Determination of Valve Coefficients

What is Valve Coefficient (Cv)

Cv = Flow coefficient of a valve.
It indicates how many US gallons per minute (GPM) of water at 60°F will flow through the valve with a pressure drop of 1 psi.

Higher Cv → higher flow capacity of the valve.

Basic Formula for Cv

For Liquids (In-compressible Flow)

Where:

• Q = flow rate (GPM)
• SG = specific gravity (water = 1)
• ΔP = pressure drop across valve (psi)

For Gases (Compressible Flow)

Gas equations depend on the flow regime.

(a) Subcritical Flow (Non-Choked)

(b) Critical Flow (Choked Flow)

Where:

• Q = SCFH (standard cubic feet/hour)
• G = specific gravity of gas
• T = temperature (°R)
• P₁ = upstream pressure (psia)
• ΔP = pressure drop (psia)

How to Determine Cv (Practical Testing)

Valve manufacturers determine Cv using standard test methods:

Test Setup

1. Flow water through the valve from tank or pump
2. Measure:
   • Upstream pressure
   • Downstream pressure
   • Flow rate
   • Temperature
3. Adjust flow until ΔP = 1 psi
4. Record the flow rate → This flow (GPM) is the Cv

Cv from Valve Opening Position

Many control valves provide Cv vs % opening curve.

Typical relation for different plug types:

Plug Type	% Opening vs Cv Relation
Linear	Cv proportional to stroke
Equal %	Cv increases exponentially
Quick Opening	Cv jumps high at low opening

How to Calculate Cv from CFD

CFD gives accurate valve Cv.

Steps for CFD-based Cv Calculation

1. Model the valve geometry
2. Mesh with fine boundary layer refinement
3. Set fluid (water, 60°F or relevant fluid)
4. Set inlet–outlet boundary condition values
5. Run several simulations at different flow rates
6. Measure:
   • Flow rate (Q)
   • Pressure drop (ΔP)

Then compute:

C_v = Q *sqrt(SG/Delta P)

CFD can also generate Cv vs % opening curves.

Example Calculation

Flow through valve:

• Q = 50 GPM
• ΔP = 4 psi
• SG = 1.0

C_v = 50 *sqrt(1/4) = 50 * 0.5 = 25

Valve Cv = 25

Typical Cv Values

Valve Size	Typical Cv
½ inch	4–10
1 inch	12–25
2 inch	40–100
4 inch	120–350
6 inch	300–800