Chapter 21: Buoyancy and Archimedes’ Principle

21.1 Introduction to Buoyancy

Buoyancy describes the upward force exerted by a fluid on an object that is partially or completely submerged. This force is responsible for objects appearing to weigh less in fluids and for objects floating or sinking.

21.2 Basic Understanding of Buoyancy

Buoyancy occurs due to the pressure difference exerted by a fluid on an object submerged in it. The pressure in a fluid increases with depth, so the pressure on the bottom surface of an object is greater than the pressure on the top surface, resulting in an upward force. This upward force is called the buoyant force.

21.3 Archimedes’ Principle

Archimedes’ Principle states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object. Mathematically, it can be expressed as:

where is the buoyant force, is the density of the fluid, is the volume of the fluid displaced by the object, and is the acceleration due to gravity.

Note: When fully submerged, is just the volume of the object itself.

In simpler terms, Archimedes’ Principle implies that the buoyant force on an object is equal to the weight of the fluid it displaces. This principle applies to both fully and partially submerged objects, as well as floating objects.

Though this may sound simple, it often ends up acting counter to intuition. Take this example. Two boxes of equal dimensions are both submerged in water. One has a mass of 1000 kilograms, the other has a mass of only 1 kilogram. However, the buoyant force acting on each box will be exactly the same because we specified that both boxes are of equal dimensions. The density of the submerged object has nothing to do with the buoyant force. The only factors affecting are those given above.

21.4 Factors Affecting Buoyancy

Several factors influence the buoyant force on an object:

1. Density of the fluid: The buoyant force is directly proportional to the fluid density. Objects will experience a greater buoyant force in denser fluids, such as saltwater, compared to less dense fluids, like freshwater.
2. Volume of the displaced fluid: The buoyant force is directly proportional to the volume of the fluid displaced by the object. Larger objects will displace more fluid and experience a greater buoyant force.
3. Acceleration due to gravity: The buoyant force is directly proportional to the acceleration due to gravity. An object’s buoyant force will be less on the Moon than on Earth, for example, due to the lower acceleration due to gravity.

Remember: The density of the object does not affect the buoyant force. Thus, if two boxes of equal dimensions are submerged in water, both will experience the same magnitude buoyant force pushing upward even if one box has a mass a thousand times greater than the other.

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Continue to Chapter 22: Momentum, Impulse, and Collisions

Back to Chapter 20: Introduction to Fluid Mechanics

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