Mechanics

# Pascal’s Principle

Pressure transmission was proposed by Blaise Pascal

Pascal was a French mathematician, physicist and philosopher who studied the transmission of pressure through liquids, establishing, through experiments, that for a confined liquid of specific mass (μ) and in equilibrium, the pressure variation caused at a point in the liquid is transmitted integrally to all points of the liquid and acts normally at all points on the inner walls of the container in which it is contained.

This pressure is felt in the daily lives of deep-sea divers. Such dives must be carried out very carefully in relation to the pressure variation to which they are being subjected. Divers know that the deeper the distance they descend, the greater the pressure they are subjected to.

Based on the principle proposed by Pascal, we will analyze how a liquid (fluid) behaves at rest. In this case, we will emphasize the pressure inside the liquid and the pressure exerted by the atmosphere. Blaise Pascal, regarding the behavior of liquids, stated the following:

The increase in pressure at one point in the liquid at equilibrium is transmitted integrally to all other points in that liquid and the walls of the container where it is contained .

Let’s assume that the liquid contained in the container below is in equilibrium. When we apply a force F to the piston, we have:

In the figure above we have an incompressible liquid confined in a container. According to Pascal, any change in pressure at any point A causes the same change at any other point B within the liquid. So, mathematically we have:

∆ pA = ∆ pB

Pascal’s principle has applicability in equipment that multiply forces and transmit them to another point of application. We can cite as common examples the hydraulic jack, the hydraulic brake and the hydraulic pressure.