Oxygen cylinder: is measured PSI proportional with remaining autonomy ?

DavidS wrote:

To turn that into a mass flow, we need the gas density

I was told that it’s (mostly?) partial pressure that matters rather than density (as it’s the partial pressure that allows for oxygen transferring to the outside air to your red cells), so that it’s actually the pressure altitude (flight level) rather than density altitude that you should worry about. (hypoxia-wise, crossing the alps at FL140 on a hot summer day (say with density altitude 16k ft) is the same as on a cold winter day (e.g. with density altitude 12k ft)

@MedEwok can probably confirm or infirm

For getting the benefit of the oxygen I am sure you are right. But I was trying to convert volume flow into mass flow from the bottle, so I think density is correct for that purpose.

Empirically speaking, I’ve been flying with oxygen since 2003 and have never noticed any nonlinearity in the way the pressure gauge reading moves downwards.

It’s linear for tanks up to some 200 bars or so (which are used in aviation). For 300 bar tanks some non-linearity is involved.

Ability of organisms to metabolze the oxygen is related exclusively to partial pressure.

This could be temperature effect… At colder temperatures, the pressure will be lower for the same quantity of gas in the the bottle.

You run out of gas, not when there is a certain quantity of gas left in the bottle, but at a certain pressure, the pressure where your regulator cannot any more deliver what you require.

Now, if you “quickly” take 1g of oxygen (the order of magnitude of 1l at ambient temperature and pressure) out of a full bottle at a temperature T1, which contains 1kg of oxygen at a pressure P1, you will cool (by expansion) the gas in the bottle only very little because you removed only 1/1000 of the matter, so (the release is quick, so no/little heat exchange happens) the expansion is only by a factor of 1000/999 = 1.001001001… So the temperature effect (which makes the pressure drop below 999/1000 of what it was) is very small, and your pressure drop will be very close to P1/1000. Now, if you take quickly 1g out of the same bottle at the same temperature T1 that had only 10g in it (thus at pressure P2=P1/100) you expanded by a factor 10/9 = 1.1111111… and the temperature drop will be bigger, thus making the pressure drop more below 9/10 of what it was! So your pressure drop will be “more than” P2/10. Since P2=P1/100, P2=P1/100/10=P1/1000, which means that your pressure drop will be “more than” P1/1000, for the same 1g of oxygen delivered.

Now, in flight, my theory is that since the release of gas from the bottle is slow compared to the quantity of gas in the bottle, there is actually heat exchange, which reheats your bottle and thus middle/long term your bottle has little temperature variation, and then the “pressure is proportional to quantity and proportional to when I’ll run out” keeps true… until the rate of release of gas becomes non-negligible compared to the amount of gas in the bottle (and the relative thermic isolation of the bottle), and the temperature effect becomes non-negligible and your pressure diminishes non-linearly with content of the bottle.

Now, why do divers notice this, but not aviators? I could be very wrong about this, but my guess is that divers run their bottles much more empty than aviators. They know how much time (thus oxygen) they need to go up to the surface (with the decompression stops and all that). Once they are at the surface, they don’t care about oxygen supply any more. Moreover, any point on the surface will do, and nobody will keep a diver from going up when he decides to. So maybe a… 5min? 15min? safety margin is enough.

By contrast, aviators worry they won’t be able to refill their bottle at the destination airport. Overflying the Alps, descending to non-oxygen altitude is not necessarily an option. They might get the descent clearance later than what they wanted for their oxygen planning. So they “refill” their bottles before departure from home base well beyond the safety margins of divers.

When the gas from the tank expands in 1st stage of regulator the temperature of gas significantly drops. That’s why it’s important that gas contains no water to avoid freezing. The gas in the bottle is not subjected to any (significant) heat exchange except environmental.

Scuba air could contain water (unless removed in some way) but oxygen can’t because the Linde cryogenic process used to make all commercial oxygen removes virtually all the water long before you get the liquid oxygen coming out.

I have never noticed any cooling of an O2 cylinder in use. It warms up substantially during filling but that’s obviously relatively rapid – one has to let it cool down and then top off again; this is worth about another 10% of gas mass

Emir wrote:

When the gas from the tank expands in 1st stage of regulator the temperature of gas significantly drops.

That’s not relevant, except for the fact that the “cold” will migrate to the bottle because of physical connections (tubing), if they are of conductive materials (metal?). I assume the effect of that is pretty small, if any.

The gas in the bottle is not subjected to any (significant) heat exchange except environmental.

Yes, exactly. That’s why I can imagine that a “quick” removal of gas will be about “no heat exchange” (for the gas remaining in the bottle) while a slow one will have stabilised temperature: the environmental heat exchange will stabilise the temperature.

Peter wrote:

Scuba air could contain water

We don’t necessarily breath air in scuba tanks. To be more precise I never breath air from scuba tank. I usually breath some mix (nitrox – mix of oxygen and nitrogen, trimix – mix of helium, nitrogen and oxygen) or pure oxygen. These mixes contain very low percentage of water if any.