There's a difference between rates that ambient pressure changes underwater with depth, differential pressure across the lungs/alveoli increases with volume change, and gas expansion rates per unit of depth.
The pressure per unit of sea water is constant regardless of depth — 0.445 PSI/FSW (Feet of Sea Water) or one atmosphere per 33FSW (rounded). So, if you go up or down 10' from any given depth the pressure change will be 4.45 PSI.
However, gas expands and compress as a function of the atmospheres of pressure acting on it. It is not a continuous rate like pressure change with depth. For example:
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Healthy human beings can voluntarily inflate their lungs as much as their muscles allow without giving themselves an embolism (thankfully). Thus the point at which the gas expands in a lung of trapped gas causes an embolism varies with the expansion rate of the gas AND the level of lung inflation when the gas is trapped. The differential pressure, which actually causes an embolism but results from gas expansion, increases at a non-linear rate. The curve starts pretty flat and increases dramatically as you approach and exceed maximum voluntary expansion.
Therefore a fully inflated lung might result in an air embolism with a 10% over expansion. That same lung starting at half-full would require about a 110% increase in volume before failure.
Don’t try this at home since nobody can precisely estimate “half-full lungs” or how much beyond the voluntarily fully-inflated level their lungs can expand without failure/embolism. The risk of underestimating is a pretty ugly death.
The pressure per unit of sea water is constant regardless of depth — 0.445 PSI/FSW (Feet of Sea Water) or one atmosphere per 33FSW (rounded). So, if you go up or down 10' from any given depth the pressure change will be 4.45 PSI.
However, gas expands and compress as a function of the atmospheres of pressure acting on it. It is not a continuous rate like pressure change with depth. For example:
[TABLE="width: 504"]
[TR]
[TD]
Depth in FSW
[/TD][TD]
ATA
[/TD][TD]
PSIG
[/TD][TD]
Volume
[/TD][TD]
Volume
[/TD][/TR]
[TR]
[TD]
0
[/TD][TD]
1
[/TD][TD]
0
[/TD][TD]
1
[/TD][TD]
7
[/TD][/TR]
[TR]
[TD]
33
[/TD][TD]
2
[/TD][TD]
14.7
[/TD][TD]
0.5
[/TD][TD]
3.5
[/TD][/TR]
[TR]
[TD]
66
[/TD][TD]
3
[/TD][TD]
29.4
[/TD][TD]
0.333333
[/TD][TD]
2.333333
[/TD][/TR]
[TR]
[TD]
99
[/TD][TD]
4
[/TD][TD]
44.1
[/TD][TD]
0.25
[/TD][TD]
1.75
[/TD][/TR]
[TR]
[TD]
132
[/TD][TD]
5
[/TD][TD]
58.8
[/TD][TD]
0.2
[/TD][TD]
1.4
[/TD][/TR]
[TR]
[TD]
165
[/TD][TD]
6
[/TD][TD]
73.5
[/TD][TD]
0.166667
[/TD][TD]
1.166667
[/TD][/TR]
[TR]
[TD]
198
[/TD][TD]
7
[/TD][TD]
88.2
[/TD][TD]
0.142857
[/TD][TD]
1
[/TD][/TR]
[/TABLE]
Healthy human beings can voluntarily inflate their lungs as much as their muscles allow without giving themselves an embolism (thankfully). Thus the point at which the gas expands in a lung of trapped gas causes an embolism varies with the expansion rate of the gas AND the level of lung inflation when the gas is trapped. The differential pressure, which actually causes an embolism but results from gas expansion, increases at a non-linear rate. The curve starts pretty flat and increases dramatically as you approach and exceed maximum voluntary expansion.
Therefore a fully inflated lung might result in an air embolism with a 10% over expansion. That same lung starting at half-full would require about a 110% increase in volume before failure.
Don’t try this at home since nobody can precisely estimate “half-full lungs” or how much beyond the voluntarily fully-inflated level their lungs can expand without failure/embolism. The risk of underestimating is a pretty ugly death.
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