Archimedes' buoyant force

Statement of the principle

Any body immersed (partially or totally) in a fluid (liquid or gas) at rest experiences from that fluid a vertical, upward-directed force, called Archimedes' buoyant force. Its magnitude is equal to the weight of the volume of fluid displaced:

Pi = rho_fluide * V_immerge * g

where rho_fluide is the density of the fluid, V_immerge is the volume of the immersed part of the object, and g is the acceleration of gravity.

Float or sink?

Comparing the buoyant force Pi to the weight P = m*g of the object:

• if Pi > P, the object rises
• if Pi = P, the object is in equilibrium (it floats, partially immersed)
• if Pi < P, the object sinks

Example: the iceberg

An iceberg floats because its density (ice, about 900 kg/m^3) is lower than that of seawater (about 1025 kg/m^3). Only a small part emerges: about 10% of the total volume, the rest (90%) remaining submerged below the surface.

Common pitfall

Frequent mistake: using the total volume of the object instead of the actually immersed volume in the formula. For a partially floating object, V_immerge is strictly less than the total volume. Another mistake: forgetting that rho_fluide is the density of the fluid (not that of the object) in the buoyancy calculation.