I'm trying to figure out how I would calculate the rate at which a submarine (or any object) ascends or descends in seawater given a certain buoyancy or change in buoyancy. For example, if my submarine is 2000 feet below sea level and weighs 393 metric tons (with empty ballast tanks) and displaces 13,583 cubic feet of water, what's the maximum rate it will rise to the surface (assuming it can reach that rate before breaking the surface) and it's acceleration/deceleration to that rate? I'd like to know if there's a reliable and accurate way to solve a problem like this that takes into account factors like the change in sea water pressure and density with depth, as well as the increase in water resistance against the submarine as it accelerates upward.
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