Formulas Used For Gases (Compressible Fluids)

Basic Formula for Gases

We use equation 17 of section 6.1 of the standard:

Where Y is a factor for the expansion of the gas and x is defined as:

Where FL was a valve characteristic determined by the manufacturer to characterize the pressure recovery in the valve in liquid flow, the factor XT is used for gases in a similar fashion. Again, this factor is measured by the manufacturer.

FK is defined as where Cp/Cv is the isentropic exponent of the gas.

The expansion factor Y is given by equation

but cannot be less than 2/3.

When fittings are used, XT should be replaced by XTP which is defined as:

Choked Flow

Similarly to liquids, gases flow can also choke. Given an upstream pressure and a valve size, as the pressure downstream is lowered, the flow increases. This continues until the downstream pressure is such that the speed of the gas at the throat of the valve (vena contracta) reaches the speed of sound. Lowering the downstream pressure even more is of no avail as information about what is happening downstream cannot propagate past the sound barrier. The flow is therefore choked.

The pressure at which choking occurs (for a given upstream pressure) is called the critical pressure, P2CRIT.

If P2 is less than P2CRIT, then simply use P2CRIT instead of P2 in the formulas.