13.6:
Application of Pascal’s Law
Hydraulic systems like the hydraulic jack are based on Pascal's law.
It consists of a U-shaped tube having columns of unequal area of cross-section. Piston A is fitted onto the smaller column, while piston B is fitted onto the larger column.
The tube is filled with a fluid such that it attains the same height in both the columns. When a force is applied to piston A, it exerts a pressure p1 on the fluid.
According to Pascal's law, this pressure is transmitted to piston B through the fluid due to which piston B is pushed outward.
The pressure p2 felt by piston B is equal to p1. Now, using the relationship between pressure and force, an expression for the forces in a hydraulic system is obtained provided that the friction in the system is negligible. The output force can be increased in the hydraulic system by applying a force on a smaller area.
13.6:
Application of Pascal’s Law
Pascal's experimentally proven observations—that a change in pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid and to the walls of its container—provide the foundations for hydraulics, one of the most important developments in modern mechanical technology.
Hydraulic systems are used to operate automotive brakes, hydraulic jacks, and numerous other mechanical systems. We can derive a relationship between the forces in a simple hydraulic system by applying Pascal's principle. In the system, there are two pistons at the same height, so there is no difference in pressure due to a difference in depth. The pressure due to the force acting on the smaller area is transmitted undiminished throughout the fluid and to all walls of the container. Thus, the pressure felt at the larger piston is equal to the pressure transmitted by the smaller area. This gives an equation that relates the ratios of force to area in any hydraulic system, provided that the pistons are at the same vertical height and that the friction in the system is negligible. Hydraulic systems can increase or decrease the force applied to them. To make the force larger, the pressure is applied to a larger area. For example, if a 100 N force is applied to the smaller cylinder, and the other cylinder has an area five times greater, then the output force is 500 N.
The hydraulic jack is such a hydraulic system. It is used to lift heavy loads, such as the ones used by auto mechanics to raise an automobile. A small force applied over a small area can balance a much larger force on the other side over a larger area. From Pascal's principle, it can be shown that the force needed to lift a car is less than the weight of the car.
This text is adapted from Openstax, University Physics Volume 1, Section 14.3: Pascal's Principle and Hydraulics.