 Share facts or photos of intriguing scientific phenomena. # Archimedes' Principle of Flotation

You must have seen huge ships sail on sea, or a hot air balloon rise high up in the air. But have you ever wondered how? Well, the answer to this can be found in the Archimedes principle of flotation and that's exactly what this article is all about. So, read on...
Mukulika Mukherjee
Last Updated: Mar 6, 2018
Archimedes was one of the greatest mathematicians of all times. He was a Greek mathematician who was also a physicist, scientist and a great inventor. Born in 287 B.C. in Sicily, Archimedes had many great inventions to his credit before his death in 212 B.C. His most famous inventions include the screw propeller and the principle of flotation, among others. His mathematical works include inventing infinitesimals and formulas on measurement of a circle, parabolas, spheres, cylinders and cones.
The one theorem that he considered to be his most prized and valuable achievement, is the one which states that if you have a sphere and a cylinder of the same height and diameter, then the volume and the surface area of the sphere will be 2/3 of that of the cylinder, with the surface area of the cylinder inclusive of the surface areas of its bases. However, the principle of flotation remains one of his most popular inventions.
Principle of Flotation by Archimedes
Ever wondered how huge ships manage to stay afloat in water, while a small iron nail sinks? Puzzling as it may appear, you can easily explain this, and many other similar phenomena, with the help of the Archimedes' Principle of Flotation. So, what is the Archimedes' Principle all about?
Principle of Flotation: Definition
The Archimedes' principle states that any object, wholly or partially immersed in a fluid, experiences an upward force equal to the weight of the fluid displaced by it.
Here the term 'fluid' refers to all liquids and gases. For an object that is completely submerged in a fluid, the weight of the fluid displaced by it, is less than its own weight. On the other hand, for an object that floats on the surface of the fluid, the weight of the fluid displaced by it, is equal to the weight of the object. Now, the upward force experienced by the body is termed as the buoyant force. Thus,

Buoyant force = weight of the fluid displaced by the body
Now, the weight of the fluid displaced by the body is directly proportional to the volume of the displaced fluid, since the density of the fluid is constant. This can be illustrated by the following equations.

Weight = Mass x g (where g is the acceleration due to gravity and is a constant)

and

Mass = Density x Volume

Thus, we can say

Weight = Density x Volume x g
From the above equation, we can conclude that a body shall float in a fluid under any of the two conditions.
• The density of the body is less than the density of the fluid.
• The volume of the fluid displaced by the immersed part of the body is such that its weight is equal to the weight of the body.