The resultant vertical force exerted on a body by a static fluid in which the body is submerged or floating. Buoyancy is the upward force exerted by a fluid (liquid or gas) on a body that is placed within it (see illustration). The buoyant force FB acts vertically upward, in opposition to the gravitational force. Its magnitude is equal to the weight of fluid displaced (a line of reasoning that is referred to as Archimedes' principle), and its line of action is through the centroid of the displaced volume, which is known as the center of buoyancy. Mathematically, the buoyant force equation is FB = γV, where γ is the specific weight of fluid (weight per unit volume) and V is the displaced volume of fluid, respectively. By weighing an object when it is suspended in two different fluids of known specific weight, the volume and weight of the solid may be determined. In addition, the magnitude of the buoyant force must be given by the difference of vertical components of fluid force on the lower and upper sides of the body. See also: Archimedes' principle; Hydrostatics
A body floating on a static fluid has vertical stability. A small upward displacement decreases the volume of fluid displaced, thereby decreasing the buoyant force and leaving an unbalanced force tending to return the body to its original position. Similarly, a small downward displacement results in a greater buoyant force, which causes an unbalanced upward force.
A body has rotational stability when a small angular displacement sets up a restoring couple (a system of two parallel forces of equal magnitude and opposite sense) that tends to return the body to its original position. When the center of gravity of the floating body is lower than its center of buoyancy, it will always have rotational stability. Many a floating body, such as a ship, has its center of gravity above its center of buoyancy. Whether such an object is rotationally stable depends on the shape of the body. When it floats in equilibrium, its center of buoyancy and center of gravity are in the same vertical line. When the body is tipped, its center of buoyancy shifts to the new centroid of the displaced fluid and exerts its force vertically upward, intersecting the original line through the center of gravity and center of buoyancy at a point called the metacenter. A floating body is rotationally stable if the metacenter lies above the center of gravity. The distance of the metacenter above the center of gravity is the metacentric height and is a direct measure of the stability of the object. See also: Couple; Ship capsizing; Ship design