According to the Archimedes principle a body totally or partially immersed in a fluid will be lifted up by a force equal to

Understanding Archimedes' Principle

Archimedes' Principle states that any object, either fully or partially submerged in a fluid, experiences an upward buoyant force that is equal to the weight of the fluid that is displaced by the object.

Mathematical Representation

The force $F_b$ (buoyant force) can be mathematically expressed as:

$F_b = \rho \cdot V_{displaced} \cdot g$

Where:

• $F_b$ is the buoyant force.
• $\rho$ is the density of the fluid.
• $V_{displaced}$ is the volume of fluid displaced by the submerged part of the body.
• $g$ is the acceleration due to gravity (approximately $9.81 \, \text{m/s}^2$ on the surface of the Earth).

Summary

Thus, according to Archimedes' Principle, the upward buoyant force acting on a body immersed in a fluid is equal to the weight of the fluid displaced, which can be calculated using the formula derived above. This principle is fundamental in understanding buoyancy and fluid dynamics, impacting various applications in engineering and science.