Theflow coefficient of a device is a relative measure of its efficiency at allowingfluid flow. It describes the relationship between thepressure drop across anorifice valve or other assembly and the correspondingflow rate.

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

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

where,

Q is the rate of flow (expressed in US gallons per minute),

SG is thespecific gravity of the fluid (for water = 1),

ΔP is the pressure drop across the valve (expressed in psi).

In more practical terms, theflow coefficientC_v 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 thedischarge coefficient.

For gas flow in a pneumatic system theC_v 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). WithC_v = 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 theC_v 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 whenC_v = 1.0, 2 psia input).

The metric equivalentflow factor (K_v) is calculated using metric units:

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

where,^[3]

K_v is the flow factor (expressed in m³/h),

Q is the flowrate (expressed in m³/h),

SG is thespecific gravity of the fluid (for water = 1),

∆P is the differential pressure across the device (expressed in bar).

K_v can be calculated fromC_v using the equation^[4]

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

The k_v 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 k_v factor of a valve indicates "The water flow in m³/h, at a pressure drop across the valve of1 kgf/cm² when the valve is completely open.The complete definition also says that the flow medium must have a density of1000 kg/m³ and a kinematicviscosity of10⁻⁶ m²/s, e.g. water.^[clarify]

• Discharge coefficient

• Fluid dynamics

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