Geeky Question: PP Nitrox Blending Formula Derivation

[Pao]

Sorry for this question but I want to know how the nitrox PP blending formula [(FO2-0.21)/0.79] X Final Tank Pressure = O2 Required. I was trying to derive the formula but got stuck with the 0.79 (presumably the %N2 in air) denominator. I tried googling it but no luck.

Thanks,
Richard

 

[dumpsterDiver]

well because you are conserving the mass of oxygen. The mass of oxygen in the tank is a function of the O2 derived from air at 21% plus the mass of oxygen derived from pure oxygen...

 

[Pao]

Thanks dumpsterDiver. Would you happen to know the actual derivation of the formula?

 

[TSandM]

This is a nuisance, because I don't know how to use special characters, but here goes:

FO2 = percentage O2 in final mix
PSIO2 = psi of oxygen added
TP = tank pressure

FO2 = [(PSIO2) + .21(TP - PSIO2)]/TP (this says that the fraction of oxygen in the final mix is equal to the psi of pure O2 added, plus .21 times the air it's topped off with, divided by the total tank pressure)

FO2 =( PSIO2 + .21TP - .21PSIO2)/TP Distributing

FO2 x TP = .79 PSIO2 + .21TP (Moved the TP in the denominator to the other side; combined the PSIO2 terms)

FO2 x TP - .21TP = .79PSIO2 (subtracted the .21TP from both sides)

(FO2 - .21)TP = .79 PSIO2 (distributive law)

[(FO2 - .21)TP/.79] = PSIO2 (divided both sides by .79)

There's your derivation.

 

[Pao]

Thanks for your patience TSandM! Finally. I was not very good with equations and hated math until I started to realize what the implications are of changing each value. It is then that I started to understand the value and beauty of these expressions.

This is a nuisance, because I don't know how to use special characters, but here goes:

FO2 = percentage O2 in final mix
PSIO2 = psi of oxygen added
TP = tank pressure

FO2 = [(PSIO2) + .21(TP - PSIO2)]/TP (this says that the fraction of oxygen in the final mix is equal to the psi of pure O2 added, plus .21 times the air it's topped off with, divided by the total tank pressure)

FO2 =( PSIO2 + .21TP - .21PSIO2)/TP Distributing

FO2 x TP = .79 PSIO2 + .21TP (Moved the TP in the denominator to the other side; combined the PSIO2 terms)

FO2 x TP - .21TP = .79PSIO2 (subtracted the .21TP from both sides)

(FO2 - .21)TP = .79 PSIO2 (distributive law)

[(FO2 - .21)TP/.79] = PSIO2 (divided both sides by .79)

There's your derivation.