Immersed and Floating Bodies

Looking at an iron ship one wonders how it is possible that it floats, possibly in a stable configuration for the safety of cargo and people, even if the iron has a mass density much greater than that of water. We also wonder about the principle behind the rising motion of hot air balloons, or behind the vertical movement of submarines or fishes. All these are called floating bodies and the analysis of their equilibrium requires only a small addition to the analysis of the hydrostatic forces acting on a curved surface. Some basic principles were discovered by Archimedes more than two thousand years ago and are perfectly suited to the modern theory of Fluid Statics. In essence, a body immersed (partially or totally) in a fluid is subject to its own weight, and receives an additional force, called Archimedes’ thrust, equal to the weight of the volume of fluid displaced by the body and directed against gravity.