Archimedes Principle

When a body is partially or fully dipped into a fluid, the fluid exerts force on the body. At any small portion of the surface of the body, the force by the fluid is perpendicular to the surface and is equal to the product of the pressure at the surface and surface area. The resultant of all these contact forces is called buoyant force (upthrust).

Let a body is immersed in a fluid of density σ as shown in the figure.

  F₁ = A(h₁ σg + p₀) and F₂ = A (h₂ σg + p₀)

As h₂ > h₁, hence F₂ > F₁

So, the body will experience a net upward force

  F = F₁ - F₂ = Aσg (h₂ - h₁) = A gσL

  = (AL) gσ =  V σg (V = volume of the body),

Hence, F = weight of fluid displaced by the body. This force is called buoyant force and acts vertically upwards (opposite to the weight of the body) through the centre of gravity of the displaced fluid.

Enquiry: If thrust on lower surface of an object immersed in a fluid is more, does the body experience a net force upwards?

  Yes, a body immersed in a fluid does experience net upward force. To understand this let us first analyse a fluid element. 

Illustration:

  Consider a stationary fluid in a container. Take a cylindrical volume of that fluid (as shown in figure) as a system. 

  Though this cylinder experiences the force of gravity due to its gravitational mass, it still remains stationary. This is so because the upward external force (P₂A-P₁A) balances the gravitational pull.

  A similar exercise can be carried out to show that the forces on the curved surface cancel each other. If an object is immersed in a fluid, it also experience an upward external force (P₂A-P₁A) which is known as the buoyant force. Whether a body floats or sinks, depends on the fact that whether the buoyant force is able to balance the weight or not.