## Why force multiplication is key to how hydraulic systems work

## What is force multiplication?

Pascal’s law states that pressure set up in a confined body of fluid, acts equally in all directions, and always at right angles to the containing surface. When a pressure is applied to a fluid trapped in a confined space, that pressure acts on each square millimeter of that surface. The force output of a hydraulic actuator is the result of the pressure applied, and the area to which that pressure is applied.

If a given pressure is applied to two identical cylinders, then they will have an equal output force.

## How does force multiplication work?

When the same pressure is applied to different sized cylinders, then the larger cylinder will have a greater force output. This is because the area which sees the hydraulic pressure is greater.

The cylinder on the right in this example is twice the diameter of the cylinder on the left.

## The area of the circle multiplies the force

The area of a circle is calculated by this formula:

When a given pressure is applied to two different sized areas, the larger area will see a larger force output than the smaller area. This force differential is often significant. For example, while a 200mm diameter circle is twenty times larger than a 10mm circle in diameter, the area differential between the two is 400 to 1. When pressure is applied, the output force increase would also be 400 to 1.

## A bottle jack piston uses force multiplication

A hydraulic bottle jack is a perfect example of force multiplication at work.

A reciprocating piston is moved with a hand lever. This piston applies pressure to the fluid, which is then fed through and applied to a larger piston. The output force is magnified due to the area differential of the two pistons, thus making it possible to lift a car by hand. The bottle jack piston moves slowly in relation to the pump piston because of the volume differential between the two chambers.

## The weight of a load affects the hydraulic pressure

The hydraulic pressure required to lift a load is dictated by the mass of the load, and the area to which it is applied.

The three cylinders on the left are all lifting the same weight, 20,000kg, (20T). This mass applies a force of 19,600N to the piston area of the cylinder. The hydraulic pressure that is created is called the load induced pressure. i.e. The pressure that is induced in the fluid by the load applied to it. When the same force applied to different cylinder areas, the load induced pressure will be highest in the smallest cylinder.

## Load induced pressure vs system pressure

When the pressure applied to a cylinder is greater than the load induced pressure, the cylinder will begin to move forward and lift the load. As the load is lifted, the pressure seen within that area of the circuit is generally that of the load induced pressure, as long as there is no resistance to movement.

As the cylinder mechanically reaches the end of its stroke, the pressure will rise to the maximum allowed within that area of the system. This maximum pressure allowed is limited by valving such as pressure relief valves, pressure reducing valves or similar hydraulic fittings.

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