Buoyancy:
Buoyancy refers to the upward force exerted by a fluid on an object immersed in it. It is a result of the pressure difference between the top and bottom of the object. The concept of buoyancy was first discovered by the ancient Greek mathematician and scientist, Archimedes.

Archimedes Principle:
Archimedes Principle states that when an object is immersed in a fluid, it experiences an upward buoyant force equal to the weight of the displaced fluid. In other words, the buoyant force acting on an object is equal to the weight of the fluid it displaces.

Differences:

1. Definition:
- Buoyancy: Buoyancy is the upward force exerted by a fluid on an object immersed in it.
- Archimedes Principle: Archimedes Principle states that the buoyant force acting on an object is equal to the weight of the fluid it displaces.

2. Discovery:
- Buoyancy: The concept of buoyancy was discovered by Archimedes.
- Archimedes Principle: Archimedes Principle was formulated by Archimedes.

3. Force Calculation:
- Buoyancy: Buoyancy is the actual force experienced by an object when immersed in a fluid.
- Archimedes Principle: Archimedes Principle provides a theoretical framework to calculate the buoyant force based on the weight of the displaced fluid.

4. Application:
- Buoyancy: Buoyancy is a fundamental concept used in various applications such as shipbuilding, floating objects, and the behavior of submarines.
- Archimedes Principle: Archimedes Principle is a specific formula derived from the concept of buoyancy and is used to calculate the buoyant force in specific scenarios.

5. Fluid Interaction:
- Buoyancy: Buoyancy is a result of the pressure difference between the top and bottom of an object immersed in a fluid.
- Archimedes Principle: Archimedes Principle explains that the buoyant force is equal to the weight of the displaced fluid, regardless of the pressure difference.

6. Mathematical Representation:
- Buoyancy: Buoyancy is not represented by a specific mathematical formula but is generally calculated by subtracting the weight of the object in air from its weight in the fluid.
- Archimedes Principle: Archimedes Principle is mathematically represented as Fb = ρfluid * Vdisplaced * g, where Fb is the buoyant force, ρfluid is the density of the fluid, Vdisplaced is the volume of the fluid displaced, and g is the acceleration due to gravity.

In summary, buoyancy is a concept that refers to the upward force exerted by a fluid on an object, while Archimedes Principle is a specific principle derived from the concept of buoyancy, providing a mathematical formula to calculate the buoyant force.

Buoyancy is the tendency of water to pull any thing upward