Archimedes' principle

A body wholly or partly immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. A fluid includes liquids and gases. For a fully submerged object, the displaced-fluid volume equals the object's volume; for a floating object, it equals the volume below the fluid surface. In equation form, the buoyant force is the displaced fluid's density multiplied by gravitational acceleration and displaced volume: Fᵦ = ρfluid g Vdisplaced.

Fluid pressure increases with depth. Consequently, pressure on an immersed body's lower surface is greater than pressure on its upper surface, producing a net upward force; horizontal pressure forces balance in a uniform fluid. The surrounding fluid's net upward force is the buoyant force. The principle equates that force to the weight of the fluid that would occupy the immersed body's displaced volume. It applies whether the object ultimately rises, sinks or stays at a depth.

An object's motion depends on comparing buoyant force with its weight. If buoyancy is greater than weight, the net force is upward; if smaller, the object sinks when released; if equal, it can remain in equilibrium. A floating object adjusts its submerged volume until the displaced fluid weighs as much as the object. Thus, shape matters because it can change how much fluid a body displaces: a shaped, hollow steel hull can displace much more water than a compact lump of steel. For an immersed object supported by a scale, buoyancy reduces its apparent weight by the weight of the displaced fluid.

Archimedes' principle is used to understand the buoyancy of ships, balloons and other bodies, and to measure the density of materials. Comparing an object's weight in air with its apparent weight when immersed can reveal the displaced fluid's weight and help determine the object's volume or density. The principle is named after the ancient Greek mathematician and inventor Archimedes. The familiar story that he discovered it in a bath and shouted “Eureka!” is often repeated, but Britannica notes that this dramatic detail is believed to be a later embellishment.