P19: Pressure
Pressure in fluids and atmospheric pressure
📋 Key Definitions
Pressure: The force per unit area. Pressure tells us how concentrated a force is. Measured in Pascals (Pa), where 1 Pa = 1 N/m².
Atmospheric pressure: The pressure exerted by the weight of air above a point. It decreases with increasing height above the ground.
Upthrust: The resultant upward force on an object submerged in a fluid. It equals the weight of the fluid displaced by the object.
📏 Pressure, Force and Area
p = F / A
p = pressure (Pa or N/m²), F = force (N), A = area (m²)
Increasing the area decreases the pressure (for the same force). This is why skis and snowshoes are wide — they spread your weight over a larger area so you do not sink. Decreasing the area increases the pressure — this is why sharp knives cut better than blunt ones.
Worked Example 1: Calculating pressure
A box of weight 500 N has a base area of 2 m². Calculate the pressure it exerts on the ground.
p = F / A = 500 / 2 = 250 Pa
Worked Example 2: Effect of area on pressure
The same 500 N box is turned onto its side with area 0.5 m². Calculate the new pressure.
p = F / A = 500 / 0.5 = 1000 Pa
Reducing the area (from 2 m² to 0.5 m²) increased the pressure by 4 times.
🌍 Atmospheric Pressure
The atmosphere is a layer of air around the Earth. The weight of this air creates atmospheric pressure.
Atmospheric pressure decreases with height. At sea level, atmospheric pressure is about 101 000 Pa (101 kPa). As you go higher, there is less air above you, so the weight of air above you is less, and the pressure is lower.
Atmospheric pressure explains why:
- Drinking straws work: you reduce the pressure inside the straw, and atmospheric pressure on the drink surface pushes the liquid up
- Suction cups stick: you push air out from under the cup, and atmospheric pressure holds it in place
- Your ears pop on aeroplanes: the pressure difference between inside and outside your ear forces your eardrum
💧 Pressure in Liquids
Pressure in a liquid increases with depth. The deeper you go, the greater the weight of liquid above you, so the greater the pressure.
p = hρg
p = pressure (Pa), h = depth of liquid (m), ρ = density of liquid (kg/m³), g = gravitational field strength (9.8 N/kg)
Pressure in a liquid depends on three things: depth (h), density of the liquid (ρ), and gravitational field strength (g). It does NOT depend on the volume of liquid or the shape of the container.
Worked Example 3: Pressure in water
Calculate the pressure at a depth of 10 m in water (density 1000 kg/m³, g = 9.8 N/kg).
p = hρg = 10 × 1000 × 9.8 = 98 000 Pa (98 kPa)
Worked Example 4: Pressure in mercury
Mercury has a density of 13 600 kg/m³. Calculate the depth of mercury that produces a pressure of 101 000 Pa.
h = p / (ρg) = 101 000 / (13 600 × 9.8) = 101 000 / 133 280 = 0.758 m (758 mm)
This is how a mercury barometer works — the height of the mercury column is about 760 mm at atmospheric pressure.
⛵ Upthrust and Floating
When an object is placed in a fluid, it experiences an upward force called upthrust.
Archimedes principle: The upthrust on an object in a fluid is equal to the weight of the fluid it displaces. If the object displaces a large volume of heavy fluid, the upthrust is large.
Why objects float or sink
| Condition | What happens | Why |
|---|---|---|
| Upthrust > weight | Object floats | Density of object is less than density of fluid |
| Upthrust = weight | Object floats at any depth | Density of object equals density of fluid |
| Upthrust < weight | Object sinks | Density of object is greater than density of fluid |
An object floats if its density is less than the density of the fluid (e.g. wood on water, helium balloon in air). An object sinks if its density is greater than the fluid (e.g. steel in water). A ship floats because its overall density (including the air inside) is less than water, even though it is made of steel.
❓ Practice Questions
Q1: Foundation A woman of weight 600 N stands on both feet with total area 0.03 m². Calculate the pressure she exerts on the ground.
Q2: Foundation Explain why atmospheric pressure decreases with height above the Earth surface.
Q3: Higher Calculate the pressure at a depth of 5 m in sea water (density 1025 kg/m³, g = 9.8 N/kg).
Q4: Higher Explain, in terms of density and upthrust, why a solid steel block sinks in water but a steel ship floats.
Q5: Foundation A drawing pin has a very small point. Explain why it is easy to push into a wall using the formula for pressure.
✅ Answers
- p = F / A = 600 / 0.03 = 20 000 Pa (20 kPa)
- Atmospheric pressure is caused by the weight of air above a point. As height increases, there is less air above, so less weight of air, and therefore lower pressure.
- p = hρg = 5 × 1025 × 9.8 = 50 225 Pa (50.2 kPa)
- The solid steel block is denser than water, so it cannot displace enough water to create an upthrust equal to its weight — it sinks. The steel ship has a hollow shape filled with air, making its overall density less than water. It displaces a large volume of water, creating an upthrust equal to its weight, so it floats.
