A couple of months ago, I validated my collapse while climbing a 5200 foot peak by using the alveolar air equation to prove that I was indeed a victim of acute altitude sickness!
Now we are experience the opposite extreme. We are on a dive trip in Placencia, Belize and diving twice daily to a depth of 60-70 feet.
Unlike the atmosphere, where the pressure slowly decreases as you climb, the inverse under water happens much more rapidly. The pressure increases 1 ATM or 760 Torr every 33 feet. Interestingly enough, gravitational acceleration is 33 ft/s^2. Is the linear increase of water pressure of 1 ATM per 33 feet related to gravitational acceleration which is 33 feet/s^2? Or is this just a peculiar coincidence.
We have a theoretical physicist on our trip so I asked him about this numerical peculiarity between dives. His first knee-jerk response was “Just a coincidence, as evidenced by the change of medium one dives in. If you were going down in mercury, which has a higher molecular weight, the pressure would climb much faster.”
“Ah,” I said smugly the way ‘ah’ usually is said, “but we build a lot of our units of measure off of the molecular weight of H2O, therefore, while other mediums may increase pressure with depths at different rates, water could be the base medium from which we originally derived those pressures, and therefore, ergo and so forth, it may still not be a coincidence.”
“Hmm I’ll have to think about that,” he said as he jumped off the boat.
After the dive I approached him, “So, any insights?”
“No. There were turtles.”
Damn turtles. Everyone loves them. But as much as we love to anthropomorphize them, they have brains the size of a pea and probably have more in common with a walnut than a human. So I still don’t know cuz turtles. #ThanksTurtles
So lets table that question for a while, because to truly answer it requires some deep digging into unit factoring and I am in Belize with a rum hangover and unit factoring is not a vacation sport.
Another question to ponder: Is there a limit to how high ones PaO2 can go.
At 66 feet, a common dive depth for 30 minutes or so, pressure goes up to 3 atm or 2280 torr. The air we breathe from a tank is completely dry, and the regulators go in the mouth, circumventing the conchae and mucosa of the nasal cavity that create turbulence and moisture respectively.
if we plug that into our Alveolar Air Equation: PAO2 = ( FiO2 * (PB- PH2O)) – (PaCO2 / RQ)
we get PAO2 = (.21 * (2280 – 0)) – (40/ .8) = 428 torr.
This is similar to what you would see if someone were breathing 70% O2 at sea level. The difference being that, at sea level as FiO2 goes up, there is less and less nitrogen in the mix, and the A-a gradient increases. While diving, it is the pressure that goes up, the gas mixture remains relative, and therefore I can assume the A-a gradient stays constant. Could this be an argument to use barometric chambers on people with severely compromised respiration that isn’t CO based?
Also, people who dive frequently don’t dive on air usually. they dive on Nitrox. Nitrox is essentially any mixture of O2 and N2 where the O2 is not the standard 20.9% as it is in regular air. Nitrox divers tend to dive at a 31% O2 to 69% N2 ratio.
we get PAO2 = (.31 * (2280 – 0)) – (40/ .8) = 656 torr.
This is more similar to breathing 100% O2 at 1 atm. However the A-a gradient would increase slightly due to the change in gas mixture.
The point of diving on Nitrox is less absorbed N2 in the blood and hence less chance of the bends, aka decompression sickness aka caisson disease. This allows longer dive times in the 50-100 foot range of depths because of the reduction in nitrogen. I hear a lot of divers say things like “Well I just feel better when I dive on Nitrox.” No you don’t. You’re not gluten intolerant either. You just get longer bottom times. And when the dive master is limiting your dives to 45 minutes anyway, you’re paying 10 bucks extra per tank for nothing.
However, on the flip side, the divers opens himself up to the potential for oxygen toxicity. There are two kinds of oxygen toxicity: Central Nervous System and Pulmonary.
CNS toxicity occurs when breathing O2 at a partial pressure of greater than 1.6 ata or 1216 torr. Diving on nitrox to a depth beyond 120 feet would put you right on that edge hence the recreational guidelines limit you to 100 feet.
Pulmonary Toxicity is not generally a problem with recreational divers as it is the result of extended exposure to high O2 contents. It can, however, be a problem with long term mechanically ventilated patients on high FiO2.
Ok enough. I’m going diving to look at turtles and forget that I still haven’t answered that other question.