Flow Coefficient (Cv) Calculator

Accurate valve sizing for liquids and gases. Follows ISA‑75.01 / IEC 60534 standards for non‑choked flow.

Cv definition: Number of U.S. gallons per minute of 60 °F water that will flow through a valve with a 1 psi pressure drop.

Liquid
Gas (non‑choked)
GPM
—
psi
Water 50 GPM, 5 psi Oil SG=0.85, 15 psi Natural gas 5000 SCFH Air (choked example)
Calculating...

Understanding Flow Coefficient (Cv)

The flow coefficient Cv is a dimensionless number that represents the capacity of a valve or orifice to pass fluid. It is widely used in valve sizing and selection.

Official definition (ISA‑75.01 / IEC 60534):
Cv is the volume of water at 60 °F (in US gallons) that will flow per minute through a valve with a 1 psi pressure drop.

Liquid Sizing Formula

Cv = Q · √(SG / ΔP)

  • Q = flow rate (GPM)
  • SG = specific gravity (water = 1.0)
  • ΔP = pressure drop across valve (psi)

This formula assumes turbulent, non‑vaporizing liquid flow.

Gas Sizing Formula (Non‑choked, Subsonic)

Cv = Q / [ 1360 · √( ΔP · Pavg · SG / ((T+460)·Z) ) ]

  • Q = flow rate (SCFH – standard cubic feet per hour at 14.73 psia and 60 °F)
  • SG = specific gravity relative to air (air = 1.0)
  • ΔP = P1 – P2 (psi)
  • Pavg = (P1 + P2)/2 (psia)
  • T = flowing temperature (°F)
  • Z = compressibility factor (dimensionless, Z=1 for ideal gases)

Validity limit: ΔP / P1 ≤ 0.5. Beyond this, choked flow occurs and more complex equations (with expansion factor Y) are required.

Choked Flow Warning

When the pressure drop exceeds about half the inlet pressure, the gas velocity reaches sonic (choked) condition. The simplified formula above underestimates the required Cv. For accurate sizing under choked conditions, refer to ISA‑75.01.01 or use specialized software.

Cv and Kv – Metric Equivalent

In Europe, the metric flow coefficient Kv is used: Kv = Cv × 0.865. Kv represents the flow of water in m³/h with a pressure drop of 1 bar.

Typical Cv Values for Common Valves

Valve Type Size (in) Typical Cv Range
Ball valve (full port) 1" 30 – 60
Ball valve (full port) 2" 150 – 300
Globe valve (single port) 1" 10 – 25
Globe valve (single port) 2" 40 – 90
Butterfly valve 2" 50 – 120
Butterfly valve 4" 300 – 800

* Actual Cv depends on design; consult manufacturer data.

How to Use Cv in Valve Sizing

  1. Determine process conditions: flow rate, fluid properties, pressures, temperature.
  2. Calculate the required Cv using the appropriate formula.
  3. Select a valve with a published Cv equal to or greater than the calculated value.
  4. Verify that the selected valve is not oversized (to avoid poor control).

Standards & References

  • ISA‑75.01.01 / IEC 60534‑2‑1 – Industrial‑process control valves, flow capacity equations.
  • ANSI/ISA‑75.02 – Control valve capacity test procedures.

Calculator Validation: Tested against known examples:

  • Water 100 GPM, SG=1, ΔP=10 psi → Cv = 31.62 ✓
  • Air 1000 SCFH, SG=1, P1=100, P2=80 psia, T=60°F, Z=1 → Cv ≈ 0.395 ✓
  • Edge cases: zero/negative inputs produce error messages.

Frequently Asked Questions

Convert to the required units before entering: 1 GPM ≈ 0.2271 m³/h, 1 psi ≈ 0.06895 bar. For metric users, compute Kv = 0.865·Cv.

It is only valid for non‑choked, subsonic flow (ΔP/P₁ ≤ 0.5). For choked flow, use the full ISA equation with expansion factor Y. The calculator warns when ΔP/P₁ > 0.5.

Yes: for liquids, ΔP = SG × (Q / Cv)². For gases, the relation is iterative because P_avg depends on ΔP.

Z corrects for deviation from ideal gas behavior. At high pressures or low temperatures, gases are denser (Z<1) or less dense (Z>1), affecting the required Cv. For most valve sizing, Z can be obtained from gas properties tables.