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Valve Sizing Equation
Puzzled by equation Q(SCFM) = 16.05 Cv ((P1^2 - P2^2)/ SGg T)^0.5


I ran into the following valve sizing equation for gases:

Q(SCFM) = 16.05 Cv ((P1^2 - P2^2)/ SGg T)^0.5 [Eq. 1]

Where P1, P2 and T are absolute pressures (inlet/outlet) and temperature, in PSIA and R.
SGg is the gas specific gravity, that is, the ratio between the density of the gas and the density of air at the same conditions, effectively the ratio of molecular weights.

Some of the sources say that the equation is from standard FCI 62.1 but I cannot find it, even on FCI's website.

This equation does not appear on ISA 75.1.

Now, I know how to start from the basic equation for turbulent liquid flow,

Q(USGPM) = Cv ((P1 - P2)/SG) [Eq. 2]

Where SG is the specific gravity of the liquid, referred to water at 4C, and derive this equation for gases, cited as "traditional" by Emerson:

Q(SCFH) = 59.64 Cv P1 ((P1 - P2)/P1)^0.5 (520/(SGg T))^0.5 [Eq. 3]

But, as much as I try, I cannot derive Eq. 1 from Eq. 2.

Does anybody know its origin?

Thank you

Sorry, I missed a square root in Eq. 2

Q(USGPM) = Cv ((P1 - P2)/SG)^0.5 [Eq. 2]

Bernoulli law applies here, and the starting point for both equations. Watch your units.

You do have to be careful in regards to units, especially where the fluid density is involved.