Isoentropic outflow through a nozzle
The formula  that is used in the collection “E”, as well as in other Italian  and foreign  standards, for the calculation of safety valves that must discharge gases or vapours, is that of the isoentropic outflow through a nozzle under critical jump conditions, which for an ideal gas is:
where the expansion coefficient C is given by:
|Fluid||P1 (bar)||T1 (°C)||q’ (kg/h)||q (kg/h)||
(q’/q) x 100
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.
Where 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.