# Flow coefficient

The flow coefficient of a device is a relative measure of its efficiency at allowing fluid flow. It describes the relationship between the pressure drop across an orifice valve or other assembly and the corresponding flow rate.

Mathematically the flow coefficient Cv (or flow-capacity rating of valve) can be expressed as

${\displaystyle C_{\text{v}}=Q{\sqrt {\frac {\text{SG}}{\Delta P}}},}$

where

Q is the rate of flow (expressed in US gallons per minute),
SG is the specific gravity of the fluid (for water = 1),
ΔP is the pressure drop across the valve (expressed in psi).

In more practical terms, the flow coefficient Cv is the volume (in US gallons) of water at 60 °F (16 °C) that will flow per minute through a valve with a pressure drop of 1 psi (6.9 kPa) across the valve.

The use of the flow coefficient offers a standard method of comparing valve capacities and sizing valves for specific applications that is widely accepted by industry. The general definition of the flow coefficient can be expanded into equations modeling the flow of liquids, gases and steam using the discharge coefficient.

For gas flow in a pneumatic system the Cv for the same assembly can be used with a more complex equation.[1][2] Absolute pressures (psia) must be used for gas rather than simply differential pressure.

For air flow at room temperature, when the outlet pressure is less than 1/2 the absolute inlet pressure, the flow becomes quite simple (although it reaches sonic velocity internally). With Cv = 1.0 and 200 psia inlet pressure, the flow is 100 standard cubic feet per minute (scfm). The flow is proportional to the absolute inlet pressure, so the flow in scfm would equal the Cv flow coefficient if the inlet pressure were reduced to 2 psia and the outlet were connected to a vacuum with less than 1 psi absolute pressure (1.0 scfm when Cv = 1.0, 2 psia input).

## Flow factor

The metric equivalent flow factor (Kv) is calculated using metric units:

${\displaystyle K_{\text{v}}=Q{\sqrt {\frac {\text{SG}}{\Delta P}}},}$

where[3]

Kv is the flow factor (expressed in m3/h),
Q is the flowrate (expressed in m3/h),
SG is the specific gravity of the fluid (for water = 1),
P is the differential pressure across the device (expressed in bar).

Kv can be calculated from Cv using the equation[4]

${\displaystyle C_{\text{v}}=1.156\cdot K_{\text{v}}.}$

The kv factor or value as it is also called is defined in VDI/VDE Richtlinien No. 2173.[5] A simplified version of the definition is: The kv factor of a valve indicates "The water flow in m3/h, at a pressure drop across the valve of 1 kgf/cm2 when the valve is completely open. The complete definition also says that the flow medium must have a density of 1000 kg/m3 and a kinematic viscosity of 10−6 m2/s, e.g. water.[clarify]

## References

1. ^ "Valve Sizing" (PDF). Technical Bulletin. Swagelok. Retrieved 21 April 2020.
2. ^ "Cv Calculator". Generant. Retrieved 21 April 2020.
3. ^ Boysen, Herman. "kV: what, why, how, whence?" (PDF). Technical paper. Danfoss. Retrieved 21 April 2020.
4. ^ "Control Valve Sizing". Control Valve Handbook (PDF) (5th ed.). Emerson Electric. September 2019. Retrieved 26 February 2022.
5. ^ Strömungstechnische Kenngrößen von Stellventilen und deren Bestimmung [Fluidic characteristic quantities of control valves and their determination] (PDF) (Standard). VDI, VDE. September 2007. 2173. Retrieved 17 April 2020.