If you doubt that the water exerts an upward pressure, try to submerge a balloon in the bathtub. You’ll feel a substantial upward push that resists your downward push.
When we lowered the Admiral Nimitz into our giant bathtub, the water level rose; it got deeper. As every diver knows, deeper water means higher pressure. This increased pressure is present everywhere throughout the water in the bathtub, because water cannot cushion or absorb a force, the way a spring or a piece of rubber can.
The water must transmit its increased pressure in all directions to everything it is in contact with, including the ship’s hull. All the north-east-south-west horizontal pushes on the hull cancel each other out, leaving only an uncanceled upward push. This is the pressure that pushes the ship upward against gravity. Voila! Buoyancy.
Okay, I know what you’re thinking. Aircraft carriers operate much more frequently in oceans than in bathtubs. Am I telling you that the level of the ocean was raised when the Nimitz was launched? I certainly am.
Spread that one hundred thousand tons of water over the surface of the entire Atlantic Ocean, though, and it comes to a pretty meager rise, quite unlikely to flood any beachfront property in Florida. Nevertheless, it’s a volume of water equal to the submerged volume of the ship’s hull up to the water line, and a buoyant force equal to that weight of water is still operating on the ship.
By the way, Archimedes didn’t have an aircraft carrier at his disposal so, as the story goes, he used his own body. He filled his bathtub to the brim, climbed in, and realized that the weight of the overflow water on the floor had to be the same as his loss of weight, his buoyancy, in the water. History does not record the reaction of his landlady.
In other news.
Exactly why does a hole in the hull of a ship make it sink?
Water rushes in through the hole because it is under a pressure, depending on how deep below the surface the hole is, the lower the hole, the harder the water rushes in. As the water enters the ship, it replaces an equal volume of air, thereby increasing the ship’s weight and hence its overall density.
When enough water has entered to make enough extra weight to overcome the buoyancy force, down she goes.