Using the general guidelines:
* we are subject to 1 atmosphere at sea level
* 2 atmospheres at 10 meters, air is compressed to 1/2 original volume
* 3 atmospheres at 20 meters, air is compressed to 1/3 original volume
* 4 atmospheres at 30 meters, air is compressed to 1/4 original volume
Lets say you swim down to the bottom of a flooded mineshaft with a spare tank. Assuming you (and your equipment) survived the descent, at a depth of 200 meters you (and your tank) would be subjected to ~210 atmospheres (2939psi). Now the guy at the LDS only gave you about 3000psi in your tank, and you've lost a couple of psi because the temperature at 200m is pretty friggin' cold, you now have a pressure differential of 0 psi.
IE: No gas is flowing out of your tank.
Working backwards from this point as you started your ascent back to the surface, as the pressure differential increases more & more gas would come out of the tank.
So just the opposite of your first assumption, you would free-flow slower at deeper depths than you would at a more shallow depth.
However, the amount time it takes until no more gas comes out would decrease as you descend (read: no more bubbles more faster
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