Short Answer:

Archimedes’ principle states that when a body is fully or partially immersed in a fluid, it experiences an upward force known as buoyant force, which is equal to the weight of the fluid displaced by the body.

In simple words, Archimedes’ principle explains why objects float or sink in a liquid. If the weight of the fluid displaced by an object is equal to or greater than the object’s weight, it will float. This principle is used in ships, submarines, hydrometers, and other floating devices.

Detailed Explanation :

Archimedes’ Principle

Archimedes’ principle is one of the fundamental laws of fluid mechanics. It was discovered by the Greek scientist Archimedes more than 2,000 years ago. This principle helps to explain how and why objects float or sink when placed in a fluid, such as water or air.

According to Archimedes’ principle:

“A body wholly or partially immersed in a fluid experiences an upward force equal to the weight of the fluid displaced by the body.”

This upward force is called the buoyant force or upthrust. It always acts in the upward direction, opposite to the direction of gravity.

When an object is immersed in a liquid, the fluid exerts pressure on all sides of the object. The pressure at the bottom of the object is greater than the pressure at the top because pressure increases with depth. This difference in pressure creates a net upward force on the object, which is the buoyant force described by Archimedes’ principle.

Explanation of Archimedes’ Principle

To understand the principle more clearly, consider an object submerged in a container filled with water. The object pushes some of the water away, or we can say it displaces a certain volume of water.

The fluid displaced by the object has a weight. According to Archimedes’ principle, the buoyant force acting on the object is equal to this weight of displaced fluid.

• If the buoyant force is equal to the weight of the object, the object floats.
• If the buoyant force is less than the weight of the object, the object sinks.
• If the buoyant force is greater than the weight of the object, the object rises in the fluid.

This simple law helps us understand how ships float on water even though they are made of heavy materials like steel, and why some objects sink.

Mathematical Expression of Archimedes’ Principle

Let,

•  = Buoyant force
•  = Density of the fluid
•  = Volume of fluid displaced
•  = Acceleration due to gravity

Then the buoyant force is given by:

According to Archimedes’ principle, this buoyant force is equal to the weight of the displaced fluid. Hence,

This equation shows that the buoyant force depends on the density of the fluid and the volume of fluid displaced by the object.

Applications of Archimedes’ Principle

Archimedes’ principle has a wide range of applications in engineering and daily life:

1. Design of Ships and Boats:
   Ships are designed with large hollow hulls so that they displace a large volume of water, producing enough buoyant force to keep them afloat even though they are heavy.
2. Submarines:
   Submarines can rise or sink by controlling the amount of water in their ballast tanks. By increasing or decreasing the weight of the displaced water, they change their buoyancy.
3. Hydrometers:
   Hydrometers work on Archimedes’ principle to measure the density of liquids. The level at which a hydrometer floats indicates the liquid’s density.
4. Hot Air Balloons:
   The principle applies to gases as well. A hot air balloon rises because the hot air inside it is less dense than the surrounding cooler air, providing an upward buoyant force.
5. Floating and Sinking of Objects:
   It helps explain why some objects like wood float in water, while others like stones sink, depending on their densities relative to water.

Importance of Archimedes’ Principle

Archimedes’ principle is one of the most practical concepts in fluid mechanics because it explains the concept of buoyancy — the reason objects float or sink. It is also useful for determining the density and specific gravity of solids and liquids.

Engineers use this principle to design ships, submarines, and other floating structures that are stable and safe. It also finds applications in fluid measuring instruments, oil storage tanks, and aeronautical design.

Archimedes’ discovery laid the foundation for the study of hydrostatics and the modern understanding of fluid behavior.

Conclusion

Archimedes’ principle states that a body fully or partially immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by it. This principle explains the floating and sinking of objects and has wide applications in engineering, science, and everyday life. It is used in the design of ships, submarines, hydrometers, and other fluid-based systems. Thus, Archimedes’ principle is a key concept that connects fluid mechanics with practical engineering solutions.