What you'll learn
This revision guide covers all aspects of pressure in fluids required for AQA GCSE Physics. You'll learn how to calculate pressure in liquids and gases, understand why pressure varies with depth, and apply these principles to real-world scenarios. These concepts appear regularly in both Foundation and Higher tier papers, particularly in calculation and application questions.
Key terms and definitions
Fluid — a substance that can flow; includes both liquids and gases
Pressure — the force exerted per unit area, measured in pascals (Pa) or N/m²
Density — the mass per unit volume of a substance, measured in kg/m³
Atmospheric pressure — the pressure exerted by the weight of air in the atmosphere, approximately 100,000 Pa at sea level
Upthrust — the upward force acting on an object submerged in a fluid, caused by pressure differences
Pascal — the SI unit of pressure; 1 Pa = 1 N/m²
Column — in fluid pressure contexts, a vertical section of fluid extending from a surface to a particular depth
Displacement — the volume of fluid pushed aside by a submerged object
Core concepts
Pressure basics in fluids
Pressure in fluids acts in all directions. Unlike solids where pressure acts perpendicular to surfaces, fluid pressure acts equally in every direction at any given point.
The basic equation for pressure is:
pressure = force / area
or
p = F / A
Where:
- p = pressure in pascals (Pa)
- F = force in newtons (N)
- A = area in square metres (m²)
This equation tells us that:
- Increasing force on the same area increases pressure
- Decreasing the area while keeping force constant increases pressure
- Pressure is inversely proportional to area for a constant force
For example, a sharp knife cuts easily because the small area of the blade edge creates high pressure. Conversely, snowshoes spread weight over a larger area to reduce pressure on snow.
Pressure in liquids
Pressure in liquids increases with depth. This occurs because the deeper you go, the greater the weight of liquid above pressing down.
The equation for calculating pressure at depth in a liquid is:
pressure = height × density × gravitational field strength
or
p = h × ρ × g
Where:
- p = pressure in pascals (Pa)
- h = height (depth) of the liquid column in metres (m)
- ρ = density of the liquid in kilograms per cubic metre (kg/m³)
- g = gravitational field strength in newtons per kilogram (N/kg), taken as 10 N/kg on Earth
Key points about liquid pressure:
- Pressure acts equally in all directions at any given depth
- Pressure depends only on depth, density, and gravitational field strength
- Pressure does NOT depend on the shape of the container
- Pressure increases linearly with depth
- At the same depth in the same liquid, pressure is the same everywhere
Total pressure at depth in a liquid = atmospheric pressure + pressure due to liquid column
For most GCSE calculations, you'll either calculate just the liquid pressure or be told whether to include atmospheric pressure.
Atmospheric pressure
The Earth's atmosphere exerts pressure because air has mass and weight. Atmospheric pressure at sea level is approximately 100,000 Pa (or 100 kPa, or 1 × 10⁵ Pa).
Atmospheric pressure varies with:
Height above sea level
- Pressure decreases as altitude increases
- Less air above means less weight pressing down
- The atmosphere is less dense at higher altitudes
- Mountain climbers and aircraft passengers experience lower pressure
Weather conditions
- High pressure systems bring settled weather
- Low pressure systems bring unsettled weather
- Barometers measure atmospheric pressure changes
Why atmospheric pressure decreases with altitude:
- Air molecules are pulled towards Earth by gravity
- Most air molecules are concentrated near Earth's surface
- As you go higher, there are fewer air molecules above you
- The atmosphere becomes less dense with increasing altitude
- Less dense air means lower pressure
Density and its relationship to pressure
Density is crucial for calculating liquid pressure. The density equation is:
density = mass / volume
or
ρ = m / V
Where:
- ρ = density in kg/m³
- m = mass in kilograms (kg)
- V = volume in cubic metres (m³)
Common densities you should know:
- Water: 1000 kg/m³
- Air (at sea level): 1.2 kg/m³
- Mercury: 13,600 kg/m³
- Ice: 920 kg/m³
Denser liquids exert more pressure at the same depth because there's more mass in the same volume, creating more weight.
