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Basic Rule of Analysis: 
Cabin Pressure Analysis
Cabin pressure analysis is performed using an empirical formula determined by Chester W. Smith in 1945, and published as "Calculation of Flow of Air and Diatomic Gases" by the Journal of the Aeronautical Sciences, June 1946 (pp 309315). The article is available as a PDF file (NOTE: it is 1.22 MB in size!).
Chester Smith's formula is:
Mdot
= (K)(Cd)(AREA)(Pcab)(N)/SQRT(Ttot)
where: 
Mdot 
= Mass Flow (lb/min) 



K 
= Constant = 31.82 
when: 
Pcab
= psi 

Cd 
= Discharge Coefficient 

AREA 
= Geometric area of "hole" 

Pcab 
= Cabin Pressure (upstream pressure) 

N 
= Restriction Factor 

Ttot 
= Total Temperature (upstream) (nominally = 535 deg R; 75 deg F) 
Also: 
Pamb = Ambient Pressure (downstream) 

N is based on the isentropic exponent (k1)/k=0.283, and is equivalent to Table 1 of the reference Journal, and may be represented by polynomial equation based on Pcab/Pamb 

Cd is not constant, is based on Pcab/Pamb, and may be represented by polynomial equations (different for orifice and uncontrolled) 
Discharge coefficients (Cd) come in three varieties; orifice, uncontrolled, and venturi. Orifice and uncontrolled coefficients are both dependent upon Pamb/Pcab, but the uncontrolled coefficient is always less efficient than an orifice. They both vary between a low of approximately 0.60 to a high nearly reaching 0.90. Uncontrolled Cd is used to express the leakage through the fuselage joints and seals, and through any "hole" that is irregular in shape, including thrust recoverytype outflow valves. The venturi is the most efficient outlet, and its value is assumed to be a constant 0.95 over all pressure ratios.
Based on Chester Smith's equation, I have written a computer programme to perform the typical types of analyses required to determine the key pressurization and component characteristics, and to provide analyses useful for certification. These characteristics include: outflow valve(s), positive and negative pressure relief valve(s), overboard exhaust valve(s) sizing; emergency descent, MEL/failure case, and minimum repressurization inflow analyses.
The programme uses the following additional equations:
PV = mRT 
The fundamental thermodynamic equation 
Alt <36089 
= 145422.156*(1(Psi/14.697)^0.190263105) 
Alt >36089 
= 20805.8257*log(3.282807/Psi)+36089.2388 
Psi <36089 
= 14.697*(1Alt/145422.156)^5.255879746 
Psi >36089 
= 3.282807/exp((Alt36089.2388)/20805.8257) 
Note: 3.2842 psia = 36089.2388 ft = the "tropopause" altitude defined by the Standard Atmosphere; 1.872 is the pressure ratio (Pcab/Pamb) for sonic flow.
It is not possible to provide details of the
programme, or to make the programme executable files or data files available for
general use.
Some Typical Example Charts and Analyses
(Note: the data shown is without numerical values on the axes on purpose)
Figure 1

Figure 1 is an analysis performed at the request of a customer. The loss of a passenger window was assumed, and the resulting cabin altitude calculated using the Chester Smith programme. As can be seen, the cabin altitude almost climbs to the cruise altitude of the aircraft prior to its descent. This type of depressurization has occurred in the past, but, luckily, today it is a very rare event. 
Figure 2

Figure 2 is the analysis of an actual depressurization event. Both the AUTO and MANUAL ability to drive the outflow valves was lost some hours earlier due to an electrical fault, and when the aircraft proceeded to initiate a step climb, the maximum differential pressure was exceeded, which caused the safety relief valves to open. The aircraft then depressurized, and had to execute an emergency descent and diversion to an alternate airport. After landing, the doors could not be opened until the last of the air inflow was turned off. This analysis was performed using the Chester Smith programme to analyse each of the different aspects of the event (based on the available data), and then add them all together into a single Excel file for display. 
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