Most manufacturers use the same Cv for liquids or vapors for a specific valve though you use different formulas. The ISA equations for control valves use Cv for gas and liquid.
No, you don't convert your cfm of CO2 into gpm and plug them into the formula for liquids (I think that is what you are asking].
Check your valve vendor catalogs, they will have the sizing equations in there. You can, depending on your pressure and temperature, use an ideal gas sizing equation or a real gas sizing equation (the latter if compressibility effects are significant].
A valve with a Cv of 1 will pass 1 gpm of water with a differential pressure of 1 psi. If you replace the water with CO2, you will pass a lot more than 1 'gpm' of CO2 gas, the amount depending on the pressure and temperature of the CO2.
It's an interesting question, I've never dug back through the sizing formulas for gas {for liquids, it's just Q = Cv * [dP/SG}^.5} to see how they 'relate' to liquids, if they do. But I think for you to find the answer to that question that would be a lot more work than what you are looking for.
As i stated previously. You can convert the Cv into a dimsionless loss coefficient (K) that can be used to calculate pressure drop for any fluid (single phase) be it a liquid or gas (allthough the formulas may differ and the valve may choke in which case the formula changes again).
You can use the same Cv for gases and liquids, but if teh pressure drop thru the valve exceeds 5% of the inelt pressure, tehn you should add a compressibility correction factor. See the ISA handbook of control valves
For liquids and low pressure drop gases;
W(lb/hr) = 63.2 * Cv *SQRT {DP(psi)/ sv,i(lbm/ft3)}
For gases where the DP/Pi > 0.05, then use the following :
W=63.2*Cv*Y*SQRT {x*Pi/sv,i}
Y=1-0.33(x/Fk/Xt)
x=min {DP/Pi, Fk/Xt)
Fk=(Cp/1.4/CV) ( this CV is heat capacity)
Xt= valve index for choked flow due to oblique shock waves, typically .75-.85 for globe, .65 angle, 0.2 ball
max value of Y is 0.67 , occurs during choked flow when
x= Fk/Xt
Thank you for the correction. However, what I wanted to emphesis is that Cv is a measure of the equivalent orifice diameter and therefore can be used with any fluid. Meaning is a property of the valve/orifice geometry only. My confussion was because I am used to Cd - discharge coefficient which is more natural to use (at least for me) because it is dimensionless and always less or equall to 1.
Its easy to get confused re this matter. In europe we tend also to favor the dimensionless coefficient (often in Denmark/Germany refered to as K) since this can be used in any pressure/flow relation and not just for a valve.
