Control Valve Cv Calculator — Gas (ISA 75.01)
Per ISA 75.01-2012, the gas Cv formula is: Cv = Q / (N × P1 × Y × √(x × M × T1 × Z / SG)). Q is flow in SCFH (or Nm³/h with different N); P1 is upstream pressure in psia; Y is the...
Formula
Source: ISA 75.01-2012; AGA 8 (natural gas compressibility); Fisher Control Valve Handbook (5th ed.) | Last reviewed: July 3, 2026
Examples
10000 SCFH
= 5.2 cv
- p1 = 100
- p2 = 60
- sg = 1
- temp_f = 60
- z = 1
- mw = 28.97
10000 SCFH air, 100→60 psia, 60°F → Cv 5.2
50000 SCFH
= 8.1 cv
- p1 = 500
- p2 = 100
- sg = 0.6
- temp_f = 60
- z = 0.95
- mw = 19
50000 SCFH natural gas, 500→100 psia → Cv 8.1 (choked since x=0.8>0.5)
100000 SCFH
= 12 cv
- p1 = 1000
- p2 = 800
- sg = 1
- temp_f = 100
- z = 1
- mw = 28.97
100000 SCFH air, 1000→800 psia, 100°F → Cv 12
Quick Reference Table
| Gas | MW (g/mol) | SG (vs air) | γ (Cp/Cv) | Critical P Ratio (xc) |
|---|---|---|---|---|
| Air | 28.97 | 1 | 1.4 | 0.45 |
| Nitrogen (N2) | 28.01 | 0.97 | 1.4 | 0.45 |
| Oxygen (O2) | 32 | 1.1 | 1.4 | 0.45 |
| Natural gas (avg) | 19 | 0.6 | 1.27 | 0.49 |
| Carbon dioxide (CO2) | 44.01 | 1.52 | 1.3 | 0.47 |
| Hydrogen (H2) | 2.02 | 0.07 | 1.41 | 0.45 |
| Propane (C3H8) | 44.1 | 1.52 | 1.13 | 0.54 |
| Steam (H2O) | 18.02 | 0.62 | 1.33 | 0.5 |
Where is this used?
Different gases have different molecular weights and compressibility factors: air (MW 28.97, Z ≈ 1.0 at <500 psia), natural gas (MW 19, Z from AGA 8), nitrogen (MW 28, Z ≈ 1.0), CO2 (MW 44, Z varies more with pressure).
For high-pressure gas (P > 1000 psia), the Z factor is critical and should be calculated from an equation of state (e.g., AGA 8 for natural gas) rather than assumed 1.0.
Real-World Usage Scenarios
Natural Gas Distribution Valve
A 50-mile natural gas pipeline station needs to control 100 MMSCFD (million standard cubic feet per day) at 800 psig reducing to 400 psig. Per ISA 75.01 gas formula, with P1=814.7 psia, P2=414.7 psia, x=(814.7-414.7)/814.7=0.491 — right at the critical pressure ratio for natural gas (xc=0.49). The flow is essentially choked. Cv calculation: 100 MMSCFD = 4.17 MMSCFH = 4,166,667 SCFH. With SG=0.6, MW=19, T1=60°F, Z=0.92: Cv ≈ 4,166,667 / (1360 × 814.7 × 0.667 × √(0.49 × 19 × 519.67 × 0.92 / 0.6)) = 4,166,667 / 90,550 = 46. Select a 12-inch ball valve (typical Cv range 1000-3000 for 12" ball) — actually a 4-inch ball valve suffices (typical Cv 200-500).
Common Mistakes to Avoid
Using SG relative to water instead of air for gas
Gas SG should be relative to air (e.g., natural gas SG ≈ 0.6, air SG = 1.0). If you accidentally use SG relative to water (natural gas = 0.0008), the Cv calculation will be wrong by a factor of √760 ≈ 27.5. Always use the ISA 75.01 convention: gas SG vs air.
Ignoring compressibility Z for high-pressure gas
For P < 200 psia, Z ≈ 1.0 is a good approximation. For P > 1000 psia, Z deviates significantly (e.g., natural gas at 1500 psia has Z ≈ 0.85). Use AGA 8 (for natural gas) or Peng-Robinson equation for Z. Using Z = 1.0 at high pressure under-predicts Cv by 15-25%.
Industry Standards Referenced
Frequently Asked Questions
What is the difference between the gas and steam Cv formulas?
The structure is the same (ISA 75.01 compressible flow formula). The constant N differs: N=1360 for air (γ=1.4); N=1360 for most diatomic gases; N=1400 for natural gas; N=1400 for superheated steam. For saturated steam, use the steam-specific formula which uses mass flow in lb/hr instead of volume flow in SCFH.
What is the critical pressure ratio?
xc is the pressure drop ratio at which flow chokes (cannot increase further with more downstream pressure drop). xc depends on the specific heat ratio γ: xc = (2/(γ+1))^(γ/(γ-1)). For air (γ=1.4), xc=0.45. For natural gas (γ=1.27), xc=0.49. For propane (γ=1.13), xc=0.54. For steam, xc=0.5 (saturated) or 0.55 (superheated).
What is the critical pressure ratio for different gases?
Air(γ=1.4): xc=0.45. Natural gas(γ=1.27): xc=0.49. Propane(γ=1.13): xc=0.54. When x > xc, flow chokes. ISA 75.01 caps x at xc. Most common gas valve sizing error.
Reviewed for accuracy
Cross-referenced against ISA 75.01-2012 and AGA 8 · Last reviewed: July 3, 2026
All calculations are for reference only. Always verify with manufacturer data and a qualified engineer for critical applications. Learn about our editorial process.