Archimedes' principle tells us that a body immersed in fluid experiences a buoyant force acting at the gravity center. The principle states that the buoyant force that is exerted on the object is equal to the weight of the displaced fluid.
This force is apparently a loss in the weight of the object. However, in reality, it is due to the pressure that the fluid exerts on the surface of the submerged object.
Archimedes' principle was discovered by Archimedes of Syracuse. He was a Greek mathematician, and engineer who lived in the 3rd century BC. C. According to legend, he discovered this principle while bathing.
What is Archimedes' principle?
Archimedes' principle is a physical law that describes the behavior of bodies floating and submerged in a fluid.
According to Archimedes' experiment, the volume of the displaced fluid is equal to the volume of the submerged object. At the same time, according to this principle, the submerged body experiences an upward buoyant force equal to the weight of the volume of fluid displaced.
This force, known as "thrust," is produced when fluids interact with solid objects. As a result, the fluid exerts pressure on each portion of the object's surface. Thrust is the sum of all these pressures per unit area and is applied at the center of gravity of the object under study.
The weight corresponding to the displaced fluid is equal to the product of gravity’s acceleration by the fluid density by the volume of this portion.
What is a fluid?
A fluid is a substance that flows continuously, either in a gaseous or liquid state. Fluids can be common liquids (such as water), gases (such as air), and special fluids (such as lubricating oils).
How does Archimedes' principle work?
Imagine that you are in a swimming pool floating, that is, partially submerged. According to Archimedes' principle, you are experiencing an upward force equal to the weight of the water you have displaced.
In other words, the force that gravity exerts on you is equal to the weight of the water displaced by you.
How is buoyant density determined?
To know if an object floats or not, you need to know the density of the object and the density of the fluid that surrounds it.
According to Archimedes' principle, if the object is lighter than the fluid (has lower density), it will float in it. In contrast, if it is heavier (has higher density), the object sinks because the thrust cannot counteract the force of gravity.
Archimedes principle experiment
King Hieron II of Syracuse asked the goldsmith to create a gold crown but had a suspicion that the material inside was not pure gold. To corroborate it, he asked Archimedes to devise a manual method to test whether it was entirely gold or included some cheaper material.
Archimedes attempted to solve this problem but was initially unable to find a way. Then, according to legend, the solution came to him while he was bathing. Sitting in the bath, he noticed the rising water level and was inspired by this.
This experiment allowed him to know the crown's volume by measuring the volume of displaced water. Then, by dividing the volume displaced by the crown's weight, he obtained the density of the crown.
Observing that the density obtained did not match the density of gold, he confirmed that the king's suspicions were correct.
Applications of Archimedes' principle
Archimedes' principle can be used in a myriad of applications; among them, we highlight the following:

First, determine the volume of irregular objects, such as those found in nature.

Using a spring balance, we can calculate the density of the objects.

Calculate the forces required to lift heavy objects, especially in architecture and engineering.
Practical examples of Archimedes' principle
Archimedes' law is one of the essential physical principles and is present in everyday life in many ways. Here are some practical examples of Archimedes' principle:

When swimming, the human body receives an upward push equal to the weight of the water it displaces.

A ship in the sea floats because the volume of the water it displaces is equal to that of the ship. The weight of the object  in this case, the boat  is counteracted by the upward thrust of the water. Knowing the density of water is easy to calculate the maximum weight a cargo could bear.

Hot air balloons are held in the air by Archimedes' principle. In this case, the fluid is air, and the balloon is completely submerged in the air whose density is greater than hot air. Therefore, the hot air balloon experiences a vertical thrust due to the weight of the displaced air that is greater than the weight of the whole balloon.

Icebergs float because frozen water has a slightly lower density than liquid water. Therefore, according to Archimedes' principle, the total weight of the iceberg is equal to the weight of the water that would occupy the submerged part of the iceberg.