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Archimedes' principle

Archimedes' principle states that the buoyant force on a submerged body equals the weight of the fluid it displaces, regardless of what the body is made of. A floating body sinks exactly until it displaces its own weight in fluid.

F_B = \rho_{fluid}gV_{displaced}

buoyant force

\dfrac{V_{under}}{V} = \dfrac{\rho_{body}}{\rho_{fluid}}

submerged volume fraction while floating

Symbols

$F_B$	buoyant force	N
$V_{displaced}$	displaced volume	m³

Example

An iceberg ( $\rho_{ice} = 917$ kg/m³) floats in seawater ( $\rho = 1025$ kg/m³). The fraction below water is $917/1025 \approx 0.895$ , so only about 10.5% sticks up.

Always use the fluid's density in

F_B = \rho gV

, not the density of the body itself.

Practise hydrostatics for free →

← Hydrostatic pressure · Hydraulic press →

Part of Fluid Mechanics: Hydrostatics.