Archimedes’ Principle Formula
When the object is immersed in the fluid, the object feels lighter due to the loss of apparent weight which is equal to the weight of the fluid displaced by the liquid.
FB = ρ × VL × g
Where,
- FB is the Upward Thurst or the Buoyant Force
- ρ is the Density of the Fluid
- VL is the Volume of the Fluid Displaced
- g is the Acceleration Due to Gravity
Archimedes Formula Derivation
Lets take a cylinder ‘PQRS’ with upper surface ‘PQ’ and lower surface ‘RS’, dipped in a liquid of density DL the height of the cylinder is ‘h’ and it is at a depth ‘d’. Since the depth at PQ is d and at RS is (d+h)
Using the formula for pressure (P = ρ × h × g)
PPQ = DL × d × g
PRS = DL × (d+h) × g
According to the laws of liquid pressure, pressure at a point inside the liquid increases with the depth from its free surface.
So, PPQ < PRS
According to the laws of liquid pressure, liquid pressure is the same in all directions about a point in a liquid. So, there will be an upward force acting on the bottom surface RS, which is the Upthrust or Buoyant Force
FB = P × A where P is Pressure and A is Area
FB = (PRS – PPQ) × A
FB = ((DL × (d+h) × g) – (DL × d × g)) × A
FB = DL × g × ( d + h – d) × A
FB = DL × g × Ah
FB = DL × g × Vo …………….. Volumeobject = volume of cylinder = Area × height
FB = DL × VL × g …………….. Volumeobject = Volume liquid displaced
Archimedes Principle Cases
There are three possible cases as per Archimedes Principle, these cases are mentioned below:
Case 1: If the FB = Weightobject then the object will float in completely submerged position;
Case 2: If FB > W then the object will float;
Case 3: When FB < W then the object will sink.
Archimedes Principle and Buoyancy
Archimedes Principle in simple words states that when an object is immersed in water it displaces the amount of liquid weight of the object. When object is immersed it experiences an upward force called buoyant force. The magnitude of this buoyant force is equal to the weight of the object immersed.
Archimedes Principle
Archimedes Principle is a fundamental concept in fluid mechanics, credited to the ancient Greek mathematician and physicist Archimedes. According to Archimedes’ Principle, when an object is immersed in a fluid the object experiences an upward force whose magnitude is equal to the weight of the fluid displaced by the object.
Archimedes’ principle has applications in various fields, from ship design to understanding the behavior of objects in water. Archimedes’ Principle is important for class 9 students.
In this article, we are going to learn about what is Archimedes Principle, its formula, how to derive it, its application, and its experimental verification of Archimedes
Table of Content
- What is Archimedes’ Principle?
- Experimental Verification of Archimedes’ Principle
- Archimedes’ Principle Formula
- Applications of Archimedes’ Principle
- Solved Examples