result would leave flow-capacity margin.
(1) For liquid service, the two calculators — two unit-system implementations of the FCI equation — agree on all three duties within display rounding; liquid Cv calculation is cross-vendor verifiable.
(2) For subcritical gas service, the two equations share the same structure; the measured 11.5%–19.4% deviations are fully explained by the constant difference: Swagelok K = 262.5–263.3 (std m³/h, bar abs) versus our 287 (Nm³/h, kgf/cm²), unit-aligned ratio 1.115.
(3) For critical gas service, the measured deviation is 29.6%, exceeding what the subcritical constant ratio could explain; the differing subcritical/critical constant ratios (1.34 vs 1.15) reveal a structural difference in choke treatment.
(4) In engineering practice, the gas Cv formula system must be paired with the valve vendor's own Cv tables; cross-system mixing is prohibited. Our metric results run systematically small — the conservative side.
[1] IEC 60534-2-1, Control valve equations for fluid flow under installed conditions[S]. International Electrotechnical Commission. (corresponding to ANSI/ISA-75.01.01)
[2] Swagelok Company. Valve Sizing Technical Bulletin (MS-06-74)[Z]. Swagelok Company, Solon, Ohio.
[3] Swagelok. Cv calculator[EB/OL]. https://www.swagelok.com.cn/zh/resources/cv-calculator, accessed 2026-10-13.
[4] Shandong Juxi Mechanical & Electrical Equipment Co., Ltd. Control Valve Cv Calculator[EB/OL]. https://www.actuators.cn/cv/, accessed 2026-10-13.
Note: This is a tool cross-validation report; data were collected on 2026-10-13, with Swagelok values recorded as displayed. Our calculation tool is available at actuators.cn/cv.
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