What you'll learn
This revision guide covers pressure in liquids and gases, including how to calculate pressure, understand pressure differences in fluids, and apply these principles to everyday situations. You'll master the core concepts needed for CIE IGCSE Co-ordinated Science (Double Award), including pressure calculations, hydraulic systems, and atmospheric pressure effects.
Key terms and definitions
Pressure — the force acting per unit area, measured in pascals (Pa) or N/m²
Fluid — a substance that can flow; includes both liquids and gases
Hydraulic system — a system that uses liquid under pressure to transmit force from one place to another
Atmospheric pressure — the pressure exerted by the weight of air in the Earth's atmosphere, approximately 100,000 Pa at sea level
Density — the mass per unit volume of a substance, measured in kg/m³ or g/cm³
Pascal (Pa) — the SI unit of pressure, equal to one newton per square metre (1 N/m²)
Barometer — an instrument used to measure atmospheric pressure
Manometer — a device used to measure the pressure of a gas in a container
Core concepts
Calculating pressure
Pressure is defined as force per unit area. The fundamental equation for pressure is:
Pressure = Force ÷ Area
P = F/A
Where:
- P = pressure in pascals (Pa) or N/m²
- F = force in newtons (N)
- A = area in square metres (m²)
This relationship shows that:
- Increasing force on the same area increases pressure
- Decreasing the area over which a force acts increases pressure
- A large force spread over a large area may produce less pressure than a small force on a small area
Practical applications:
- Sharp knives have small contact areas, creating high pressure to cut effectively
- Snowshoes spread weight over a larger area, reducing pressure on snow
- Drawing pins have sharp points (small area) to create high pressure for penetration
- Tractor tyres are wide to reduce pressure on soft ground
- High-heeled shoes create high pressure on floors due to small contact area
Pressure in liquids
Liquids exert pressure in all directions due to the weight of the liquid above. Key characteristics of pressure in liquids:
Pressure increases with depth — the deeper you go in a liquid, the greater the weight of liquid above, so pressure increases
Pressure acts in all directions — at any point in a liquid, pressure acts equally in all directions (upwards, downwards, and sideways)
Pressure depends on density — denser liquids exert more pressure at the same depth
Pressure is independent of container shape — pressure at a given depth is the same regardless of the shape of the container
The pressure in a liquid can be calculated using:
Pressure = height × density × gravitational field strength
P = h × ρ × g
Where:
- P = pressure in pascals (Pa)
- h = height/depth of liquid in metres (m)
- ρ (rho) = density of liquid in kg/m³
- g = gravitational field strength in N/kg (approximately 10 N/kg on Earth)
Note: This equation gives the pressure due to the liquid only. To find total pressure, add atmospheric pressure.
Applications of liquid pressure:
- Dams are thicker at the bottom because pressure is greatest at depth
- Submarine hulls must withstand enormous pressure at great depths
- Water towers use height to create pressure for water distribution
- Divers experience increasing pressure as they descend
Hydraulic systems
Hydraulic systems use liquids to transmit pressure and multiply forces. They operate on two key principles:
Pascal's principle: Pressure applied to an enclosed fluid is transmitted equally to all parts of the fluid and to the walls of the container.
Force multiplication: A hydraulic system can multiply force by using pistons of different areas.
In a hydraulic system:
- Pressure is the same throughout the liquid (assuming no friction)
- A small force on a small piston creates pressure
- This pressure acts on a larger piston
- The larger piston experiences a larger force
The hydraulic formula:
Since pressure is the same on both pistons:
P₁ = P₂
F₁/A₁ = F₂/A₂
Rearranging:
F₁/F₂ = A₁/A₂
This shows the force ratio equals the area ratio.
