Archimedes Principle & Buoyancy force (Basic Concept of Fluid Mechanics Part-2)

Have you ever given a thought whenever you place a body over water it either sinks or floats? But why? 

Let’s understand why.

Archimedes Principle

According to Archimedes principle whenever a body is placed in liquid( completely immersed or partially in liquid), it is lifted by force equal to weight of fluid displaced by the body.

Buoyancy: When a body is submerged in the fluid then an upward force is exerted by the fluid on the body that force is called buoyancy.

The upward force is equal to the weight of the fluid displaced by the body

Let’s see a case where a cylindrical object is partially submerged in the water.

Buoyant force: Weight of fluid displaced by body.

Buoyant force on cylinder: Weight of fluid displaced by cylinder

 

F = ρ*g*volume of fluid  displaced

Volume of fluid displaced will be the volume of cylinder that is submerged in the water.

→ F = ρ*g*volume of cylinder submerged inside the fluid.

When body floats?

According to archimedes principle,body will float if weight of the body is equal to the buoyant force.

In above image cylinder is floating that means

Centre of buoyancy:It’s like center of gravity but for the portion of body that is submerged in the water or in other words point at which buoyant force acts is called centre of buoyancy.

Metacentre:If a body if floating in liquid and given a small angular displacement, it starts oscillating. Point about which the body is oscillating is called metacentre.

Stability of submerged body

1. Stable equilibrium

When the center of buoyancy lies above the center of gravity, submerged body is in stable equilibrium.

2. Unstable equilibrium

When the center of buoyancy lies below the center of gravity, submerged body is in unstable equilibrium.

3. Neutral equilibrium

When both centers of buoyancy lie & center of gravity lie at the same point, submerged body is in neutral equilibrium.

Stability of floating body

1. Stable equilibrium

When a body is given a small angular displacement by external means and if the body comes to its original position due to internal forces then it is in stable equilibrium.

2. Unstable equilibrium

When a body is given a small angular displacement by external means and if the body does not comes to its original position due to internal forces then it is in unstable equilibrium.

3. Neutral equilibrium

When a body is given a small angular displacement and it set on new position instead of oscillation then it is in neutral equilibrium.

 

Relationship between Cebtre of buoyancy B, Centre of gravity G,  Metacentre M is given by 

Where,

GM = Distance between centre of gravity and metacentre

BG = distance between centre of buoyancy and cetre of gravity

I = least moment of inertia of plane of body at water surface

V = volume of submerged part of the body

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