# Flow coefficient

In other countries, use Kv (flow factor)

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 can be expressed as:

$C_v = F \sqrt{\dfrac{SG}{\Delta P}}$

where:
Cv = Flow coefficient or flow capacity rating of valve.
F = Rate of flow (US gallons per minute).
SG = Specific gravity of fluid (Water = 1).
ΔP = Pressure drop across valve (psi).

In more practical terms, the flow coefficient Cv is the volume (in US gallons) of water at 60°F that will flow per minute through a valve with a pressure drop of 1 psi 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 as follows:

Coefficient of discharge is the ratio of actual flow rate to theoretical discharge.

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 that 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).