Pressure

What is Pressure?

Pressure is the force applied per unit area. The same force spread over a smaller area produces greater pressure; spread over a larger area, it produces less pressure.

Formula: Pressure = Force / Area

P = F / A

Units: Pascals (Pa) = N/m squared

Rearranged:

• Force = Pressure x Area (F = P x A)
• Area = Force / Pressure (A = F / P)

Worked Example 1

A box weighs 200 N and has a base area of 0.5 m squared. What pressure does it exert on the floor?

P = F / A = 200 / 0.5 = 400 Pa

If the same box is turned on its side with an area of 0.1 m squared:

P = 200 / 0.1 = 2000 Pa

Same force, smaller area → much greater pressure.

Everyday Examples of Pressure

Situation	Explanation
Sharp knife cuts more easily than blunt	Smaller area → higher pressure for same force
Snowshoes prevent sinking in snow	Large area → lower pressure
Drawing pin penetrates surfaces	Very small pointed tip → very high pressure
Wide tyres on tractors	Large area → low pressure, does not damage soft ground
Stiletto heels damage floors	Tiny area → very high pressure
Camel's wide feet on sand	Large area → low pressure, does not sink

Atmospheric Pressure

Earth's atmosphere is a layer of air roughly 100 km deep. The weight of all this air pressing down creates atmospheric pressure — approximately 101,325 Pa (about 1 atmosphere) at sea level.

Atmospheric pressure decreases with altitude because:

• There is less air above at higher altitudes
• Therefore less weight pressing down
• Air also becomes less dense at altitude

Effects:

• At high altitude: lower air pressure → less oxygen available → altitude sickness
• Aircraft cabins are pressurised to maintain a safe pressure for passengers
• Ears "pop" when ascending or descending rapidly — pressure equalises across the eardrum

Measuring atmospheric pressure: a barometer (historically a mercury barometer; now often an aneroid barometer). Falling pressure indicates approaching bad weather; rising pressure indicates improving weather.

Pressure in Liquids

Pressure in a static liquid has three key properties:

1. Increases with depth — more liquid above exerts more weight
2. Acts in all directions — unlike solid pressure which acts only downward
3. Depends on density — denser liquids create more pressure at the same depth

Formula: P = rho x g x h

Where:

• rho (rho) = density of the liquid (kg/m cubed)
• g = gravitational field strength (10 N/kg on Earth)
• h = depth below the surface (m)

Worked Example 2 — Pressure in Liquid

Calculate the pressure at a depth of 30 m in seawater (density = 1025 kg/m cubed, g = 10 N/kg).

P = rho x g x h = 1025 x 10 x 30 = 307,500 Pa

This is about 3 times atmospheric pressure — which is why divers must equalise pressure in their ears and use pressurised equipment at depth.

Hydraulic Systems

Pascal's Law: pressure applied to an enclosed, incompressible liquid is transmitted equally in all directions throughout the liquid.

Because liquids are incompressible, hydraulic systems can multiply force:

If a small force is applied to a small piston, the pressure generated is transmitted to a large piston. Since pressure is the same throughout, the larger area of the second piston produces a much larger force.

Formula: F1 / A1 = F2 / A2 (pressure is constant throughout)

Worked Example: Small piston area = 0.01 m squared, force applied = 100 N Pressure = 100 / 0.01 = 10,000 Pa

Large piston area = 0.1 m squared Force = Pressure x Area = 10,000 x 0.1 = 1000 N

A force of 100 N produces a force of 1000 N — a 10x multiplication.

Applications of hydraulics:

• Car brakes — foot pressure on brake pedal transmitted to all four brake pistons
• Hydraulic lifts — used in garages to raise vehicles
• JCB digger arms — small cab movements produce large forces at the bucket
• Aircraft landing gear — deploying and retracting undercarriage
• Dentist's chair — smooth, controlled height adjustment

Key Terms

• Pressure — force per unit area (Pascals, Pa)
• Pascal (Pa) — unit of pressure; 1 Pa = 1 N/m squared
• Atmospheric pressure — pressure exerted by the weight of the atmosphere (~101,325 Pa at sea level)
• Hydraulics — systems using liquid pressure to transmit and multiply forces
• Pascal's Law — pressure in an enclosed liquid is transmitted equally in all directions

Common Mistakes

• Forgetting to square the area units — pressure is N/m squared, not N/m
• Thinking a larger force always means greater pressure — pressure depends on both force and area
• Saying hydraulic systems increase energy — they multiply force but the energy in = energy out (conservation of energy)
• Confusing atmospheric pressure (decreases with altitude) with liquid pressure (increases with depth)

Tips and Tricks

• Formula triangle: P on top, F and A on the bottom — cover the unknown to find the formula
• For liquid pressure: deeper = more pressure; denser liquid = more pressure
• Hydraulics: small piston, small area, small force → same pressure → large piston, large area, LARGE force
• Remember: Pa = Pascal = N/m squared — the unit named after Blaise Pascal who formulated the hydraulic law