### q’= flow rate calculated with k = Cp/Cv (20 °C, 1 atm)

q = flow rate calculated with *k = (Cp/Cv) • (Z/Zp)*

By introducing the experimental coefficient k of safety valve outflow, which globally considers the real outflow performance of the valve, a safety coefficient of 0.9 and the compressibility factor Z_{1} for the real fluid, we arrive at the formulation of the collection “E”:

[1]

*The isoentropic exponent k can be expressed as:*

[2]

For an **ideal gas**, for which** P x V / R x T =1** , it is demonstrated that k is equal to the ratio Cp/Cv between the specific heats at constant pressure and volume.

For a **real gas**, k can be expressed (see Appendix B) by:

[3]

where Z is the compressibility factor defined by Z=**P x V / R x T** and Zp is the “derived compressibility factor”. When applying formula [3], according to collection “E”, the values of Cp/Cv, Z and Zp must be evaluated at discharge conditions P_{1} and T_{1}.

The derived compressibility factor Zp is defined in formula [4] as:

The compressibility factor Z can be expressed as:

[4]

and similarly, can be expressed as:

[5]

where the values of Z^0, Z^1, Zp^0, Zp^1 are tabulated in Appendix A as a function of Pr and Tr.

In [4] and [5], Ω is Pitzer’s acentric factor defined by:

[10]

Where Pr^SAT is the reduced vapour pressure corresponding to a reduced temperature value Tr=T/Tc=0,7. Appendix A shows the Ω values of some fluids. Z e Zp can also be derived directly from an analytical equation of state.