Upthrust and floating
When an object is submerged in a fluid, it experiences upthrust — an upward force. This occurs because:
- Pressure increases with depth
- The bottom of the object experiences higher pressure than the top
- Higher pressure at the bottom creates a greater upward force
- The resultant force is upward
The upthrust on an object equals the weight of fluid displaced (Archimedes' principle):
upthrust = weight of fluid displaced
Whether an object floats or sinks depends on the balance between upthrust and weight:
Object floats when:
- Upthrust = Weight of object
- Density of object < Density of fluid
- Example: ice floats on water because ice is less dense
Object sinks when:
- Weight > Upthrust
- Density of object > Density of fluid
- Example: a steel bolt sinks in water
Object is neutrally buoyant when:
- Weight = Upthrust throughout the fluid
- Density of object = Density of fluid
- Example: a submarine can adjust its density to hover at any depth
Applications:
- Ships are shaped to displace large volumes of water, creating sufficient upthrust despite being made of steel
- Submarines control buoyancy by filling or emptying ballast tanks with water
- Hot air balloons rise because heated air is less dense than surrounding cool air
Pressure differences and applications
Understanding pressure in fluids explains many everyday phenomena and technologies:
Hydraulic systems
- Liquids are virtually incompressible
- Pressure applied to an enclosed fluid is transmitted equally throughout
- Force can be multiplied using different piston areas
- Used in car brakes, hydraulic jacks, and construction equipment
Water supply systems
- Water towers store water at height to create pressure
- Higher towers create greater pressure in pipes below
- Ensures water reaches upper floors of buildings
Dams
- Must be thicker at the base because pressure increases with depth
- Massive pressure at the bottom requires stronger construction
- Reinforced concrete withstands the high pressure forces
Submersibles and diving
- Deep-sea vessels must withstand enormous pressure
- Divers experience approximately 1 atmosphere (100 kPa) additional pressure for every 10 metres depth in seawater
- Pressure-related injuries occur if divers ascend too quickly
Worked examples
Example 1: Calculating pressure in a liquid
Question: A swimming pool is 2.5 m deep. Calculate the pressure due to the water at the bottom of the pool. (Density of water = 1000 kg/m³, g = 10 N/kg)
Answer:
Write down the equation: p = h × ρ × g
Substitute values: p = 2.5 m × 1000 kg/m³ × 10 N/kg
Calculate: p = 25,000 Pa (or 25 kPa)
[3 marks: 1 mark for correct equation, 1 mark for correct substitution, 1 mark for correct answer with unit]
Example 2: Pressure and area calculations
Question: A rectangular concrete block has dimensions 2 m × 1 m × 0.5 m and a weight of 25,000 N. Calculate: (a) The maximum pressure it can exert on the ground [3 marks] (b) The minimum pressure it can exert on the ground [3 marks]
Answer:
(a) Maximum pressure occurs with smallest area in contact with ground:
Smallest area = 1 m × 0.5 m = 0.5 m²
p = F / A
p = 25,000 N / 0.5 m²
p = 50,000 Pa (or 50 kPa)
[3 marks: 1 mark for identifying smallest area, 1 mark for correct substitution, 1 mark for answer with unit]
(b) Minimum pressure occurs with largest area in contact with ground:
Largest area = 2 m × 1 m = 2 m²
p = F / A
p = 25,000 N / 2 m²
p = 12,500 Pa (or 12.5 kPa)
[3 marks: 1 mark for identifying largest area, 1 mark for correct substitution, 1 mark for answer with unit]
Example 3: Upthrust and density
Question: A cube of wood has sides of length 0.1 m and density 800 kg/m³. (a) Calculate the weight of the cube (g = 10 N/kg) [4 marks] (b) Explain whether the cube will float in water (density 1000 kg/m³) [2 marks]
Answer:
(a) First calculate volume: V = 0.1 m × 0.1 m × 0.1 m = 0.001 m³
Then calculate mass using ρ = m / V: m = ρ × V = 800 kg/m³ × 0.001 m³ = 0.8 kg
Then calculate weight: W = m × g = 0.8 kg × 10 N/kg = 8 N
[4 marks: 1 mark for volume, 1 mark for mass calculation, 1 mark for weight calculation, 1 mark for correct answer with unit]
(b) The cube will float because its density (800 kg/m³) is less than the density of water (1000 kg/m³). The upthrust from the water will equal the weight of the cube when only part of it is submerged.
[2 marks: 1 mark for correct conclusion, 1 mark for correct reasoning using densities]
Common mistakes and how to avoid them
Confusing units: Always convert to standard SI units before calculating. Convert cm to m, and ensure density is in kg/m³ not g/cm³. A common error is using depth in centimetres rather than metres.
Forgetting to square or cube dimensions: When calculating area, multiply two dimensions; for volume, multiply three. Students often forget to cube the side length when finding the volume of a cube.
Mixing up the pressure equations: Remember p = F/A is for force on an area, while p = h × ρ × g is specifically for liquid pressure at depth. Using the wrong equation loses all marks.
Incorrectly stating that pressure depends on container shape: Pressure at a given depth depends only on height, density, and gravitational field strength, NOT on the width or shape of the container.
Confusing mass and weight: Mass is measured in kg, weight is a force measured in N. To convert mass to weight, multiply by g (10 N/kg). Many students write weight in kg.
Assuming upthrust equals weight: Upthrust equals the weight of displaced fluid, not necessarily the weight of the object. They're only equal when the object floats in equilibrium.
Exam technique for "Pressure in fluids"
Command words matter: "Calculate" requires working shown with equation, substitution, and answer with unit. "Explain" requires reasoning using physics principles, not just description. "State" needs only a brief answer without explanation.
Show all working: Even if you get the final answer wrong, you can gain method marks for correct equations and substitution. Write the formula, substitute values clearly (with units), then calculate.
Use standard form for large numbers: Atmospheric pressure (100,000 Pa) is better written as 1 × 10⁵ Pa in calculations. Examiners accept either, but standard form reduces arithmetic errors.
Check answer magnitude: Does your calculated pressure seem reasonable? If you calculate 5 Pa for deep ocean pressure, you've made an error. Use estimation to verify answers make physical sense.
Quick revision summary
Pressure in fluids acts equally in all directions at any point. Calculate pressure using p = F/A or p = h × ρ × g for liquids at depth. Atmospheric pressure is approximately 100,000 Pa at sea level and decreases with altitude. Denser fluids exert greater pressure at the same depth. Upthrust arises from pressure differences and equals the weight of displaced fluid, determining whether objects float or sink. Objects float when their density is less than the fluid's density.