Do you know the Eureka story ? The story of how this word became famous. Do you know the man who was behind the word becoming famous ? Have you heard about Archimedes’ before ? Many of us have heard something called Archimedes’ Principle. Actually this story is what is believed to be the base for Archimedes’ Principle.

Let me tell you the story behind the word “Eureka”

Archimedes’ is a Greek mathematician, physicist, inventor, engineer and an astronomer. A multi talented personality. One of the great Scientists, the world has witnessed. He lived in Syracuse, Italy when the following incident which I am going to narrate happened. Hieron was the king of Syracuse at that point of time. He won a great war around 250BC. After winning the war, he wanted to thank the gods by placing a Wreath shaped golden crown on the statue of the God, he had in his palace. Wreath is nothing but the type of crown, the Greek kings used to wear in their heads which has leaf shaped designs covering the whole crown.

So he called out to a goldsmith and gave him a particular amount of Gold coins with calculated weight to make this wreath shaped crown. Let us now assume it as 1 Kg now. So this goldsmith takes the gold coins home and he designs and makes the crown as like how the King asked him. After some days, he brings it to the king and gives it to him. The King weighed the crown which the goldsmith gave him and it was exactly the same weight as the gold coins, meaning 1 Kg as we assumed. But still the King was not satisfied with the colour of the Crown and also he started hearing rumours about how the goldsmith had stolen some amount of gold coins and mixed the remaining gold with some other metals like silver to compensate the weight. King was so pissed off on hearing this and he wanted a solution on this problem.

He thought his best philosopher cum scientist, Archimedes’ was the best person to solve this problem. So, he called out to Archimedes’ and explained him what the problem was. Archimedes’ after realizing how serious this problem was, since the king himself requested him for help started thinking about finding a solution for this at each and every minute of the day. He thought about a lot of ways over a long period of time to find out if the gold crown was made completely using all of the gold coins that the king gave, but he could not find it.

One evening, when he was about to take bath in his bath tub. He was thinking about the same problem which is yet to be solved since long time. Since he was now lost in thoughts he never noticed that the water in the tub is filled to the brim (means till the edge of the tub).

When he kept his leg inside the tub, he got slipped and he fell inside it. At that time he noticed what was happening with the water and the tub and he found the solution for the King’s problem of the crown. After realizing the potential solution, without realizing he was naked, he started shouting “Eureka! Eureka!” and ran in the streets of Syracuse naked towards the king’s palace. That is where the word “Eureka!” got famous. Eureka is nothing but “I have found it” in Greek language. So, People started using this word prominently whenever they found a solution to their long lasting problem or at a breakthrough moment etc. Archimedes’ falling and getting up from his bath tub and running naked on the roads is what is called the “Eureka Moment”.

So now coming back to the story, when Archimedes’ fell into the tub of water, the water got displaced. He understood that Volume of water displaced is equal to the volume covered by the object getting immersed in the water. He knows that different metals of the same weight have different volumes. And Objects, put in water, will displace water. Thus the displaced water will be equal to their original volume.

As we all know,

Density of an object is equal to its mass per unit Volume. And as we know Density of gold is equal to 19.32 g cm^3.

So,

Density = Mass/Volume

Density of Gold Crown, D1= M1/V1

Density of Gold coins, D2= M2/V2

So Archimedes’ now knows as per King’s information that the weight/Mass of both Gold crown and Gold Coins are the same.

So,

M1 = M2

They cancel each other.

So, D1V1 = D2V2

And since Density of gold is always a constant,

Thus,Volume V1 should be equal to Volume V2, meaning the Volume of gold crown should be equal to the Volume of Gold coins and vice versa (If Volume is equal then it’s density is the equal).

In those Old times, there were no instruments to measure the Volume of the objects directly. So, Archimedes’ tried to use this water displacement idea.

Since Volume of the Object immersed in water should be equal to the Volume of water displaced which he got to know by accident while bathing, he devised an experimental setup based on this with two small vessels filled with water to the brim and both the vessels were placed inside another larger vessel so that the water displaced will get stored into the larger vessel where this small vessel is kept. Then he picked up the Gold crown and Gold Coins and dropped them in the respective vessels of water. The water got displaced and it got stored in the outer vessel. Then when he measured the quantity of displacement of water in both vessels. He found that the Vessel of water immersed with Gold crown displaced more water than the vessel of water immersed with Gold coins. Thus it is clear that there are some impurities in that Gold crown. It has some other metals mixed in it’s composition. He made this conclusion because, when the Volume of water displaced is not equal, then the density of the objects is not equal. The mass of atoms, their size, and how they are arranged determine the density of a substance. Thus density of an object is a constant value. The only way it changes is when it is mixed with other metals and its composition is changed.

Thus Archimedes’ found the solution to the problem that the Golden Crown is actually not made of pure gold and the Goldsmith had stolen some of the golden coins that the king gave. King called out for the goldsmith and asked an explanation on this and the Goldsmith confessed his crime. Thus Archimedes’ proved to the world about his geniusness again.

This also served as a base for his principle, “Archimedes’ Principle”. Archimedes’ Principle is nothing but “The upward Buoyant force exerted on an object immersed in a fluid, whether partially or fully immersed, is equal to the weight of fluid that the object displaces”. This is the fundamental principle of fluid mechanics. But the basis for this is the Eureka moment.

Archimedes’ principle allows the buoyancy of an object partially or fully immersed in a fluid to be calculated. The downward force on the object is simply its weight. The upward, or buoyant force on the object is that stated by Archimedes’ principle, above. Thus, the net force on the object is the difference between the magnitudes of the buoyant force and its weight. If this net force is positive, the object rises, if negative, the object sinks and if zero, the object is neutrally buoyant – that is, it remains in place without either rising or sinking. In simple words, Archimedes’ principle states that, when a body is partially or completely immersed in a fluid, it experiences an apparent loss in weight that is equal to the weight of the fluid displaced by the immersed part of the body.

Weight of the displaced fluid (proportional to) Weight of the object in fluid.

So, Weight of displaced fluid = Weight of the object in Vaccum – Weight of the object in fluid.

This serves as the base for many things like swimming, Ship Mechanisms etc. This is the most basic principle of Fluid mechanics.