# Pascal's theorem

When we apply a force to a liquid, the pressure caused is distributed integrally and evenly in all directions and directions.

From Stevin's theorem we know that: So, considering two points, THE and B:  When we apply any force, the pressures at the point THE and B will be added:  If the liquid in question is ideal, it will not be compressed, so the distance H, will be the same after force application.

Like this: Pascal's theorem:

"The increased pressure exerted at one point on an ideal equilibrium liquid is transmitted integrally to all points of that liquid and to the walls of the container containing it."

## Hydraulic press

One of the main applications of Pascal's theorem is the hydraulic press.

This machine consists of two cylinders of different radii. THE and B, interconnected by a tube, inside there is a liquid that holds two pistons from different and .

If we apply an intensity force F to the area piston , we will put extra pressure on the liquid given by: From Pascal's theorem, we know that this pressure increase will be transmitted integrally to all points of the liquid, including the area piston. but transmitting a force different from that applied: Since the pressure increase is equal for both expressions we can match them: Example:

Consider the following system: Dice: What is the force transmitted to the larger piston?   