How is the area ratio of two pistons related to their distance moved?

In hydraulic systems, the principle of Pascal's Law states that when pressure is applied to a confined fluid, it transmits that pressure throughout the fluid in all directions. The movement and force transmission can be understood using the concept of area ratios of the pistons involved.

When comparing two pistons in a hydraulic system, the area ratio of the pistons directly affects their movement distances. The larger piston has a greater surface area compared to the smaller piston, which means that for a given force applied, the larger piston will experience a lower movement distance than the smaller piston.

This is because the work done on both pistons must be equal, as work is defined as force times distance. Since force is proportional to the area of the piston (as pressure is consistent throughout the system), a larger piston can exert more force but will move a shorter distance. Conversely, the smaller piston must move further to compensate for the larger piston's movement, given that the product of force and distance remains constant.

This principle is foundational in hydraulic systems, illustrating how mechanical advantage is achieved through varying piston sizes—where the larger piston moves a shorter distance compared to the smaller piston, which moves a greater distance.