Just to wrap this up, I went ahead and used the simplified barometric formulas (derived from the ideal gas law) as described in the wiki link provided by @joeyd999. One assumes the temperature increases with the lapse rate, and the other assumes constant temperature. Both can be found implemented in many places on the internet but you need to be careful to make sure which one is being used.

Anyway, assuming a constant temperature gives you 3.68 atm at the bottom of the trench. Using a constant lapse rate as it is at sea level gives you a lower 3.20 atm due to the higher temperatures and lower densities of the air column above.

It's unlikely that the lapse rate would remain constant, so this is definitely a "ballpark" estimate, IMHO. And the ideal gas law becomes increasingly less precise as pressure increases. Four atmospheres is still a "low" pressure though and I wouldn't expect a huge error from assuming ideal behavior.

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You should add humidity in as a variable. The air density difference between 0 and 100% humidity should make for a considerable pressure difference over 11km.

 

Also, four atmospheres is equivalent to diving at about a 40m depth. Maybe it could not be survivable ... at least not in the long term.

 

You should add humidity in as a variable. The air density difference between 0 and 100% humidity should make for a considerable pressure difference over 11km.

It's a common misconception (that I'm not accusing you of) that moist air is denser than dry air. It sure feels that way. However water (18) has a lower molecular weight than N2 (28) and O2 (32) and so reduces the average density of air.

At 3.2 atmospheres and 30°C, air at 5% RH is 268.6 L/kg. At 95% RH, it's 271.8 L/kg. Note that even at 95% RH, air is only 0.79% water by mass ratio at these conditions. At 1atm and 20°C, water saturates at 2.73% mass.