Common hydraulic applications:
- Car braking systems — foot pressure on small pedal creates large force at wheel brakes
- Hydraulic car jacks — small input force lifts heavy vehicles
- Hydraulic presses — used in manufacturing to shape metal
- Dentist chairs — hydraulic systems allow smooth height adjustment
- Excavator arms — hydraulic rams provide powerful lifting force
Advantages of hydraulic systems:
- Multiply force with mechanical advantage
- Smooth and precise control
- Can transmit force around corners through pipes
- Liquids are incompressible, giving immediate response
Pressure in gases
Gases also exert pressure, but the mechanism differs from liquids. Gas pressure results from:
Molecular collisions — gas molecules move randomly at high speeds and collide with container walls
Momentum transfer — each collision transfers momentum to the wall, exerting a tiny force
Cumulative effect — billions of collisions per second create a measurable pressure
Factors affecting gas pressure:
Temperature: Increasing temperature increases molecular speed, causing more frequent and forceful collisions, increasing pressure (at constant volume)
Volume: Decreasing volume forces molecules into smaller space, increasing collision frequency, increasing pressure (at constant temperature)
Amount of gas: More gas molecules mean more collisions, increasing pressure (at constant temperature and volume)
Unlike liquids, gas pressure does not significantly increase with depth in small containers because gases are much less dense.
Atmospheric pressure
The Earth's atmosphere exerts pressure due to the weight of air above us.
Standard atmospheric pressure at sea level ≈ 100,000 Pa (or 100 kPa or 1 × 10⁵ Pa)
This is also called:
- 1 atmosphere (1 atm)
- 1 bar (approximately)
- 1013 millibars (mb) — commonly used in weather forecasting
Why we don't feel crushed:
- Air pressure acts equally in all directions
- Pressure inside our bodies equals external atmospheric pressure
- We only notice pressure changes, not constant pressure
Variation of atmospheric pressure with altitude:
Atmospheric pressure decreases with height above sea level because:
- There is less air above you
- Air density decreases with altitude
- The column of air pressing down is shorter
Consequences of changing atmospheric pressure:
- Aircraft cabins must be pressurized at high altitude
- Ears "pop" when altitude changes rapidly
- Water boils at lower temperature at high altitude
- Sealed packets expand when taken to high altitude
- Weather systems involve areas of high and low pressure
Measuring pressure
Barometers measure atmospheric pressure:
Mercury barometer:
- Consists of a glass tube filled with mercury inverted in a dish of mercury
- The atmosphere pushes down on the mercury in the dish
- This supports a column of mercury in the tube (approximately 760 mm at sea level)
- Height of mercury column indicates atmospheric pressure
- Reading can be given in mmHg (millimetres of mercury)
Aneroid barometer:
- Contains a sealed metal chamber with partial vacuum
- Atmospheric pressure compresses or expands the chamber
- Mechanical linkage moves a pointer on a scale
- More portable than mercury barometer
- Used in aircraft altimeters
Manometers measure gas pressure:
U-tube manometer:
- A U-shaped tube containing liquid (often water or mercury)
- One end connects to the gas supply
- The other end is open to atmosphere or sealed
- Pressure difference causes liquid level difference in the two sides
- Height difference indicates pressure difference
Worked examples
Example 1: Calculating pressure from force and area
Question: A rectangular block has dimensions 0.5 m × 0.2 m and weighs 300 N. Calculate the pressure it exerts when resting on its largest face. [3 marks]
Solution:
Step 1: Calculate the area of the largest face Area = length × width = 0.5 m × 0.2 m = 0.1 m²
Step 2: Identify the force Force = weight = 300 N
Step 3: Calculate pressure using P = F/A Pressure = 300 N ÷ 0.1 m² Pressure = 3000 Pa (or 3000 N/m² or 3 kPa)
Mark scheme notes: 1 mark for correct area calculation, 1 mark for correct formula, 1 mark for correct answer with unit.
Example 2: Pressure in a liquid
Question: A diver descends to a depth of 15 m in seawater. The density of seawater is 1030 kg/m³ and g = 10 N/kg.
