A body immersed, partially or wholly, in a fluid experiences an upthrust U pushing it against gravity with magnitude equal to the weight of the fluid displaced by the body. This buoyancy principle was first discovered by Archimedes.
Consider a cylinder of height h and area A made of a material of density 
, immersed in a fluid of density 
.
The weight of the cylinder can also be expressed as
If the object is in equilibrium,
The buoyant force on the cylinder is given by
The pressure difference is given by
Therefore, the buoyant force, or upthrust U, is equal to
which is the weight of the fluid displaced.
