How can I calculate the acceleration of an air bubble released 10m under water?
A complication is that the bubble will dissolve partially in the water, so to make the calculation simpler, consider an air balloon. You must also consider water resistance (drag). According to Archemedes Principle, the buoyant force exerted on a submerged body is equal to the weight of the liquid displaced by the body. 1 litre of water weighs 1 kg. The pressure under water increases linearly by 1atm (atmosphere) every 10m, so the volume of the balloon will increase as it ascends, and so will its acceleration. According to Boyle’s Law, for twice the pressure you get half the volume, so the volume of the balloon at 10m is half its volume at the surface.
