Pressure and Pressure in Liquids
Pressure is the force acting per unit area. Two formulae cover the topic, and the marks are lost in unit conversion and in which symbol means what.
1. Pressure on a surface
Pressure = Force ÷ Area p = F / A
Unit: the pascal (Pa), where 1 Pa = 1 N/m².
Pressure is FORCE PER UNIT AREA. Tutors flagged this exact wording. A recorded error wrote the formula as “F / E” — the denominator is the area, and getting the words right protects the formula.
Example: a 600 N force on 0.5 m².
- p = 600 ÷ 0.5 = 1200 Pa
Remember to divide by the area — forgetting the division entirely was recorded.
Convert area to m². Since 1 m² = 10 000 cm², you divide by 10 000 to convert cm² to m². Forgetting this conversion was recorded, and it is the biggest single source of error here — the factor is squared, not 100.
The consequences of the formula:
Smaller area → greater pressure for the same force. This is why knives are sharpened, drawing pins have points, and nails are thin. Larger area → lower pressure. This is why skis, snowshoes and tractor tyres are wide, and why camels have broad feet.
2. Pressure in liquids
p = ρ g h pressure (Pa) = density (kg/m³) × gravitational field strength (N/kg) × depth (m)
Example: the pressure at 5 m depth in water (ρ = 1000, g = 9.8).
- p = 1000 × 9.8 × 5 = 49 000 Pa
ρ (rho) is the DENSITY, not pressure. A recorded error used “P” for density in the formula. The two symbols look similar in handwriting — write ρ clearly, and remember that pressure is the subject, density an input.
h is the DEPTH below the surface, not the total height of the container or the height above the ground.
Key facts about liquid pressure:
Pressure increases with DEPTH, because there is a greater weight of liquid above. Pressure increases with DENSITY of the liquid. At a given depth, pressure acts equally in ALL directions. Pressure does not depend on the shape or width of the container — only on the depth.
Confusion about how pressure varies with depth was recorded. The rule is simple and always the same: deeper means higher pressure, because more liquid is pressing down from above.
This is why dam walls are thicker at the bottom, and why deep-sea submersibles need such strong hulls.
Note: this formula gives the pressure due to the liquid alone. To find the total pressure you add atmospheric pressure.
3. Atmospheric pressure
The atmosphere exerts pressure because of the weight of air above us.
At sea level, atmospheric pressure is about 100 000 Pa (10⁵ Pa).
Atmospheric pressure DECREASES with altitude, because there is less air above you.
The barometer
A barometer measures atmospheric pressure.
In a simple mercury barometer, atmospheric pressure supports a column of mercury in a sealed tube, with a vacuum above.
Higher atmospheric pressure supports a TALLER column — so a higher reading means higher pressure. A recorded error had it backwards: greater atmospheric pressure gives a greater barometer reading, because more pressure can support more mercury.
Mercury is used because it is very dense, so the column is a manageable height (about 76 cm). A water barometer would need to be over 10 m tall.
The manometer
A manometer is a U-tube of liquid used to measure the pressure of a gas supply.
The difference in the two liquid levels gives the pressure difference:
p = ρ g h, where h is the height difference between the two surfaces.
If the gas pressure is greater than atmospheric, the liquid is pushed down on the gas side and up on the open side.
4. Gas pressure and the gas laws
Gas pressure is caused by particles colliding with the container walls.
Increasing the temperature (at constant volume) → particles move faster, collide more often and harder → pressure increases. Decreasing the volume (at constant temperature) → particles hit the walls more frequently → pressure increases.
State the condition. A recorded error said “as temperature increases, pressure increases” without noting that this holds at constant volume. Each gas relationship has a condition, and the mark scheme wants it.
Boyle’s law
At constant temperature, for a fixed mass of gas: p V = constant, so p₁V₁ = p₂V₂
Pressure and volume are INVERSELY proportional.
Increasing the pressure DECREASES the volume. Two recorded errors got this backwards. Squeeze a gas into a smaller space and its pressure rises; let it expand and the pressure falls.
Example: 300 cm³ at 100 kPa is compressed to 100 cm³ at constant temperature.
- p₂ = (100 × 300) ÷ 100 = 300 kPa
5. Mistakes that cost marks
Not converting cm² to m² (÷ 10 000).
Forgetting to divide by area.
Using P for density instead of ρ.
Using the container height instead of the depth.
Saying pressure depends on the container’s shape or width.
Getting the barometer relationship backwards.
Omitting the condition (constant volume or temperature) in a gas law.
Saying increasing pressure increases volume.
Omitting units — pressure is in pascals.
Frequently asked questions
What is pressure? Force per unit area: p = F/A, in pascals.
What is 1 pascal? 1 newton per square metre.
How do I convert cm² to m²? Divide by 10 000 — the conversion factor is squared.
Why is a sharp knife more effective? A smaller area gives a greater pressure for the same force.
What is the formula for pressure in a liquid? p = ρgh, where h is the depth.
Why does pressure increase with depth? There is a greater weight of liquid above.
Does the shape of the container matter? No — only the depth and the liquid’s density.
What does a barometer measure? Atmospheric pressure.
What happens to the barometer reading if pressure rises? The column gets taller — a higher reading.
What is Boyle’s law? pV = constant at constant temperature for a fixed mass of gas — pressure and volume are inversely proportional.
Quick revision checklist
- I know p = F/A and can state it as force per unit area
- I know pressure is in pascals
- I convert cm² to m² by dividing by 10 000
- I can explain why small areas give high pressure
- I know p = ρgh and what each symbol means
- I use depth, not container height
- I know pressure increases with depth and density
- I know pressure acts equally in all directions
- I know the container’s shape is irrelevant
- I know atmospheric pressure ≈ 10⁵ Pa and falls with altitude
- I can explain how a barometer works
- I can use a manometer height difference
- I can explain gas pressure with collisions
- I know pV = constant and its conditions
These notes cover pressure and pressure in liquids in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
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