### FLOW COEFFICIENT (Cv) - Formulas for Liquids, Steam and Gases

The flow coefficient ( CV ) - is important for proper design of control valves, which provides flow comparison of different sizes and types of valve of different manufacturer’s. Cv is generally determined experimentally and express the flow capacity - GPM (gallons per minute) of water that a valve will pass for a pressure drop of 1 lb/in2 (psi). The flow factor (Kv) - is also in common use, but express the capacity in SI-units.

Specific formulas used to estimate Cv for different fluids is indicated below:

Flow Coefficient - Cv - for Liquids

For liquids the flow coefficient - CV - expresses the flow capacity in gallons per minute (GPM) of 600F water with a pressure drop of 1 psi (lb/in2).

**Flow expressed by volume**

C = Q x (SG / ▲p)1/2

Where

• Q = water flow (US gallons per minute)

• SG = specific gravity (1 for water)

• ▲p = pressure drop (psia)

**Flow is expressed by weight**

CV = w / (500 x (▲p x SG)1/2 )

Where

• w = water flow (lb/h)

• SG = specific gravity (1 for water)

• ▲p = pressure drop (psia)

F

**low Coefficient - Cv - for Saturated Steam**

Since steam and gases are compressible fluids, the formula must be altered to accommodate changes in the density.

**Critical (Choked) Pressure Drop**

At choked flow the critical pressure drop the outlet pres sure - p0 - from the control valve is less than 58% of the inlet pressure - pi . The flow coefficient can be expressed as:

CV = m / 1.61 pi

Where

• m = steam flow (lb/h)

• pi = inlet s team absolute pressure (psia)

• po = outlet steam absolute pressure (psia)

**Non Critical Pressure Drop**

For non critical pressure drop the outlet pressure - po - from the control valve is greater than 58% of the inlet pressure - pI . The flow coefficient can be expressed as:

Cv = m /3.2 ((pI - po) x po)1/2

**Flow Coefficient - Cv- for Air and other Gases**

For critical pressure drop the outlet pressure - po - from the control valve is less than 53% of the inlet pressure - pI . The flow coefficient can be expressed as:

Cv = Q x [SG (T + 460)]1/2 / 660pI

Where

• Q = free gas per hour, standard cubic feet per hour (Cu-foot/h)

• SG = specific gravity of flowing gas gas relative to air at 14.7 psia and 600F

• T = flowing air or gas temperature (°F)

• pI = inlet gas absolute press ure (psia)

For non critical pressure drop the outlet pressure - po - from the control valve is greater than 53% of the inlet pressure - pI . The flow coefficient can be expressed as:

CV = Q x [SG (T + 460)]1/2 / [1360 (▲p x pO ) ]1/2

Where

• ▲p = (pI - pO )

• pO = outlet gas absolute pressure (psia)