K323 / 2027
Pressure overview

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

Identify what is being compared before calculating
SituationWhat to identify
Contact surfaceThe force perpendicular to that surface and its contact area. Do not use the object's volume.
Point in a liquidVertical depth below the surface and the pressure acting on that surface. Equal levels in the same connected stationary liquid have equal pressure.
Two pistonsThe piston areas and the extra forces. For the simple model, use equal levels, the same atmosphere, and negligible piston weights and friction.
BarometerThe 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 manometerThe 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 surface

Practise exam questions

Write your answer first, then tick the mark points it makes.

Exam-style question

Define pressure and state its SI unit. [2]

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Exam-style question

A diver swims 12 m below the surface of the sea. The density of sea water is 1030 kg/m3, g = 10 N/kg and atmospheric pressure is 1.0 x 105 Pa. Calculate the total pressure on the diver. [4]

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Exam-style question

In a hydraulic jack, a force of 200 N is applied to a small piston of area 0.0020 m2. The large piston has an area of 0.050 m2. Explain how the jack produces a larger force, and calculate the force on the large piston. [3]

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Exam-style question

A student measures the pressure due to a liquid at different depths. Her graph of pressure against depth is a straight line through the origin, passing through (0.50 m, 4000 Pa). Taking g = 10 N/kg, use the graph to find the density of the liquid. [3]

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Exam-style question

Data-based question: Water pressure from a roof tank [9]

A water tank on the roof of a block of flats supplies the taps below it. A plumber turns off the taps and uses a gauge to measure the water pressure at a tap on three floors. The gauge reads the pressure above atmospheric pressure. The density of water is 1000 kg/m3 and g = 10 N/kg.

Table 1. Gauge pressure at taps on different floors
floorheight of tap above ground / mgauge pressure / kPa
26.0255
515.0165
824.075
  1. (a) Use two readings to show that the pressure falls by 10 kPa for each metre of height, and show that this agrees with p = ρgh. [2]
  2. (b) Calculate the height of the water surface in the tank above the ground. [2]
  3. (c) Predict the gauge pressure at a tap on floor 10, 30.0 m above the ground. [1]
  4. (d) State one assumption you made in (b) or (c). [1]
  5. (e) A washing machine needs a gauge pressure of at least 50 kPa. A resident on floor 10 says it will work if the tank is raised by 3.0 m. Evaluate her suggestion. [3]

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Quick recall

Card 1 of 5. Answer in your head, then check.

A pad's perpendicular force doubles while its contact area becomes four times as large. How does its average pressure change?

Review a topic

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