Archimedes Principle Formula

When we go swimming, we feel a little weightless in the water. The reason for this is that liquids exert an upward force to objects submerged in them. This is known as thrust and is a consequence of the difference in pressure a liquid exerts at different heights. As we submerge an object (considering it is fully submerged) deeper into a liquid, the pressure exerted by the liquid keeps on increasing but the thrust force remains the same. This article will explain the concept of buoyant force with the help of Archimedes Principle formula and examples. Let us learn the concept!

What is the Archimedes Principle?

According to the Archimedes’ principle: the upward buoyant force which is exerted on a body immersed in a fluid may be partially or fully submerged, will be equal to the weight of the fluid that the body displaces. Also, it acts in the upward direction at the centre of mass of the displaced fluid.

The value of this thrust force will be given by the Archimedes principle. It was discovered by Archimedes of Syracuse of Greece. When an object is partially or fully immersed in a liquid, then the apparent loss of weight will be equal to the weight of the liquid displaced by it.

Therefore, this principle says that the upward buoyancy force exerted on a body partially or completely immersed in a fluid will be equal to the weight of the fluid displaced. The Archimedes principle is a fundamental law of physics useful in fluid mechanics.

Source:en.wikipedia.org

The apparent weight of the body will be: Apparent weight= Weight of object in the air – Thrust force (buoyancy)

Archimedes principle states that this loss of weight will be equal to the weight of the liquid that the object displaces. If the object has a volume of V, then it will displace the same volume V of the liquid when we fully submerge it. Also, if only a part of the volume is submerged, then the object can only displace that much of liquid.

The Formula of Archimedes Principle

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:

\(F_b = \rho \times g \times V\)

\(F_b\)	buoyant force
\(\rho\)	the density of the fluid
V	submerged volume
g	acceleration due to gravity

We also know the thrust force as the buoyant force as it is responsible for objects to float. Thus, this equation is the law of buoyancy.

Solved Examples for Archimedes Principle Formula

Q.1: Determine the resulting force using the Archimedes Principle Formula, if a steel ball of radius 6 cm is immersed in water. Assume the density of lead as \(7900 kg m^{-3}\).

Ans: Given parameters in the question

Radius of the steel ball, r = 6 cm = 0.06 m

Thus Volume of the steel ball will be,

\(V = \frac{4}{3} \pi r^{3}\)

i.e. \(V = \frac{4}{3} \pi (0.06) ^{3}\)

thus, \(V = 9.05 \times 10^{-4}   meter^3\)

Density of water, \(\rho  = 1000 kg m^{3}\)

\(g = 9.8 m s^{2}\)

Now, the formula for Archimedes principle is:

\(F_b = \rho \times g \times V\)

\(= 1000 kg m^{3} \times 9.8 m s^{2} \times (9.05 \times 10^{-4}   meter^3)\)

= 8.87 N

Thus resulting force will be 8.87 N.