 # What is Buoyant force? Formula, Examples, Uses

If we throw some balls of different weight in a container filled with water or pond or swimming pool, we can see some balls will float and some will sink. Why this happens? This is the effect of buoyant force. Now, the question is what is buoyant force?

Take another example, when we get into a pond or swimming pool, we feel lighter, it is easy to float. Now think, your waterproof wrist-watch has dropped in the deepest part of the swimming pool. You need to put a lot of effort to get the wrist-watch back. Because the more you go deeper the more upward force you feel. This happens because of the buoyant force applied by water on you.

## What is Buoyant force?

Buoyancy is a force that enables objects to float on water. When an object is partially or fully immersed, this force is applied to it. The net upward force applied to the submerged or fully immersed body does not change with height. Fluid or gas exerts a buoyant force on both the upper and lower sides of an object, so when an object is forced to go deeper, the buoyant force increases on both side. The buoyant force is the difference between the exerted force on the lower side and upper side of an object.

## Unit of Buoyant force

As it is a force so SI unit of Buoyant force is Newton (N). According to Archimedes principle the amount of buoyant force is the weight of the displaced liquid, don’t write unit of buoyant force in terms of the unit of weight.

## Archimedes’s Principle

Greek mathematician Archimedes invented an excellent way with which anybody can calculate the buoyant force applied to anybody.

According to Archimedes,

Any partially or fully immersed object experienced an upward force i.e. buoyant force which is equal to the weight of the fluid displaced by the object.

## How Archimedes invented Buoyancy: the Eureka Moment

King Hiero II of Syracuse suspected that his crown is not made of pure gold. And the responsibly was given to Archimedes to prove if the crown was made of pure gold or mixed with other material. One day, Archimedes was bathing in a pool. He noticed that the more he was drowning the more water overflowed. That point stroked in his mind. He was running shouting Eureka!…. Eureka!… Archimedes made two crowns one with silver and other using pure gold keeping the same weight as the original crown. He sank the silver crown and pure gold crown in a tub full of water. He noticed that the amount of water overflowed was more when the silver crown was sunk.

Again he sank the original crown in the tub and found that the amount of water overflowed is more than that of water overflowed when the pure gold crown was sunk. Archimedes concluded that the original crown of a king is not made of pure gold, it was a mixture of gold and silver.

This is the story behind the famous word Eureka and invention of Buoyancy.

## Formula of Buoyancy

We stated earlier that, the fluid exerts buoyant force on both sides of any partly or fully immersed object. The amount of force applied to the upper part of any object is less that of the lower part. Suppose the net buoyant force applied on an object of length h is Fbuoyant , applied force on the upper part is Fupper and water is pushing the object with Flower from the lower side. Now,

Fbuoyant​=Flower​−Fupper

We know that pressure is equal to force divided by area. ie. P=F/A. or F=PA. Now put those value in the above equation, it will convert to:

Fbuoyant​=A(Plower – Pupper) ——(I)

Using Hydrodrasic pressure, P=ρgh, where ρ is the density of the fluid, g is the gravitational force. Now apply the formula to equation (I).

Fbuoyant​=Aρgh, where h is the height of object. And Ah is equal to volume of any object (V).

So, Fbuoyant​=Vρg, now the question arises, V represents what? the volume of object or volume of displaced fluid?

If the object is partially immersed, obviously the whole volume of the object is not using in this case volume of displaced fluid is to be considered. And for the fully immersed object, the same concept applies.

So, Fbuoyant​=Vfluidρg

## Formula of the Archimedes Principle

So we derived that Fbuoyant​=Vfluid ρg. Where ρ is the density of the displaced fluid, density is equal to mass divided by volume. (ρ=m/V) or m=ρV.

Fbuoyant​=mf g=Wf​, This is the formula derived from Archimedes Principle.

Archimedes’s principle states:

The upward buoyant force that is exerted on a body is equal to the weight of the fluid that the body displaces.

## Applications of Buoyancy

We see the application of buoyancy in swimming pool, pond, bathtub when we swim or drop any object on the water. Fluid and gas both exert buoyant force any objects immersed in it.

Ship

Ships are made in a scientific way so that the weight of the displaced fluid is large enough that can support the weight of the ship. The shape of a ship is hollow, this special construction let it to displace enough water so that amount of buoyant force becomes large.

Submarine

A submarine has three large tanks and these tanks help to control the movement of the submarine. The submarine will submerge when water will be filled in tanks, this makes submarine heavier than displaced water. By letting out water from tanks the submarine floats on the sea.

Hot Balloons

A burning board is attached to hot balloons that create pressure on air and it generates lift. When upward buoyant force is greater than the weigh of balloons, it starts to float on air.

Gas balloon are filled with helium gas that is lighter than air so buoyant force by atmospheric air makes the gas balloon afloat.

## Summary

So Buoyancy is one of the main aspects of fluid mechanics. Archimedes discovered it before Newton’s law on fluid. Many scientific invention is still going on this concept and theory.

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