What is the formula for hydraulic force multiplication?

The formula for hydraulic force multiplication is grounded in Pascal's principle, which states that pressure applied to a confined fluid is transmitted undiminished throughout the fluid. In hydraulic systems, this principle allows for the multiplication of force: the output force can be significantly greater than the input force.

The correct answer shows how output force is calculated by using the input pressure and the areas of the cylinders involved. Specifically, it indicates that the output force is equal to the input pressure multiplied by the area of the output cylinder, then divided by the area of the input cylinder. This reflects the relationship between force, pressure, and area in a hydraulic system.

By focusing on the areas of both cylinders, it becomes clear how force is augmented. A larger output cylinder area means that even a small amount of input pressure can result in a larger output force. This concept is fundamental in hydraulic systems, such as hydraulic lifts or brakes, where significant lifting or clamping forces can be achieved with relatively little manual effort.

This understanding of how area and pressure interact is pivotal for effectively designing and utilizing hydraulic systems. The emphasis on cylinder areas is critical to correctly applying the theory of hydraulic mechanics in practical applications.