It is essential to understand the forces that an object undergoes when immersed in a fluid. The buoyancy force is one of them. This knowledge enables various applicationsb such as the development of ships, ferries, submarines and other aquatic devices. The easiest way to understand this force is through the principle of Archimedes.

Archimedes' Principle

Any body immersed or floating in a fluid, within a gravitational field, is subject to the action of a force exerted by the fluid called buoyancy (\(E\)), which has the following characteristics:

  1. The value of the buoyancy module is equal to the weight of the displaced liquid volume.
  2. The direction axis of buoyancy is vertical from bottom up.
  3. The net force of buoyancy acts on the center of gravity of the displaced fluid, which is called impulse center.
Mathematically, we have: $$E = P_{\text{displaced fluid}} = \rho_{\text{fluid}} \cdot V_{\text{body}} \cdot g,$$ where \(g\) is the acceleration of gravity, \(V_{\text{body}}\) is the volume of the object inserted, and \(\rho_{\text{fluid}}\) is the liquid density.

Importantly, if only part of the body is immersed in the liquid, \(V_{body}\) should only correspond to the volume of the body part immersed in the liquid.

The figure below illustrates the principle of Archimedes.

Liquid displaced and buoyancy. Consider a container containing a liquid only (left figure). If we insert in this container an object (right figure) the height of fluid will rise. This displaced fluid volume, \(\Delta V\) is exactly equal to the volume \(V\) of the object that was inserted. The Archimedes' principle says: the buoyancy on the inserted object is the weight of an imaginary object, that has the volume of the inserted object and density equal to the displaced liquid.