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Hi Sean! I can give you an approximate formula.
I know that the vacuum of a barometer can lift a column of mercury about 29 in. high, and can lift a column of water about 33 ft high. In reality, atmospheric pressure is PUSHING the columns up (since vaccum cannot suck!) One atmosphere will balance the pressure of 33ft of water. Therefor, if you go 33ft deep into water, the pressure increases by one atmosphere (it increases by 15 pounds per square inch).

pressure equals depth times 15 divided by 33

pressure (lbs-per-sq-in) = depth(ft) * 15(lbs-per-square-inch-per-atm) / 33(ft-per-atm)For example, if you go 66ft down under water, thats 30psi pressure. For one mile down (5280 feet), calculate:

5280 * 15 / 33 = 2400 psi (over a ton per square inch!)The size of the hole in the bottom of the box does not matter. All you need to do is match the air pressure to the pressure of the water outside.

This is approximate. For exact calculations, we need a much more complicated equation which takes into account the water's salinity, temperature, and water's slight compressibility. I don't know where to find such a thing. Maybe navy submariner's training textbook would have it.

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