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Physics Formulas

Buoyancy Formula

Let us do one small experiment. Go to a swimming pool and jump on in. While we are underwater, we may note that it is easy to lift the entire weight of our bodies. This is because of something we may experience in the water called the buoyant force. It is the upward force of a fluid. Buoyancy is an easy concept to understand about pressure in a fluid. In a fluid may be a gas or a liquid, pressure increases with depth. Learn the buoyancy formula here.

Buoyancy Formula

What is Buoyancy?

Not only does the buoyant force create an upward lift on an object in a fluid, but it is also equal to the weight of the fluid displaced by that object. This was discovered by Archimedes during the 3rd century B.C. So, we call this as Archimedes’ Principle. It’s important to remember that we are talking about fluids, so both liquids and gases, like water and air.

Imagine that we have a full glass of water. It’s so full that if we put anything else into it, the water will spill over the top of the glass. If we were to collect the water which spills out, we would find that this is the same volume as that of the object we put into the glass.

This is what we mean by displacing the fluid and it is a simple way to measure the volume of an irregularly shaped object also. Therefore we can say that the buoyant force is equal to the weight of this displaced fluid, and not the weight of the object itself.

This means that if the weight of the submerged object itself is equal to the buoyant force (the weight of the displaced fluid), then the object will neither sink nor float. If the weight of the object is more than the buoyant force, then the object will sink. And, if the weight of the object is less then it will rise to the surface and float.

Therefore, buoyancy is the phenomenon stated by Archimedes, which says the object experiences the upward force when it is completely or partially submerged in a liquid.

Buoyant Force formula

Buoyant force in terms of pressure is given as:

\( F_b = PA\)

Where,

\(F_b\) Buoyant force
P Pressure
A Area

Using area, height and volume, the formula is:

\( F_b = \rho \times g \times h \times A \)

Where

\(F_b\) Buoyant Force
\(\rho\) Density of liquid
g The acceleration due to gravity
V The volume of the part of the body immersed in the fluid
h The height of the immersed part
A Area

Solved Examples

Q.1: An ice cube of density \( 0.5 gcm^{-3} \) has a Buoyant force of 9 N. It is immersed in water. Calculate the volume of the ice cube.

Answer:

Density of ice, \( \rho = 0.5 gcm^{-3}\) ,

Buoyant force,

\(F_b = 9 N\) ,

Now apply the formula,

\( F_b = \rho \times g \times h \times A \)

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

\(V = \frac{F_b}{\rho \times g} \)

Putting the values,

\(F_b = \rho \times g \times h \times A \)

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

\(V = \frac{F_b}{\rho \times g} \)

= \( \frac{9}{9.8 \times 0.5 \times 10^{-3}}\)

= 1836 cm³

Thus volume is 1836 cm³.

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