Archimedes' principle

Physical law of buoyancy discovered by Archimedes

Diagram illustrating Archimedes' principle

Archimedes' principle is a fundamental law of physics that describes how the buoyancy of an object is determined by the fluid it displaces. This principle is named after the ancient Greek mathematician and inventor Archimedes, who first discovered this relationship.

Statement of the Principle

Archimedes' principle states that any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid that the object displaces. This principle applies to both liquids and gases.

Explanation

When an object is submerged in a fluid, it experiences an upward force known as the buoyant force. This force is equal to the weight of the fluid displaced by the object. The principle can be understood by considering the pressure differences at different depths in the fluid. The pressure at the bottom of the object is greater than the pressure at the top, resulting in a net upward force.

Pressure distribution on an immersed cube

Mathematical Formulation

The buoyant force \( F_b \) can be calculated using the formula:

\[ F_b = \rho \cdot V \cdot g \]

where:

• \( \rho \) is the density of the fluid,
• \( V \) is the volume of the fluid displaced by the object,
• \( g \) is the acceleration due to gravity.

Applications

Archimedes' principle is used in various applications, including:

• Designing ships and submarines, where the buoyancy must be carefully calculated to ensure they float or submerge as desired.
• Determining the density of an object by measuring the volume of fluid it displaces.
• Understanding the behavior of balloons and airships, which float in air due to the buoyant force.

Historical Context

According to legend, Archimedes discovered this principle while taking a bath, leading him to exclaim "Eureka!" upon realizing how he could determine the purity of a gold crown by measuring its displacement of water.

Related Concepts

• Buoyancy
• Density
• Hydrostatics
• Pascal's law

Related Pages

• Archimedes
• Fluid dynamics
• Hydrostatic equilibrium

Forces on an immersed cube

Visual Illustrations

The following images provide visual representations of Archimedes' principle and related concepts:

Approximation of an arbitrary volume as a group of cubes

See Also

• Hydrostatic pressure
• Specific gravity
• Archimedes' screw