Pressure as force per unit area, the relationship P equals F over A, and how a pneumatic cylinder uses air pressure to produce an output force.

What this key area is asking

The SQA wants you to define pressure as force per unit area, use the relationship $P = \dfrac{F}{A}$, and explain how a pneumatic cylinder uses air pressure acting on a piston to produce a useful output force.

Pressure

Rearranging gives $F = P \times A$ (to find force from pressure and area) and $A = \dfrac{F}{P}$ (to find the area needed).

Pneumatic systems

Inside a cylinder, compressed air pushes on a movable piston. The output force is the air pressure multiplied by the area of the piston, $F = P \times A$. This is a direct use of the pressure relationship, and it shows two ways to increase the output force: raise the air pressure, or use a piston with a larger area.

A typical pneumatic system has four parts working in order. A compressor squeezes air and stores it under pressure in a receiver (a storage tank). A control valve then directs the compressed air to the cylinder when it is wanted. Finally the cylinder converts the air pressure into a useful linear movement and force. A single-acting cylinder uses air pressure to push the piston out and a spring to return it, while a double-acting cylinder uses air to drive the piston in both directions, giving a controlled force on both the out-stroke and the return.

Pneumatics is chosen for many factory jobs because compressed air is clean, cannot catch fire, and a cylinder moves quickly. If a pneumatic system is overloaded the air simply compresses rather than the machine breaking, which can be a safety advantage over a rigid mechanical drive.

Why this matters

Pressure and pneumatics connect force to area and are widely used in real engineering: factory automation, vehicle brakes, robotics and clamping rigs. The pressure relationship also explains structural design choices, such as spreading a load over a larger area (a wide foundation) to keep the pressure on the ground low enough.

Try this

Q1. State the unit of pressure and what it is equivalent to. [1 mark]

• Cue. The pascal (Pa), equal to one newton per square metre.

Q2. A force of $200 \text{ N}$ acts on an area of $0.010 \text{ m}^2$. Calculate the pressure. [2 marks]

• Cue. $P = F/A = 200/0.010 = 20000 \text{ Pa}$.

Q3. A piston of area $0.0050 \text{ m}^2$ has air at $200000 \text{ Pa}$ acting on it. Calculate the output force. [2 marks]

• Cue. $F = P \times A = 200000 \times 0.0050 = 1000 \text{ N}$.