Physics

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?