What is Valve Cv (Flow Coefficient)?

The valve flow coefficient (Cv) is defined as the flow rate of water in US gallons per minute (GPM) at 60F that will pass through a valve with a pressure drop of 1 psi. It provides a standardized way to compare valve flow capacities regardless of valve size or type.

Cv = 1 means the valve will flow 1 GPM of water with a 1 psi pressure drop.

The metric equivalent is Kv, defined as the flow rate of water in cubic meters per hour (m3/h) at 16C with a 1 bar pressure drop. Conversion: Kv = Cv / 1.156

Liquid Flow Formula

For incompressible liquids (water, oil, glycol, etc.), the Cv is calculated using:

Cv = Q * sqrt(SG / dP)

• Q: Flow rate in GPM
• SG: Specific gravity (water = 1.0)
• dP: Pressure drop across valve in psi

Gas Flow Formula

For compressible gases, the flow equation depends on whether flow is choked (critical) or non-choked (subcritical):

Non-Choked (Subsonic) Flow:

Cv = Q * sqrt(Gg * T / (dP * (P1 + P2)))

Choked (Sonic) Flow: (when dP/P1 > 0.5 approximately)

Cv = Q * sqrt(Gg * T) / (0.667 * P1)

• Q: Flow rate in SCFH (Standard Cubic Feet per Hour)
• Gg: Gas specific gravity (air = 1.0)
• T: Absolute temperature in Rankine (F + 460)
• P1, P2: Inlet and outlet pressures in psia

Steam Flow Formula

For saturated steam flow, a simplified formula is used:

Cv = W / (2.1 * sqrt(dP * (P1 - dP/2)))

For superheated steam:

Cv = W * sqrt(1 + 0.00065 * (T_sh - T_sat)) / (2.1 * sqrt(dP * (P1 - dP/2)))

• W: Steam flow rate in lb/hr
• dP: Pressure drop in psi
• P1: Inlet pressure in psia

Choked Flow (Critical Flow)

Choked flow occurs when the fluid velocity at the vena contracta (narrowest point) reaches sonic velocity. Beyond this point, further reducing downstream pressure does not increase flow rate.

• For Gases: Occurs when pressure ratio P2/P1 drops below approximately 0.53 (varies with gas properties)
• For Liquids: Related to cavitation and flashing when downstream pressure approaches vapor pressure

The valve recovery factor (FL) determines when choked flow begins. Low FL values (e.g., 0.55 for butterfly) indicate higher recovery and earlier choking.

Valve Characteristic Curves

The inherent flow characteristic describes how flow changes with valve travel (% open):

• Linear: Flow is directly proportional to travel. Best for constant pressure drop systems.
• Equal Percentage: Equal increments of travel produce equal percentage changes in flow. Most common for control valves because it provides consistent gain.
• Quick Opening: Most flow change occurs near closed position. Used for on-off service or safety applications.

Cavitation and Flashing

Cavitation: Occurs when pressure drops below vapor pressure, forming bubbles that collapse when pressure recovers. Causes noise, vibration, and damage.

Flashing: When downstream pressure remains below vapor pressure, bubbles do not collapse. Flow becomes two-phase.

Cavitation index: sigma = (P1 - Pv) / dP. Lower sigma indicates higher cavitation risk.