Question

Pascal's law of liquid pressure

Answer 1

$\mathcal{PASCAL'S\:LAW}$

$\implies$It states that if gravity effect is neglected, the pressure at every point of liquid in equilibrium of rest is same.

$\implies$ Pascal's law also states that the increase in pressure at one point of enclosed liquid in equilibrium of rest is transmitted equally to all other points of the liquid and also to the walls of the container, provided the effect of gravity is neglected.

In simple words, Pressure applied to a confined liquid is transmitted equally undiminished to every part of liquid and to all the walls of the containing vessel, and is always exerted at right angles to the walls.

A liquid confined by solid boundaries from the four sides and the base in shown in the first figure.

At the free surface the atmosphere is exerting a pressure $\sf{p_0}$ on this confined liquid which is transmitted to every part of the liquid.

This principle is also used in a hydraulic jack or a lift where a heavy load can be lifted up by a small force. In the second figure, the pressure due to a small force $\sf{F_1}$ applied to a piston of area $\sf{A_1}$ is transmitted to larger piston of area $\sf{A_2}$. The pressure at the two pistons is the same because they are at the same level.

$\sf{p=\dfrac{F_1}{A_1}=\dfrac{F_2}{A_2}}\\\sf{\implies\:F_2=\left(\dfrac{A_2}{A_1}\right)F_1}$

Thus, a small force $\sf{F_1}$ acting on a small area $\sf{A_1}$ results in a larger force $\sf{F_2}$ acting on a larger area $\sf{A_2.}$