Pascal’s Law

Pascal’s Law

It states that the increase in pressure at one point of the enclosed liquid in equilibrium of rest is transmitted equally without loss to all other points of the liquid and also to the walls of the container, provided the effect of gravity is neglected.

Proof.

Let us consider that an incompressible liquid is filled in a spherical vessel having 4 cylindrical tubes A, B, C and D which are fitted with frictionless pistons having cross section areas a, a/2, 2a and 3a respectively.

Let the piston A is pushed with force F, then the pressure developed = F/a

According to Pascal’s law this pressure is transmitted equally in all directions due to which all other pistons will be pushed outwards. It is found that to keep the pistons at their respective positions, force F/2, 2F and 3F are to be applied on the pistons B, C and D respectively.

So pressure developed at pistons B, C and D are [(F/2)/(a/2)], [2F/2a] and [3F/3a], i.e., each equal to F/a.

This implies that the pressure applied is transmitted equally in all directions.