**P3 3.5**

Definition: a system that transmits a force from one place to another through a fluid.

Hydraulic systems are classed as **force multipliers**.

For this topic, it’s important to remember about **pressure in liquids** → they are **incompressible**.

An example of a hydraulic system is in **car brakes **(please spell it brakes, not breaks).

Hydraulic systems are useful because they essentially convert a **small force on a small area** to a **large force on a large area**, meaning people are able to exert a huge force on a massive object, such as breaks in a car.

To see how they do this, we look at the idea of **pressure**.

Here is a diagram of a hydraulic system:

Now, we know that pressure is equal to force divided by area (shown below).

And due to liquids being **incompressible**, the **pressure** is **equal** throughout the whole liquid – it remains **constant**. This is why it is an issue when **break fluid** leaks in cars, as the pressure is not transferred through the liquid, and so the force exerted on the break pads is not transferred to the whole vehicle.

So if the pressure exerted by the small force on the small area is **equal** to the pressure transmitted by the liquid to the large area, we can conclude:

The pressure is the **same **as that exerted by the small force on the small surface area. The **surface area** is **bigger**. This means that the **force** is **bigger** too, due to the equation for pressure rearranging like this:

I know this is difficult to get your heads round, but to summarise:

A **small force** is exerted on a **small surface area** → this results in a** pressure** → this pressure remains **constant** as it is **transmitted** through an **incompressible liquid** to a **larger surface area** → the pressure is being **exerted on** a surface area which is **larger than the first one** → due to the equation **force = pressure x area**, the **force** exerted on the **second surface** is **larger** than the force exerted on the first.

Since it’s quite complicated, here’s an example question:

*A force of 30N is applied to piston A with a surface area of 0.2m² in a hydraulic system.*

*The surface area of piston B is 1.0m².*

*What is the force exerted by piston B?*

So, the pressure exerted on piston A is force/area : 30N divided by 0.2m² is 150Pa.

To find the force exerted by piston B, we rearrange the equation to get pressure x area. So 150Pa x 1 m² = 150N.

So, the answer is 150 N.