Submarine buoyancy Maybe a silly question but..
A submarine has ballast tanks to control it's buoyancy. To submerge, water is allowed to fill the ballast tanks which displaces the air inside.
When a submarine is submerged it contains a fixed amount of air compressed and uncompressed. By filling the ballast tanks with compressed air the submarine rises to the surface.
How is this possible? The submerged submarine has $x$ quantity of air. Filling the ballast the sub still has $x$ quantity of air, it's just being redistributed.
 A: Submarines adjust depth by taking seawater into ballast tanks through vents and forcing the water out using compressed air, thus adjusting seawater/air ratio inside the submarine. Since seawater is denser than air, higher seawater/air ratio makes it heavier, causing the submarine to sink, and higher air/seawater ratio makes it lighter, causing it to rise. The buoyancy  of the submarine actually remains the same, because the volume is not changing, its just the net buoyancy-weight of the submarine that is changing.
A: The air in the submarine that is used for blowing water out of the buoyancy tanks is greatly compressed, to between 3000 and 6000 PSI. The volume displaced by the compressed air stored in the tanks inside the pressure hull is lots less than than of uncompressed air, and this pressure is great enough to empty the tanks even at the submarine's maximum service depth.
Note also that a submarine can increase its buoyancy by pumping water out from inside its pressure hull. In so doing, the air pressure inside the hull will go down but this effect can be countered by venting high pressure air into the hull as the pumps are running.
A: The buoyant force is equal to the weight of the water that is displaced by the submarine.  It comes down to the average density of the total submarine volume versus the density of water.  By replacing water in the ballast tanks with air you are effectively shifting this balance because the air is about 1000x less dense than the water it is displacing.  Since the air was previously compressed it wasn't displacing that much water.  As it is released and expands to fill the ballast tanks it now displaces much more water.
