# How deep underwater could you breathe using a tube which breaks the surface until the water pressure makes it impossible to inhale air?

I'm struggling with a question asking how deep you can breathe underwater using a hollow reed before the water pressure makes it impossible to inhale. The question asked to use this data of maximal respiratory pressures:

The question also gave a hint that for every metre below the surface, hydrostatic pressure increases by 100 cm H2O.

I'm seriously lost on this question, from my research, all I could find was that a difference of approximately 50 cm H2O is needed in order to inhale, but I'm unsure if that is information I should deduce from the table instead of looking up. Even knowing that information, how would I then find out how deep that means you could breathe? Any help would be greatly appreciated.

Thanks

• It shouldn't affect the question, but note that to get sufficient air past a certain point (depending on the tube volume), two tubes would be needed, one for inhalation and one for exhalation, otherwise you'd be rebreathing too much of your own exhaled air. Commented Nov 19, 2021 at 20:49
• Different graph here: ncbi.nlm.nih.gov/pmc/articles/PMC1501025/table/T3/… your lungs and the different levels of the tube equalize to the surrounding water pressure, so the maths is simple, a male can fill their lungs till about 50% full at 75cm although it would take your maximum force and it would require a tube with almost zero flow friction. To breathe comfortably at that depth, the tube body could be about 7cm diameter. Applying maximum force to achieve only 50% breaths would require training because it would be claustrophobic and cause heart acceleration. Commented Feb 16, 2023 at 7:43
• I won't write an answer because I don't know the tube resistance relative to diameter, however the faster the breath the higher the tube resistance so the maths chart requires a tube with nearly zero friction, which is probably 4 inches or forearm sized. Commented Feb 16, 2023 at 7:46

First, a sanity check. Snorkeling isn't generally done at much depth, and this question reflects some subjective sense of that.

My guess (after much confusion) is the table they're providing is apparently the pressures that the subjects were able to apply, when striving to breathe in or out at various levels of "Lung Volume". But what is "Lung Volume"? Not Total Lung Capacity - is it Tidal Volume, Expiratory Reserve Capacity, something else?

If I read it that the person, at 22-54% "Lung Volume", can apply only 53 cm H2O of pressure differential while inhaling, that implies that at this depth of external pressure, they can't inhale. (Oddly, if they lose the battle and go to 1%, the data says their ability to inhale is reduced!) In theory the fluid pressure of water or air on the body should be similarly positioned.

Even so, there are two things that make me doubt this. First, the inability to inhale should be coupled with a greater ability to exhale. So I still wonder if sort of shallow breathing might still be possible at the limit of the expiratory reserve, or even in the range of "residual volume", as the external pressure is opposed by connective tissue. Second, the diaphragm and the external intercostal muscles are, well, muscles, so it should be possible that someone could train those muscles well and resist more pressure.

• It should not show greater ability to exhale as exhaling is controlled by inhalation, if you can't inhale your lungs are already at equilibrium pressure so you can't exhale either.
– John
Commented Mar 24, 2021 at 16:25

I'm a moderately-experienced scuba diver who's also done quite a bit of snorkeling, mostly no deeper than 10m.

I think the simple thing is to consider inhalation vs exhalation separately looking for the limiting factors. At best, the inhalation table suggests you can generate -53 cmH20 pressure.

Therefore the max breathable depth would be 53/100 x 1m = 0.53m.

That also roughly matches the assertion in the article of 1.5 to 2ft.

The link Mike Serfas used to a snorkeling site makes the same argument about CO2 remaining in the tube when you exhale as outas's comment.

That's a common mistake - yes with a normal snorkel you inhale and exhale through the same tube but that is not mandatory! If you were breathing through a long tube, assuming bubbles were allowed, you could exhale through your nose to avoid pushing CO2 back into the tube.