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Flow Coefficient - Cv - Formulas for Liquids, Steam and Gases - Online Calculators
The flow coefficient - Cv - is important for proper design of control valves
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The flow coefficient - Cv - let us compare flow capacities of valves at different sizes, types and manufacturers. The flow coefficient is in general determined experimentally and express the flow capacity in imperial units - GPM (US 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.
The flow coefficient - Cv - required for a specific application can be estimated by using specific formulas for the different fluids or gases. With the estimated Cv value - the correct valve can be selected from the manufacturers catalogues.
Flow Coefficient - Cv - for Liquids
For liquids the flow coefficient - Cv - expresses the flow capacity in gallons per minute (GPM) of 60oF water with a pressure drop of 1 psi (lb/in2).
Flow expressed by volume
Cv = q (SG / dp)1/2 (1)
where
q = water flow (US gallons per minute)
SG = specific gravity (1 for water)
dp = pressure drop (psi)
or alternatively in SI units:
Cv = 11.6 q (SG / dp)1/2 (1b)
where
q = water flow (m3/h)
SG = specific gravity (1 for water)
dp = pressure drop (kPa)
Flow is expressed by weight
Cv = w / (500 (dp SG)1/2) (1c)
where
w = water flow (lb/h)
SG = specific gravity (1 for water)
dp = pressure drop (psia)
or alternatively in SI units:
Cv = 5.8 w / (500 (dp SG)1/2) (1d)
where
w = water flow (kg/h)
SG = specific gravity (1 for water)
dp = pressure drop (kPa)
Example - Flow Coefficient Liquid
The flow coefficient of a control valve which in the full open position passes 25 gallons per minute of water with a one pound per square inch pressure drop can be calculated as:
Cv = (25 gpm) (1 / (1 psi))1/2
= 25
Flow 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 pressure - po - 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 (2)
where
m = steam flow (lb/h)
pi = inlet steam 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 / (2.1 ( (pi + po) dp) 1/2) (2b)
Flow Coefficient - Cv - for Superheated Steam
The flow coefficient for superheated steam should be multiplied with a correction factor:
Cv = Cv_saturated (1 + 0.00065 dt) (3)
where
dt = steam temperature above saturation temperature at the actual pressure (oF)
Example - flow coefficient superheated steam
The flow coefficient for steam superheated with 50oF can be calculated as:
Cv = Cv_saturated (1 + 0.00065 (50oF) =1,0325 Cv_saturated
Flow Coefficient - Cv - for Saturated Wet Steam
Saturated wet steam includes non evaporated water particles reducing the "steam quality" and very wet saturated steam should be multiplied with a correction factor:
Cv = Cv_saturated ζ1/2 (4)
where
ζ = dryness fraction
Example - Flow Coefficient Wet Saturated Steam
For steam with moisture content 5% the dryness fraction can be calculated as:
ζ = ws / (ww + ws)
= 0.95 / (0.95 + 0.05)
= 0.95
where
ww = mass of water
ws = mass of steam
The flow coefficient can be calculated as:
Cv = Cv_saturated (0.95)1/2
= 0.97 Cv_saturated
Flow Coefficient - Cv - for Air and other Gases
Note! - there is a difference between critical and non critical pressure drops.
For critical pressure drop, where 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 [SG (T + 460)]1/2/ 660 pi (5)
where
q = free gas per hour, standard cubic feet per hour (Cu.ft/h)
SG = specific gravity of flowing gas gas relative to air at 14.7 psia and 60oF
T = flowing air or gas temperature (oF)
pi = inlet gas absolute pressure (psia)
For non critical pressure drop, where 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 [SG (T + 460)]1/2/ [1360 (dp po)1/2] (5b)
where
dp = (pi - po)
po = outlet gas absolute pressure (psia)
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