The excellent book, Thinking Physics by Paul Hewitt and Lewis Epstein has a question and answer format. One question asks if a battleship can float in a bathtub. Ignore the obvious fact that no real bathtubs are as large as a battleship. The question is really about the amount of water required for a ship to float. Very little water is actually required.
Archimedes's Principle
According to Archimedes's principle, the buoyant force on a ship or any other object in water equals the weight of the water displaced. The weight of the displaced water will exceed the ship's weight when the ship has an average lower density (density=mass/volume) than water. The buoyant force will then be enough to float the ship. Ships having an average density greater than the density of water will weigh more than the displaced water and therefore sink.
Reading the statement of Archimedes's principle might lead one to think that there must be at least enough water surrounding the ship to equal the weight of the ship. That is not the case. The weight of the water displaced, not the weight of the water surrounding the ship, determines if the ship will float. The displaced water does not actually need to be there, hence there does not need to be much water actually surrounding the ship.
Ships in the Panama Canal Locks
Archimedes's principle therefore predicts theoretically that a battleship could float in a sufficiently large bathtub. If there were a battleship-bathtub combination that provided at least a thin unbroken layer of water between the outside of the ship and the inside of the bathtub, the ship would float on the water. The ship could just barely fit inside the tub with an amount of water that weighs much less than the ship. Most bathtubs are however much smaller than battleships. How can we experimentally test this theoretical prediction?
The locks in the Panama Canal provide a good experimental illustration of this principle. The images accompanying this article show a large ship barely fitting but still floating in the Miraflores locks of the Panama Canal. Even ships that barely fit into the locks float on the very small amount of water surrounding the ship in the lock. Here observations of nature confirm the theoretical predictions from Archimedes's principle.
Yes it is possible for a battleship to float in a bathtub.
Further Reading
Hewitt, P. and Epstein L. Thinking Physics, Insight Press, 1981.
Paul A. Heckert - I have a Ph.D. in astrophysics, over 30 years experience teaching physics and astronomy, and over 60 published research articles.
