Name: A Formal Proof of Archimedes' Principle
Uploaded: 2019-07-19
Duration: 4 min 58 s
Description: Is Archimedes' principle just experimental, or can it be proved mathematically, as well? Watch the video to understand a mathematical proof of Archimedes' pr...

Question

What is a fluid? Show that fluid exerts pressure. Prove that if a liquid is in equilibrium then the force acting on it is perpendicular to its surface.

Accepted Answer

The term fluid refers to a substance which has no definite shape of its own, and assumes the shape of the containing vessel. It has the ability to flow. Thus, the term fluid applies to both liquids and gases.

When a fluid is kept in a vessel, the molecules of the fluid, due to thermal agitation, are in random motion and are continuously colliding with the walls of the vessel and rebounding from them. Thus, they suffer change in momentum, transferring some momentum to the walls. The rate of change of momentum of the walls is equal to the force, or thrust, of the fluid exerted on the walls of the vessel.
In the same way, when an object is submerged in a fluid, say a liquid at rest, the liquid exerts a force on the surfaces of the object.

This force is always ‘normal’ to the surface. If this were not so, there would have been a component of force tangential to the liquid surface. Since the liquid is at rest, it cannot withstand any tangential force (because if a tangential force is applied to a liquid, it begins to flow).

Hence, the tangential component of the force should necessarily be zero. In other words, the force exerted by a fluid at rest has to be perpendicular to the surface in contact with the fluid.

What is a fluid? Show that fluid exerts pressure. Prove that if a liquid is in equilibrium then the force acting on it is perpendicular to its surface.

Important Questions on Fluid Pressure

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