G3 Physics and O-Level Pressure Hub

G3 Physics and O-Level pressure hub: density, pressure in solids, hydrostatic pressure, hydraulics, barometers and manometers.

  • SEC G3 Physics 2027
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

Pressure describes how a perpendicular force is distributed over an area. This topic covers density, contact pressure, pressure due to liquid columns, hydraulic pressure transmission, and the use of barometers and manometers.

Boyle’s law and upthrust are separated below as optional extension material, so the main route stays at the required depth.

Start Here

Before you begin:

Follow this order:

  1. Density
  2. Pressure in solids (p = F/A)
  3. Hydrostatic pressure (Δ p = ρ gh)
  4. Hydraulic systems
  5. Barometers and manometers

What you will learn

The lessons build the topic in three connected groups:

  1. Pressure and density: define and calculate p = F/A, and calculate ρ = m/V.
  2. Liquid columns and measurement: calculate Δ p = ρ gΔ h; explain how a barometer measures atmospheric pressure and how a manometer measures pressure difference.
  3. Hydraulics: describe and explain how a pressure change is transmitted through an enclosed, approximately incompressible liquid, with particular reference to the hydraulic press.
Keep the quantities distinct

A hydraulic system transmits a pressure change, not an unchanged force. A larger output piston produces a larger force because the same pressure acts over a larger area.

Lessons

Foundations

  • Density

    Calculating mass per unit volume and floating/sinking.

  • What is pressure?

    Relationship between force, area, and pressure in solids.

Liquid pressure and hydraulics

  • Hydrostatic Pressure

    Pressure in liquids depending on depth, density, and gravity.

  • Hydraulic Systems

    Transmission of pressure in liquids and force multipliers.

Pressure-measuring instruments

  • Barometers

    Measuring atmospheric pressure using mercury columns.

  • Manometers

    Measuring gas pressure differences using U-tubes.

Optional extension

Revision

Quick Reference
QuantityFormulaSI Unit
Densityρ = m/Vkg m⁻³
Pressure (solids)p = F/APa = N m⁻²
Pressure increase (liquids)Δ p = ρ ghPa
Total pressure at depthpₜₒₜₐₗ = pₐₜₘ + ρ ghPa
Atmospheric pressurepₐₜₘ ≈ 1.0 × 10⁵ PaPa
Standard atmosphere1 atm ≈ 101 kPa≈ 760 mmHg

Units & Conversions (Quick Check)

  • 1 Pa = 1 N m⁻² and 1 kPa = 1000 Pa.
  • Area: 1 m² = 10,000 cm².
  • Volume: 1 m³ = 10⁶ cm³.
  • Density: 1 g cm⁻³ = 1000 kg m⁻³.
Quick facts to remember
  • Pressure: Force acting per unit area.
  • Density: Mass per unit volume of a substance.
  • Hydraulic pressure transmission: a pressure change applied to an enclosed liquid is transmitted throughout the liquid.
  • Atmospheric Pressure: The pressure exerted by the weight of the air in the atmosphere (approx. 10⁵ Pa at sea level).

Liquid pressure: what formula does the question want?

  • Pressure increase due to depth: Δ p = ρ gh.
  • Total (absolute) pressure at depth: pₜₒₜₐₗ = pₐₜₘ + ρ gh.

Hydrostatic questions (method checklist)

  1. Identify whether the question asks for Δ p or pₜₒₜₐₗ.
  2. Use vertical depth h (not distance along a slope).
  3. Convert ρ to kg m⁻³ and h to m before substituting.
  4. If comparing two points, use Δ h between the points: Δ p = ρ g Δ h.

Hydraulics (force multiplier)

  • For piston faces at the same level in an ideal hydraulic system, F₁/A₁ = F₂/A₂.
  • Trade-off: the smaller input piston moves farther than the larger output piston; A₁x₁ = A₂x₂ and ideal input work equals output work.

Manometer rule (U-tube)

  • In the same connected liquid, points at the same horizontal level have the same pressure.
  • Use the vertical height difference Δ h to relate pressures: Δ p = ρ gΔ h.
Visual Snapshots (graphs)

These are schematic. Use them to remember how pressure changes when you change area or depth.

Pressure in solids: same force, different areaBar chart showing pressure decreases as contact area increases for a fixed force (P = F/A).Pressure in solids: same force, different areaContact areaPressure (kPa)
Using p = F/A: increasing area reduces pressure (inverse relationship).
Data table
Contact areaForce = 100 N
0.01 m²10
0.02 m²5
0.03 m²3
0.04 m²3
0.05 m²2

Hydrostatic pressure increases with depth

Pressure increase in water versus depth, showing a straight-line proportional relationship (P = hρg).

Scroll across the graph to read all labels.

Pressure increase in water versus depth, showing a straight-line proportional relationship (P = hρg).Pressure increase in water versus depth, showing a straight-line proportional relationship (P = hρg).
Using Δ p = ρ gh: pressure increase is proportional to depth (straight line).
Open full-size graph
View figure data
Values for Hydrostatic pressure increases with depth
Depth (m)Water (ρ≈1000 kg m⁻³, g≈10 m s⁻²)
00
110
220
330
440
550
Top Exam Traps
  1. Area units: area must be in m² for pressure in pascals. Remember: 1 m² = 10,000 cm², not 100.
  2. Column or total pressure: ρ gh gives the pressure due to the liquid column. Add surface pressure only when total pressure is requested.
  3. Barometer height: use the vertical height difference, independent of tube diameter or tilt.
  4. Manometer sign: in a U-tube, the side with the lower liquid level is acted on by the higher pressure.
  5. Approximately incompressible liquid: do not say that force is transmitted or that pressure transmission creates energy.
  6. Vertical height: in ρ gh, use vertical depth or vertical level difference, not length along a sloping tube.
  7. Pressure difference: a manometer directly gives Δ p. Add or subtract atmospheric pressure only if a gas pressure is requested.
  8. Density units: convert consistently between g cm⁻³ and kg m⁻³.

Check your understanding

Worked example: A 3.0 kg block rests on a face of area 0.020 m². Taking g = 10 N kg⁻¹, its weight is 30 N, so the contact pressure is

p = F/A = 30/0.020 = 1.5 × 10³ Pa.

The force here is the perpendicular contact force. Do not substitute mass directly into p = F/A.

Practise this: Find the pressure increase 0.80 m below the surface of water using ρ = 1000 kg m⁻³ and g = 10 N kg⁻¹. Then explain why a manometer uses a vertical height difference rather than the length measured along a sloping tube.

Practice

  1. Use the Pressure check for density, contact pressure, fluid pressure, hydraulics and pressure instruments.
  2. Use the Pressure and Hydraulics Explorer to test predictions, then complete the structured questions with full working and units.

Continue learning

Continue to Thermal Physics, where the kinetic particle model explains gas pressure microscopically. Return to Work, Energy and Power if the hydraulic distance-and-work trade-off needs revision.

Course and syllabus information
Course
SEC G3 Physics
Edition
SEC G3 Physics 2027