Pressure
Density, pressure on surfaces, pressure in liquids, hydraulic systems, barometers and manometers for G3 Pure and O-Level Physics.
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Before you begin
Pressure measures how concentrated a force is. The lessons start with density, then pressure on a surface, then the pressure a liquid exerts because of its own weight. Hydraulic systems use liquid pressure to multiply force, and barometers and manometers use the height of a liquid column to measure atmospheric pressure and pressure differences.
Be comfortable with: mass and weight, because most pressure questions start by finding a weight with W = mg.
Learning goals
- Define pressure as force per unit area
- Apply pressure = force ÷ area
- Explain pressure transmission in a hydraulic press
- Apply density = mass ÷ volume
- Apply liquid-column pressure = height × density × gravitational field strength
- Explain how liquid-column height measures atmospheric pressure
- Explain how a manometer measures pressure difference
Syllabus statements covered
- define pressure in terms of force and area
- recall and apply the relationship pressure = force / area to new situations or to solve related problems
- describe and explain the transmission of pressure in hydraulic systems with particular reference to the hydraulic press
- recall and apply the relationship density = mass / volume to new situations or to solve related problems
- recall and apply the relationship pressure due to a liquid column = height of column × density of the liquid × gravitational field strength to new situations or to solve related problems
- describe how the height of a liquid column may be used to measure the atmospheric pressure
- describe the use of a manometer in the measurement of pressure difference
Lessons
Work through them in order.
Foundations
Liquid pressure and hydraulics
Pressure-measuring instruments
Practise and check
Or choose
Topic reference
Quick reference
| Quantity | Equation | Unit |
|---|---|---|
| density | ρ = m/V | kg m⁻³ or g cm⁻³ |
| pressure | p = F/A | pascal (Pa), 1 Pa = 1 N m⁻² |
| pressure due to liquid column | p = hρ g | Pa |
| total pressure at depth | p = pₐₜₘ + hρ g | Pa |
| hydraulic press | F₁/A₁ = F₂/A₂ | — |
| manometer | Δ p = Δ h ρ g | Pa |
Useful values and conversions: 1 g cm⁻³ = 1000 kg m⁻³; 1 cm² = 10⁻⁴ m²; 1 cm³ = 10⁻⁶ m³. Water is 1000 kg m⁻³ and mercury is 13.6 × 10³ kg m⁻³. Atmospheric pressure at sea level is about 1.0 × 10⁵ Pa, or about 76 cm of mercury.
Core knowledge to remember
- Density is mass per unit volume.
- Pressure is the perpendicular force per unit area. For the same force, a smaller area gives a larger pressure.
- The pressure due to a liquid column is height × density × gravitational field strength. It depends on vertical depth, not on the shape of the container, and acts in all directions.
- A pressure change applied to an enclosed liquid is transmitted throughout the liquid. In a hydraulic press, the larger piston receives a larger force but moves a shorter distance.
- Atmospheric pressure is caused by the weight of the air above. A mercury barometer measures it as the vertical height of the mercury column it supports.
- A manometer measures a pressure difference from the vertical difference between its liquid levels. The side with the lower level has the higher pressure.
Common mistakes
- Leaving areas in cm² or volumes in cm³ when working in SI units, or converting them with 10⁻² instead of 10⁻⁴ or 10⁻⁶.
- Using a mass in kilograms as the force in p = F/A instead of the weight in newtons.
- Using a slanted length instead of the vertical height in hρ g.
- Adding atmospheric pressure when only the pressure due to the liquid is asked for, or leaving it out when the total pressure is asked for.
- Saying a hydraulic system transmits force. It transmits pressure.
- Using the diameter ratio instead of the area ratio for circular pistons.
- Reading a manometer the wrong way round: the lower liquid level is on the higher-pressure side.