- Pressure = force / area. The point of the drawing pin has a very small area, so the same force produces a very large pressure, easily piercing the wall. The large head has a large area, producing a small pressure on your thumb.
🎯 Exam Tips
- For pressure calculations, make sure area is in m² — convert cm² to m² (divide by 10 000)
- Pressure in liquids depends on depth, density and g — not on the volume or shape of the container
- When explaining floating/sinking, always compare the density of the object to the density of the fluid
- Upthrust = weight of fluid displaced, NOT weight of the object
- Atmospheric pressure is caused by the weight of air above — it is not magic
- A ship floats because of its shape (hull displaces lots of water) — not because steel floats
🔢 Maths Skills
Mathematical Skills
Use p = F/A for pressure on a surface (ensure area is in m² — divide cm² by 10 000). Use p = hρg for pressure in a liquid (depth in m, density in kg/m³, g = 9.8 N/kg). Rearrange equations: F = pA, h = p/(ρg), A = F/p. Convert kPa to Pa by multiplying by 1000.
Maths Example
A diver is at 15 m depth in sea water (ρ = 1025 kg/m³). Pressure from the water: p = hρg = 15 × 1025 × 9.8 = 150 675 Pa (≈ 151 kPa). Total pressure including atmosphere (101 kPa) = 251 675 Pa. A 60 N force on 0.002 m² gives p = 60/0.002 = 30 000 Pa (30 kPa).
⚠️ Common Misconceptions
Watch Out!
1. Wrong: Pressure in a liquid depends on the volume of liquid or the shape of the container. Correct: Pressure in a liquid depends only on depth, density and g (p = hρg). It does NOT depend on volume or container shape.
2. Wrong: An object floats because it is light, and sinks because it is heavy. Correct: Whether an object floats or sinks depends on its DENSITY compared to the fluid. A heavy steel ship floats because its overall density (including air inside) is less than water.
3. Wrong: Upthrust equals the weight of the object. Correct: Upthrust equals the weight of the FLUID DISPLACED by the object, not the weight of the object itself. A floating object has upthrust = weight, but a sinking object has upthrust < weight.
✍️ 6-Mark Question
Extended Answer
6 marks: Explain, in terms of forces and pressure, why a ship made of steel can float on water but a solid block of the same steel sinks. Include the role of upthrust and density.
A solid block of steel has a density of about 7800 kg/m³, which is much greater than the density of water (1000 kg/m³). When placed in water, it displaces a volume of water equal to its own volume, but the weight of this displaced water (the upthrust) is less than the weight of the steel block. Since upthrust < weight, the block sinks. A steel ship is hollow and contains a large volume of air, which significantly reduces its overall density to below that of water. When the ship is placed in water, its hollow shape allows it to displace a much larger volume of water than the solid block. The weight of this displaced water (upthrust) is equal to the weight of the ship when it floats. At equilibrium, upthrust = weight, and the ship floats. This works because the ship's overall density (mass / total volume including the air space) is less than the density of water, even though the steel itself is much denser.
Mark scheme: 1 mark for solid steel has density > water; 1 mark for solid block displaces small volume → upthrust < weight → sinks; 1 mark for ship is hollow → contains air → overall density < water; 1 mark for ship displaces large volume of water; 1 mark for upthrust = weight when floating; 1 mark for clear link between density comparison and floating/sinking. (6 marks total)
📊 AO3: Analyse & Evaluate
Analysis and Evaluation
A student measures the pressure at different depths in a tank of fresh water (ρ = 1000 kg/m³). They use a pressure sensor connected to a data logger. Their results are:
| Depth (m) | Measured pressure (kPa) | Calculated pressure (kPa) |
|---|---|---|
| 0.5 | 4.9 | 4.9 |
| 1.0 | 9.8 | 9.8 |
| 1.5 | 14.7 | 14.7 |
| 2.0 | 19.5 | 19.6 |
| 2.5 | 24.2 | 24.5 |
| 3.0 | 28.8 | 29.4 |
(a) Describe the relationship between depth and pressure shown by the data.
(b) At greater depths, the measured values are increasingly lower than calculated values. Suggest a reason for this.
(c) The student then tests salt water and finds the pressure at 1.0 m depth is 10.1 kPa. Calculate the density of the salt water.
Answers: (a) Pressure is directly proportional to depth — as depth increases, pressure increases linearly (roughly 4.9 kPa per 0.5 m). (b) The pressure sensor may not be perfectly calibrated, or there may be systematic error at higher readings. More likely: the sensor was zeroed at the surface but atmospheric pressure may not have been accounted for consistently, or the sensor position has slight error at greater depths. The discrepancy grows with depth, suggesting a systematic error in the depth measurement (the sensor may be slightly less deep than recorded). (c) ρ = p/(hg) = 10 100 / (1.0 × 9.8) = 1031 kg/m³. Salt water is denser than fresh water due to dissolved salts.
📝 Exam Questions by Topic
🎬 Video Resources
Ready to ace your GCSE Combined Science exams?
Get the best revision books and guides to boost your grades.