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 C_v (or flow capacity rating of valve) can be expressed as:

${\displaystyle C_{v}=Q{\sqrt {\dfrac {SG}{\Delta P}}}}$

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 C_v 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 C_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). With C_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 that the flow in scfm would equal the C_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 when C_v = 1.0, 2 psia input).

Flow factor

The metric equivalent flow factor (K_v; commonly used in Europe and Asia) is calculated similarly, but the rate of flow is expressed in units of cubic meters per hour, and the pressure in bar. K_v can be calculated from C_v using the equation ^[3]

${K_{v}}=(0.865)({C_{v}})$

It can also be obtained directly in metric: The k_v factor or value as it is also called is defined in VDI/VDE Richtlinien No. 2173. 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 of 1 kg /cm² when the valve is completely open. The complete definition also says that the flow medium must have a specific gravity of 1000 kg /m³ and a kinematic viscosity of 10−6 m²/s. e.g. water

${\displaystyle {K_{v}}={\dfrac {Q}{\sqrt {\Delta P}}}}$

where:^[4]

• Kv is the flow factor in ${\displaystyle {{m^{3} \over hr} \over {\sqrt {1bar}}}={m^{\left({\frac {7}{2}}\right)} \over {\sqrt {kg}}}}$ in case of water
• Q is the flowrate (expressed in cubic metres per hour);
• ∆p is the differential pressure across the device (expressed in bar).

References

1. Swagelok C_v Flow Coefficient "Swagelok CV Flow Coefficient"
2. "Generant C_v Calculator"
3. Control Valve Handbook Search Chapter 5.
4. http://heating.danfoss.com/PCMPDF/VFHBG202_kv.pdf

External links

• Online-Calculation of pressure drop with flow coefficient