Chapter revision
Revision summary
Key ideas, equations and common mistakes. Open any topic below for the full explanation.
- Pressure at a surface
- p = F / A; F = pA. Use the perpendicular force and actual contact area. N divided by m2 gives Pa. Compare the force/area ratio when both change.
- Density
- ρ = m / V. Use matched mass and volume measurements: g with cm3, or kg with m3. 1 g/cm3 = 1000 kg/m3.
- Liquid pressure difference
- Δp = ρgh for a stationary liquid of uniform density. h is vertical depth or level difference. Total pressure at depth = surface pressure + ρgh.
- Hydraulic press
- F1 / A1 = F2 / A2 for the stated ideal comparison. The transmitted pressure increase is equal; a larger piston area gives a larger additional force.
Choose the diagram and the pressure reference
| Situation | What to identify |
|---|---|
| Contact surface | The force perpendicular to that surface and its contact area. Do not use the object's volume. |
| Point in a liquid | Vertical depth below the surface and the pressure acting on that surface. Equal levels in the same connected stationary liquid have equal pressure. |
| Two pistons | The piston areas and the extra forces. For the simple model, use equal levels, the same atmosphere, and negligible piston weights and friction. |
| Barometer | The vertical height above the reservoir and the near-vacuum at the top. Atmospheric pressure is approximately ρgh only when the top pressure is negligible. |
| Open-end manometer | The full vertical separation and which surface is lower. Gas side lower: add ρgh to atmospheric pressure. Gas side higher: subtract it. |
Measurement reminders
mmHg (mm Hg) is a conventional pressure unit; mm alone is a length unit. With the supplied approximation 1 mmHg = 133 Pa, 760 mmHg is approximately 1.01 x 105 Pa. Keep this unit conversion separate from a column calculation using ρgh and a supplied g = 10 N/kg.
- For a regular solid, weigh it and determine volume from its shape and dimensions.
- For a suitable irregular solid, use the increase in liquid reading on full submersion. Avoid trapped air, water loss, absorption and dissolving.
- For a liquid, subtract the dry empty container's mass or tare correctly. Match the measured mass with the measured volume.
- Read fluid heights vertically from a common reference, with consistent meniscus readings at eye level.
- Convert square and cubic units properly: 1 cm2 = 0.0001 m2; 1 cm3 = 0.000001 m3.
Pressure is a scalar; a pressure force acts perpendicular to a surface. Keep total pressure distinct from a pressure difference, and keep equal pressure distinct from equal force.
Back to pressure at a surfaceReview a topic
- Pressure at a surface
- Density from measurements
- Pressure in a liquid
- Hydraulic systems
- Measuring atmospheric pressure
- Manometers and pressure differences