Archimedes' Principle

An object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.

Archimedes' Principle

When an object is submerged (or partly submerged) in a fluid, the fluid pushes back with an upward force called the buoyant force.

Buoyant Force

F_b = \rho_{fluid} \cdot g \cdot V_{displaced}

ρ = fluid density (kg/m³), g = 9.8 m/s², V = volume of fluid displaced (m³).

Floating, Sinking, and Neutral Buoyancy

Condition	Result
$F_b > W$	Object rises / floats
$F_b = W$	Neutral buoyancy (hovers)
$F_b < W$	Object sinks

This depends on the average density of the object compared to the fluid.

Comparing Densities

$\text{Floats if } \overline{\rho}_{object} < \rho_{fluid}$

A steel ship floats because its hollow shape increases its average volume, making its average density less than water.

Note Archimedes reportedly discovered this principle in his bath and famously shouted "Eureka!" ("I have found it!").

A wooden block (volume 0.002 m³) is fully submerged in water. What buoyant force acts on it?

$F_b = 1000 \times 9.8 \times 0.002 = 19.6 \text{ N}$

If the block weighs less than 19.6 N it will rise and float.

Real world: Submarine — diving and surfacing

A submarine controls its depth by adjusting ballast tanks fitted inside its hull. To dive, the crew opens valves that flood the tanks with seawater, increasing the submarine's total weight until it exceeds the buoyant force and the vessel sinks. To surface, compressed air is blown into the tanks to push the water out, reducing average density until the buoyant force lifts the submarine back up.

Real world: Fish swim bladder

Most bony fish have a swim bladder — a gas-filled sac inside their body. By adjusting the amount of gas in the bladder, a fish changes its average density to match the surrounding water, achieving neutral buoyancy and hovering effortlessly at any depth without using muscle energy. Sharks lack a swim bladder and must swim continuously to avoid sinking.

Real world: Scuba diving — managing buoyancy

A scuba diver wears a buoyancy compensator device (BCD) — an inflatable vest connected to their air tank. Adding air to the BCD increases the diver's volume (and buoyant force) without adding mass, allowing them to rise. Releasing air reduces buoyancy and they sink. Skilled divers adjust their BCD to hover neutrally at exactly the depth they want to explore.

Tip Where do you see Archimedes' principle in real life? Submarines, ships, fish, scuba divers, hot-air balloons, and even the humble rubber duck in the bath — all depend on the buoyant force of a displaced fluid!

Practice Problems

An object displaces 0.5 litres (0.0005 m³) of water. What is the buoyant force?

Show answer

F_b = 1000 × 9.8 × 0.0005 = 4.9 N.

Why does a submarine sink or rise?

Show answer

It changes its average density by filling or emptying ballast tanks with water or air, changing its total weight relative to the buoyant force.