5.1 Definition of pressure

Pressure is the force acting normally (at right angles) on a surface per unit area of that surface. It tells us how concentrated a force is: the same force spread over a large area gives a low pressure, while the same force on a small area gives a high pressure. Pressure is a scalar quantity, because at any point in a fluid it acts equally in all directions. Example: a hardware shop in Nyatike advises builders that a sharp chisel cuts stone more easily than a blunt one because the same hammer blow acts on a much smaller area.

Formula and unit

Pressure = normal force ÷ area

P = F ÷ A

• P: Pressure, in pascals (Pa).
• F: Force acting at right angles to the surface, in newtons (N).
• A: Area over which the force acts, in square metres (m²).
• Pascal: 1 Pa = 1 N/m², a small pressure (about the pressure of a sheet of paper lying flat on a table). Larger units are the kilopascal (1 kPa = 1,000 Pa), the megapascal (1 MPa = 10⁶ Pa) and the bar (1 bar = 10⁵ Pa).

Worked examples

Take g = 9.81 m/s² where needed.

Example 1: a force of 600 N acts on an area of 0.04 m². Find the pressure.

P = F ÷ A

P = 600 ÷ 0.04

P = 15,000 Pa = 15 kPa

Example 2: a person weighing 700 N stands on both feet, each of area 0.03 m². Find the pressure on the floor.

P = F ÷ A

P = 700 ÷ (2 × 0.03)

P = 700 ÷ 0.06 = 11,700 Pa (11.7 kPa)

Example 3: the same person stands on one stiletto heel of area 2.0 cm² (2.0 × 10⁻⁴ m²) with all their weight on it. Find the pressure.

P = 700 ÷ 2.0 × 10⁻⁴

P = 3,500,000 Pa = 3.5 MPa

This is about 300 times the pressure of standing on flat feet, which is why stiletto heels damage soft floors.

Factors that affect pressure

• Force: For a fixed area, pressure is directly proportional to the force. Doubling the force doubles the pressure.
• Area: For a fixed force, pressure is inversely proportional to the area. Halving the area doubles the pressure.

Increasing pressure (small area)

• Cutting tools: Knives, scalpels, chisels and blades are sharpened so the force acts on a tiny edge.
• Pointed objects: Nails, needles, drawing pins and syringe needles have fine points to pierce materials.
• Spikes: Athletes' shoes have spikes to grip the track; cork borers in the laboratory have sharpened edges.

Reducing pressure (large area)

• Wide tyres and tracks: Tractors and bulldozers have broad tyres or caterpillar tracks so they do not sink into soft soil.
• Foundations: Buildings stand on wide foundations to spread their weight on the ground.
• Shoulder straps and handles: Wide straps on bags and broad handles on buckets are more comfortable to carry.
• Snowshoes and camel feet: Large feet spread the weight on soft snow or sand.

Pressure in the laboratory

• Pressure readings: Gas cylinder regulators, vacuum pumps, autoclaves, HPLC pumps and gas chromatographs all display pressure, often in bar, psi or kPa.
• Pellet presses: In infrared spectroscopy, a hydraulic press applies a large force on a small die to compress potassium bromide and sample into a clear disc.
• Conversions: 1 bar = 100 kPa = 14.5 psi; 1 standard atmosphere = 101.325 kPa = 760 mmHg.