Derivation of the Formula
After rearranging the formula ρV is the density of the displaced fluid multiplied by the volume of the displaced fluid, and we know the mass, density, and volume relation.
m = ρV
That means the term ρV corresponds to the mass of the displaced fluid.
Fb = ρ × g × V
Fb = mg i.e., The mass of the displaced fluid times the magnitude of the acceleration due to gravity is just the weight of the displaced fluid.
Fb = W
The above equation, when stated in words called Archimedes’ principle. Assuming Archimedes’ principle to be reformulated
Apparent immersed weight = weight – Weight of displaced fluid
Then inserted into the quotient of weights, which has been explained by the mutual volume.
The density of the immersed object relative to the density of the fluid can be calculated:
Fb = PA = g ρ V = ρ g h A ⇢ (i)
- P = pressure
- Fb = force of buoyancy in Newton,
- A = Area in meter square,
- g = acceleration due to gravity,
- h = Height at which force acts taken from the surface
- p = density of the fluid,
- V = volume of the object inserted into the fluid.
Fb = Wa – Wf ⇢ (ii)
- Fb = force of buoyancy
- Wa = Weight of the object in the air
- Wf = Weight of the object when it is immersed in the fluid
Using (l) and (ll),
g ρ V = Wa – Wf ⇢ (iii)
If the object is not sinking, then Fg – Fb:
Mg = ρ g V
Buoyant Force
Buoyancy is a phenomenon due to the buoyant force that causes an object to float. When you put an object in a liquid, an upward force is exerted on the object by the liquid. This force is equal to the weight of the liquid that has been displaced. The amount of liquid that has been displaced depends upon the density and the volume of the object immersed in the liquid. Have you ever wondered why an iron nail sinks in water, but a ship made up of iron floats? And why does an iron ball sink but a plastic ball of the same size floats in water? These wonders happen due to the phenomenon known as Buoyancy. Let’s learn the buoyancy definition, buoyancy equation, and its examples in detail.
Table of Content
- What is Buoyant Force?
- What causes Buoyant Force?
- Archimedes’ Principle
- Formula for Archimedes’ Principle
- Derivation of the Formula
- Demonstration of Buoyant Force
- Why does an Object float or sink in the water?
- Types of Buoyancy
- Applications of Buoyancy
- Solved Examples on Buoyancy
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