## Simple hydraulic machines: how do they work?

Physics Narrative for 11-14

#### Simple hydraulic systems

The simplest hydraulic system consists of a pair of cylinders with moveable pistons in each and the whole system filled with a fluid. Push one piston in and the other moves out.

If the area of the input piston and the output piston are the same then the forces will be the same. The pressure of the hydraulic fluid is the same throughout the machine and equal to force divided by area. If the pistons have the same surface area there will be the same force acting on them.

- An output piston with a larger area has more force acting on it by the fluid.
- An output piston with a smaller area has less force acting on it by the fluid.

In other words a hydraulic machine can produce a large force by simply having a larger area output cylinder and piston.

Seen in this way, there are clear parallels between hydraulic machines and simple levers.

#### Designing hydraulic machines

Designing hydraulic machines involves choosing the relative areas of the pistons in just the same way that the design of levers involves choosing the relative lengths of the line of action of the forces from the pivot point.

Being able to tap into the pressure in the fluid at any point makes hydraulic machines quite simple to engineer. You can easily design a machine that exerts an output force of some fixed size compared to the input force, at any angle you choose.

You can also easily have the same effect in two different places, simply by creating two pistons of equal cross-sectional area. This can be used, for example, to exert equal braking forces on all four wheels of a car.

Producing a *big* force by providing a large area output piston seems to be too good to be true. There must be a catch! The downside is that the output piston which exerts the large force cannot move very far (compared to the input piston). It's just like a lever.

For example:

If the output piston has four times the area of the input piston and the output force is therefore four times the input force then the output piston will move only one quarter the distance of the input piston.

**Teacher Tip: **Once again, the hydraulic machine acts exactly like a simple lever (where you must move the effort force through four times the distance to increase the load force four times).