If you exert a force F1 on the small piston with a cross section S1,
you create a pressure P in the liquid under the small piston with the value F1 / S1.
This same pressure P is manifested in all the fluid mass, and exerts on the large piston with cross section S2 a force F2
so that:
That is, the force that the liquid exerts on the large piston is F2.
The force that the press exerts (F2) is the force that you have exerted (F1) multiplied by the relationship between the surface areas of the pistons (S2 / S1).
If the surface of the large piston is double that of the small piston,
the force exerted by the press is double that which you exerted, if the
relation is triple, the force is triple, etc.
There shouldn't be any gas between the pistons
and the liquid. The gas is compressible and the hydraulic press is
based on a property of incompressible liquids.
Why doesn't the hydraulic press, in spite of multiplying the force we apply by a factor, also increase the amount of work?