(a) Calculate the pressure due to the seawater at this depth. [3 marks] (b) Calculate the total pressure on the diver, including atmospheric pressure (100,000 Pa). [1 mark]
Solution:
(a) Using P = h × ρ × g
Step 1: Identify values h = 15 m ρ = 1030 kg/m³ g = 10 N/kg
Step 2: Substitute into equation P = 15 × 1030 × 10
Step 3: Calculate P = 154,500 Pa (or 154.5 kPa or 1.545 × 10⁵ Pa)
(b) Total pressure = pressure from water + atmospheric pressure Total pressure = 154,500 + 100,000 = 254,500 Pa (or 254.5 kPa)
Mark scheme notes: In part (a), 1 mark for correct formula, 1 mark for correct substitution, 1 mark for answer with unit. In part (b), 1 mark for adding atmospheric pressure.
Example 3: Hydraulic system calculation
Question: A hydraulic system has a small piston with area 0.002 m² and a large piston with area 0.05 m². A force of 80 N is applied to the small piston.
(a) Calculate the pressure in the hydraulic fluid. [2 marks] (b) Calculate the force produced at the large piston. [2 marks]
Solution:
(a) Using P = F/A for the small piston
Pressure = 80 N ÷ 0.002 m² Pressure = 40,000 Pa
(b) Pressure is transmitted equally throughout the fluid, so pressure at large piston = 40,000 Pa
Using P = F/A, rearranged to F = P × A
Force = 40,000 Pa × 0.05 m² Force = 2000 N
Alternative method for part (b): F₁/A₁ = F₂/A₂ 80/0.002 = F₂/0.05 F₂ = (80 × 0.05)/0.002 = 2000 N
Mark scheme notes: Award marks for correct method even if earlier calculation error is carried forward (error carried forward principle).
Common mistakes and how to avoid them
• Confusing force and pressure — Remember that pressure = force ÷ area. Force and pressure are different quantities with different units (N vs Pa). Always check what the question asks for.
• Forgetting to convert units — Areas must be in m² for pressure in Pa. Convert cm² to m² by dividing by 10,000. Depths must be in metres. Check all units before calculating.
• Not adding atmospheric pressure — When calculating total pressure on a submerged object, remember to add atmospheric pressure (100,000 Pa) to the pressure from the liquid unless specifically asked only for liquid pressure.
• Wrong way around for area and force in pressure calculations — Pressure = force ÷ area, not area ÷ force. Pressure decreases as area increases for the same force. Check your answer makes physical sense.
• Mixing up density values — Water density is 1000 kg/m³ (not 1 g/cm³ in calculations requiring kg/m³). Memorize common densities in correct units: water = 1000 kg/m³, mercury = 13,600 kg/m³, air ≈ 1.3 kg/m³.
• Incorrect rearrangement of hydraulic formulas — When using F₁/A₁ = F₂/A₂, be careful with cross-multiplication. Draw a line to separate known and unknown values clearly.
Exam technique for "Pressure in fluids and the atmosphere"
• Command words matter: "Calculate" requires working and a numerical answer with unit. "State" needs a brief answer without explanation. "Explain" requires reasons using scientific principles. Always check the command word and allocate time according to marks available.
• Show your working clearly: In calculations, write the formula first, substitute values with units, then calculate. If you make an arithmetic error, you can still earn method marks. Write each step on a separate line for clarity.
• Units are essential: Always include the correct unit with your final answer. Pressure can be given as Pa, N/m², or kPa. Be prepared to convert between these (1 kPa = 1000 Pa). One mark is often awarded purely for the correct unit.
• Use the data provided: Questions often give values like g = 10 N/kg or atmospheric pressure = 100,000 Pa. Use these given values even if you know slightly different ones. Examiners expect you to use their data for consistency in marking.
Quick revision summary
Pressure is force per unit area (P = F/A), measured in pascals. In liquids, pressure increases with depth (P = hρg) and acts equally in all directions. Hydraulic systems use Pascal's principle to multiply forces through different piston areas. Gas pressure results from molecular collisions with container walls. Atmospheric pressure is approximately 100,000 Pa at sea level and decreases with altitude. Always include units in calculations and remember to add atmospheric pressure when calculating total pressure on submerged objects.