Archimedes' Principle

Since hydrostatic pressure increases with depth, when a body is submerged in a fluid each part of it is subjected to a different pressure. Therefore there is an unbalanced force pointing upwards acting on it. This force is called buoyant force.

In order to calculate the magnitude of the buoyant force we can carry out the thought experiment depicted in the figure above. We can “remove” the submerged object and consider the volume of fluid that it occupied. The pressure at each part of the “fluid body” has to be exactly the same as the pressure acting on the different parts of the body. And since the “fluid body” is at rest the magnitude of the buoyant force acting upwards on it must equal its weight.

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Archimedes of Syracuse, in his book On Floating Bodies, written around 250 BCE, stated:

The buoyant force on a submerged object is equal to the weight of the fluid displaced.

This is known as the Archimedes’ principle.

From Archimedes’ principle it follows that bodies of equal volume will experience equal buoyant forces. However, not all of them will float because their weights will be different depending on their density. Heavier objects will sink and lighter objects will float.

That’s the reason why a boat floats by if we throw in the ocean a block of the same material having the same mass, it will sink. The boat, due to her shape, displaces a larger volume of water thus the magnitude of the buoyant force acting on her will be larger (see figure below).

If we call F the buoyant force acting on the body, when it floats its weight must equal F:

And at equilibrium:

The density of a body determines whether it will float or sink when placed in a liquid. If it is less dense than the liquid, it will float. If it is denser than the liquid it is placed in, it will sink. But the buoyant force will be the same . In the figure below the three possible situations are shown.

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