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 Z1 for the real fluid, we arrive at the formulation of the collection “E”:
The isoentropic exponent k can be expressed as:
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:
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 , according to collection “E”, the values of Cp/Cv, Z and Zp must be evaluated at discharge conditions P1 and T1.
The derived compressibility factor Zp is defined in formula  as:
The compressibility factor Z can be expressed as:
and similarly, can be expressed as:
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  and , Ω is Pitzer’s acentric factor defined by:
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.