Archimedes Principle

Archimedes principle deals with the forces applied to an object by fluids surrounding it. This applied force reduces the net weight of the object submerged in a fluid. In this article, let us familiarize ourselves with Archimedes principle.

What is Archimedes Principle?

Archimedes’ principle states that:

“The upward buoyant force that is exerted on a body immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid”.

The value of thrust force is given by the Archimedes law which Archimedes of Syracuse of Greece discovered. When an object is partially or fully immersed in a liquid, the apparent loss of weight is equal to the weight of the liquid displaced by it.

Archimedes Principle Explanation

If you look at the figure, the weight due to gravity is opposed by the thrust provided by the fluid. The object inside the liquid only feels the total force acting on it as the weight. Because the actual gravitational force is decreased by the liquid’s upthrust, the object feels as though its weight is reduced. The apparent weight is thus given by:

Apparent weight= Weight of object (in the air) – Thrust force (buoyancy)

Archimedes’s principle tells us that the weight loss is equal to the weight of liquid the object displaces.

Archimedes Principle Formula

In simple form, the Archimedes law states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. Mathematically written as:

Fb = ρ x g x V

Where F_b is the buoyant force, ρ is the density of the fluid, V is the submerged volume, and g is the acceleration due to gravity.

Archimedes Principle Derivation

The mass of the liquid displaced is.==

M a s s

D e n s i t y   ×   V o l u m e

ρ   ×   V

This is because density (ρ) is defined as==

D e n s i t y , ρ

M a s s /V o l u m e

M /V

Thus the weight of that displaced liquid is:===

W e i g h t

M a s s   ×   A c c e l e r a t i o n   d u e   t o   g r a v i t y

W

M   ×   g

ρ   ×   V   ×   g

Thus, from the Archimedes principle, we can write:

The apparent loss of weight = weight of water displaced = ρ×V×g

Thus, the Thrust force is,=T h r u s t

ρ   ×   V   ×   g

Where ρ is the density of the liquid and V is the volume of liquid displaced.

The thrust force is also called the buoyant force because it is responsible for objects to float. Thus, this equation is also called the law of buoyancy.