Hydraulic press
Through Pascal’s principle, it was possible to build the hydraulic elevator
It’s not common, but whenever we stop at a gas station, we come across huge elevators, like the one in the picture above. This type of equipment is called a hydraulic lift or hydraulic press . Its operation is based on Pascal’s Principle and helps to lift large masses.
Hydraulic presses consist of a tube filled with a liquid confined between two pistons in different areas. When we apply a force 
to the piston of area A 1 , a pressure arises in the region of the liquid in contact with this piston. As the pressure increment is transmitted integrally to any point in the liquid, we can say that it also acts on the piston of A 2 with a force 
proportional to the area of the piston 2. Let’s see the figure below:
F 1 – force applied to piston 1;
F 2 – force that appears on piston 2;
A 1 – cross-sectional area of cylinder 1;
A 2 – cross-sectional area of cylinder 2.
The pressure increase (Δp) is given from Pascal’s Principle. So we have:
∆p 1 = ∆p 2
Where:
According to this relationship, we see that force and area are directly proportional quantities. In this way, we say that the smaller piston receives a force of less intensity, while the piston with greater area receives greater force.
As a result of the equation stated above (Pascal’s Principle), numerous pieces of equipment were built in order to facilitate human work. We can find the hydraulic press in hydraulic brakes, in the steering of a car, in airplanes, heavy machinery, etc.
For the displacement of the piston we can say that the decrease in volume on piston 1 is equal to the increase in volume on piston 2. So we have:
∆V 1 = ∆V 2
Knowing that the change in volume is a function of the area and displacement of the piston, we have:
∆V = Ad
Since the change in volume is equal, we have:
A 1 .d 1 = A 2 .A 2