13.9:
Archimedes’ Principle
Consider an object at rest, completely immersed in a fluid. It displaces an equal volume of fluid to occupy that space.
An upward buoyant force keeps the object stationary.
If the object is removed from the fluid, the space gets filled by the same volume of fluid earlier displaced by it.
This fluid volume is now acted upon by the same buoyant force earlier acting on the object. Since the fluid volume is at rest, the buoyant force is balanced by its weight.
Thus, the magnitude of the buoyant force acting on an object in a fluid equals the weight of the fluid displaced by it. This is known as Archimedes' Principle.
Mathematically, the buoyant force is equal to the product of mass of the fluid displaced and the acceleration due to gravity.
Using the relationship between mass and density, the buoyant force can also be represented as the product of density of fluid, volume of displaced fluid, and the acceleration due to gravity.
13.9:
Archimedes’ Principle
Archimedes' principle states that an upward buoyant force exerted on a body that is immersed partially or entirely in a fluid is equal to the weight of the fluid displaced by it. To understand how much buoyant force is needed to make an object float, let us think about what happens when a submerged object is removed from a fluid. If the object were not in the fluid, the space occupied by the object would be filled by the fluid having a weight wfl. This weight is supported by the surrounding fluid, so the buoyant force must equal to wfl, the weight of the fluid displaced by the object.
This principle is named after the Greek mathematician Archimedes (ca. 287–212 BCE), who stated this principle long before the concepts of force were well established. Archimedes' principle refers to the force of buoyancy that results when a body is submerged in a fluid, whether partially or wholly. The force that provides the pressure of a fluid acts on a body, perpendicular to the surface of the body. In other words, the force due to the pressure at the bottom is pointed up, while at the top, the force due to the pressure is pointed down; the forces due to the pressures at the sides are pointing into the body. Since the bottom of the body is at a greater depth than the top of the body, the pressure at the lower part of the body is higher than the pressure at the upper part. Therefore, a net upward force acts on the body. This upward force is buoyancy.
This text is adapted from Openstax, University Physics Volume 1, Section 14.4: Archimedes’ Principle and Buoyancy.