At which point is the air coming out from the cylinder subjected to ambient pressure?

[garywong007]

During the OWD course, students are often told that the reason air is depleted faster at greater depth is because the volume of air is compressed with increasing depth. For example, a body of air with 10 litre volume is only 5 litre at 10 meters so a diver taking one breath (say, 3 litres) at the surface is equivalent to taking 6 litres of air at 10 meters with the same breath.

But since the air tank is a concealed space and made of solid material that won't deform under water pressure (within a certain depth), therefore the pressure and volume of the air inside is not affected by depth (i.e. if the air inside the tank is at 200 bars and 12 litres on the surface, it should remain the same at 20 meters). My question is then: when the air comes out from the tank, going into the HP chamber of the 1st stage, then the IP chamber, the LP hose, the inlet tube, the housing and finally into the lung of the diver, at which point in time during this route its volume becomes subject to the influence of the ambient pressure?

If one litre of air is released at the surface (i.e. 1 atmospheric pressure) from an air tank with air inside compressed to 200 bars, its volume should expand to 200 litres, but what would the volume of that same 1 litre of air be if it is released at 10 meters (2 atmospheric pressure), 20 meters (3 atmospheric pressure)... and so on and so forth?

Thank you.

 

[inquis]

Ambient pressure impacts the intermediate pressure (around 9.5 bar above ambient, so that's up to the second stage. When the second stage lever opens (when you start to inhale), those molecules in the mouthpiece are at ambient.

200 surface liters of gas will occupy 100 L at 10 m depth.

It may be helpful to look at it the other way around as well as focus on number of molecules. Your lungs are the size they are, so let's say in a normal breath, they expand by 2 L volume. When you inhale at 10 m, your lungs still expand by that same 2 L. However, it takes twice the number of molecules of gas to make them do that. Because that's a huge number (around 54 with 21 zeros after it), we can normalize it to a more manageable (and intuitive) number by calling it 2 bar.liters of molecules.

Removing that number of molecules from a tank reduces the tank pressure, but by how much? That depends on the tank. A 10 L tank will drop by 2 bar.liters / 10 liters = 0.2 bar in that single breath. A smaller 5 L tank would drop by 0.4 bar for each breath.

 

[broncobowsher]

I'll go to your diver taking a 3L breath at 10m. Consuming the 6L of gas from the tank.
When the diver exhales, 3L of air will leave and turn into bubbles. 3L of bubbles at 2 atmospheres of pressure. As the bubbles rise, they will expand back into 6L of gas on the surface.
Does that better explain where the faster consumption goes?

 

[Nemrod]

The gas released from the HP cylinder finally reaches ambient pressure of the surrounding water when it is discharged from the demand second stage. That last drop in IP pressure would occur at the LP seat and orifice.

Each 10 meters of seawater equals 1 bar (14.5 psi) and therefore approximately one atmosphere. Thus divide the cylinder compressed capacity (at sea level) by the number of atmospheres.

 

[Scared Silly]

Ambient is existing or present on all sides : encompassing. That occurs when the gas leaves the second stage regulator.

Boyle's law is a gas law, stating that the pressure and volume of a gas have an inverse relationship. If volume increases, then pressure decreases and vice versa,

 

[rsingler]

Therefore, using Boyle's Law as cited by @Scared Silly above, the volume changes at every point where the pressure drops from tank pressure.
HP gas inside the first stage, upstream from the valve has not expanded. That tiny part of the regulator is at tank pressure. On the other side of the valve when the first stage creates Intermediate Pressure, the gas has expanded 20x (200 bar to 10 bar). It expands slighty less at depth as absolute Intermediate Pressure rises with ambient pressure (absolute IP at 10m is now 11bar), requiring slightly more tank gas to fill that small volume. That extra volume is held in whatever system is at that pressure (IP compartment of the first stage, LP hoses, second stages upstream of the valve).
It expands for the second to last time when pressure drops from IP to ambient, and since it expands less at depth than at the surface, you need to draw more from the tank via the entire mechanism to fill a constant lung volume.
And as pointed out above, it expands for the last time when you exhale, as the bubbles grow as they ascend, and at the surface finally reaching the 1atm gas pressure that was used to compress to 200 atmospheres and 1/200th of the volume inside the tank.

 

[NW Dive Dawg]

Per the OP's question, I actually believe that the moment that any gas exits the tank valve and enters the first stage, that it is then subjected to ambient pressure. But maybe I'm mistaken on that...

 

[Feye]

Closed system and Open system;

"But since the air tank is a concealed space and made of solid material that won't deform under water pressure (within a certain depth), therefore the pressure and volume of the air inside is not affected by depth (i.e. if the air inside the tank is at 200 bars and 12 litres on the surface, it should remain the same at 20 meters).": Yes, when your tank valve was closed.

"My question is then: when the air comes out from the tank, going into the HP chamber of the 1st stage, then the IP chamber, the LP hose, the inlet tube, the housing and finally into the lung of the diver, at which point in time during this route its volume becomes subject to the influence of the ambient pressure?": Now your tank valve is opened (when you breath). This is simple open system and the pressure gap between the tank and environment makes air flow from hi to low till equilibrated. All the eqipment are just restrictors or way of airflow. Your lung is considered as environment, because you are now 20 msw.
Now you can use Boyle's law:

1 ATM with 200 bar X 12 litres = 3 ATM with 200 bar x 4 litres or 3 ATM with 66.6 bar x 12 litres. Your available air amout is "decreased" when you go to 20 m bottom. Anyway, your lung requires same "2.5 litres" of air for breathing, without consideration of environmetal pressure.

 

[Mobulai]

I actually believe that the moment that any gas exits the tank valve and enters the first stage, that it is then subjected to ambient pressure

you are right, but you can approximate that kind of non-linearity to the simpler model of "starting from the IP chamber"

In for example a Diesel injection systems where perssures reach ~4k bar, and you are working with percision timing (0.2 mS), you would have to consider it and not approximate, generically referred to as "Pressure wave" or 1-D pressure models.
Technically it still applies to regulators wich have huge pressure deffrentials, but maybe more to a reg designer/maker than a user. I can't tell with certainty how they choose to model things tho

regardless how you choose to model it; Boyles law always stands -- and it brings all the intuition needed for a diving application without having to consider the inner workings of a regulator.

 

[tursiops]

The air from the tank does not see ambient pressure until it exits the 2nd stage.
It is at tank pressure (say, 200 bars/3000 psi) in the tank, and also while in the entry/HP side of the first stage. The first stage drops that tank pressure to an Intermediate Pressure, around 9-10 bars (140 psi) or so, and then the pressure drops again to ambient pressure at the exit of the 2nd stage.
This had all been said above, but is worth saying again to counteract some misinformation above.

Added: The point being that you cannot apply Boyles Law for volumes until you know the pressure....and it is the pressure that is dropped from tank to ambient in the two stage regulator system. Stage one (in the first stage) drops the pressure from tank pressure to IP; stage 2 (in the second stage) drops it from IP to ambient.