15.7 : Buoyancy and Stability for Submerged and Floating Bodies

In fluid mechanics, buoyancy and stability are key concepts for understanding the behavior of submerged and floating bodies. When a stationary body is fully or partially submerged in a fluid, the fluid exerts a force on the body known as the buoyant force. This force acts vertically upward through a point called the center of buoyancy, which is the center of the displaced fluid volume. According to Archimedes' principle, the magnitude of the buoyant force is equal to the weight of the fluid displaced by the body.

The stability of a body in a fluid depends on its ability to return to its original position after displacement. For submerged bodies, stability is determined by the positions of the center of gravity and the center of buoyancy. If the center of gravity is below the center of buoyancy, the body remains in stable equilibrium. For floating bodies, stability arises from the interaction between the buoyant force and the body's weight. When the body tilts, the center of buoyancy shifts, creating a restoring couple that returns the body to equilibrium. However, tall, slender bodies may experience an overturning couple, causing instability and potential capsizing.