Let's say we have a closed chamber filled with incompressible liquid and there are two area's(smaller(a) and larger(A)) where we can apply force or keep objects.We keep an object of weight W on larger area.Due to this,pressure at every point in a liquid will increase by W/A ,according to pascal's law.The situation is depicted in picture below.

enter image description here Now,we apply force f on smaller area .Due to this the pressure at every point will even further increase by f/a.Now the situation looks something like the picture below.

Now from what I have read in books W/A=f/a

Why the pressure exerted by the box W has to be equal to the pressure exerted by force f?

enter image description here


This equality is a equilibrium condition, i.e. a condition for the fluid to be in rest. In general, inertia force terms must be added if the fluid is not in equilibrium.


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