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AQA GCSE Physics · Topic 4.5 Forces · Physics only (Triple)
Pressure in Fluids
In this lesson you'll learn to: calculate pressure with p = F ÷ A; calculate the pressure from a column of
liquid with p = h ρ g; explain why pressure increases with depth, acts equally in all directions and
doesn't depend on the shape of the container; and explain why atmospheric pressure is greatest at the surface.
Physics only Pressure in fluids is in GCSE Physics (Triple), not
Combined Science: Trilogy. Combined students: skip to the next lesson.
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Prefer to watch? Scroll to the bottom for the video on this topic
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A video walkthrough is coming soon — it will appear at the bottom of this page
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Start here — have a play
Don't read anything yet. Pour water into tubes of different shapes, pull the plugs out of a tank, and squeeze a ball full of holes. Then send a diver deeper and watch the column of water above them grow.
The diver
Liquid:
density in kg/m³ · g = 9.8 N/kg
Your turn · g = 9.8 N/kg
Pa
Pressure in a fluid acts at right angles to any surface and equally in all directions. It depends only on the height of fluid above (and the density), not on the shape of the container. p = F ÷ A · p = h ρ g · pressure in pascals (Pa = N/m²).
Physics With Kate · physicswithkate.com — AQA GCSE Physics 4.5.5 · Physics only
Three experiments, three facts: same height → same pressure · deeper → more pressure · pressure acts in all directions.
Deeper means more fluid above you, so more weight on the same area
That one sentence is behind every pressure-in-fluids explanation. The notes show you how to write it for the marks.
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Revision notes
What a fluid is, and how it pushes
A fluid is a liquid or a gas. Its particles move about and collide with any surface they touch, so a fluid pushes on every surface in contact with it. The pressure in a fluid causes a force at right angles (normal) to that surface.
Pressure from a force on an area
⭐ The equation
pressure = force normal to a surface ÷ area of that surface p = F ÷ A
p in pascals (Pa), F in newtons (N), A in square metres (m²). 1 Pa = 1 N/m².
Same force on a smaller area = bigger pressure. A 600 N crate on a 0.20 m² base: p = 600 ÷ 0.20 = 3000 Pa.
Pressure from a column of liquid Higher tier
⭐ The equation
pressure = height of the column × density of the liquid × gravitational field strength p = h ρ g
p in Pa, h in metres (m), ρ (rho) in kg/m³, g in N/kg. h is the height of liquid above the point, which is its depth. It's on the equation sheet.
- Water: ρ = 1000 kg/m³. At a depth of 2.5 m: p = 2.5 × 1000 × 9.8 = 24 500 Pa.
- Where it comes from: the weight of the column of liquid above an area, divided by that area. Weight = m g = (h A ρ) g, so p = weight ÷ A = h ρ g.
- For a liquid with constant density, pressure is directly proportional to depth: double the depth, double the pressure.
- A denser liquid gives a bigger pressure at the same depth.
The three experiments on page 9
| Experiment | What you see | What it shows |
|---|---|---|
| Connected tubes of different shapes (Pascal's vases) | the liquid stands at the same level in every tube | pressure is the same at the same height in a fluid, whatever the shape or width of the container |
| Tank with holes at different depths | the jet from the lowest hole comes out fastest and most horizontally | pressure increases as the height of fluid above increases |
| Sphere with holes on a syringe | water squirts out of every hole equally | pressure in a fluid acts equally in all directions |
The answer that gets the marks: why is the pressure greater at the bottom of a swimming pool?
p = h ρ g. At the bottom of the pool there is a greater height of water
above, so a greater weight of water (a greater force) acts on the same area, so the
pressure is greater at the bottom than just below the surface.
write the formula out first height above → weight so the pressure is greater
Upthrust and floating
An object in a fluid has a greater pressure on its bottom (deeper) than on its top. That difference gives a resultant upward force: upthrust. The upthrust equals the weight of fluid the object pushes out of the way (displaces). If the upthrust can balance the object's weight before it is fully under, it floats; if not, it sinks. That's why an object less dense than the fluid floats.
Atmospheric pressure
- The atmosphere is a thin layer of air round the Earth. It gets less dense with height.
- Air molecules collide with surfaces, causing atmospheric pressure. At the Earth's surface there is the greatest height of air above you, so the greatest weight of air: the greatest pressure.
- Higher up there's less air above, so less weight, and the pressure decreases with height.
- You can't use p = h ρ g for the whole atmosphere, because the density is not constant: there's no single ρ to put in.
⚠ Trap — units
Area in m²: 1 cm² = 0.0001 m² (÷ 10 000, not ÷ 100). Depth in metres: 40 cm = 0.40 m. Answers in Pa; if you give kPa, say so (24 500 Pa = 24.5 kPa).
🗣 Words to use in a written answer
Tick each one off as you use it.
How to write it in the exam
Explain why the pressure at the bottom of a swimming pool is greater than the pressure just below the surface. (3 marks)
p = h ρ g. At the bottom there is a greater height of water above, so a greater weight of water pressing down on the area below it, so the pressure is greater. Water has a constant density, so pressure is directly proportional to depth.
A tank is filled with water to a depth of 1.2 m. Density of water = 1000 kg/m³, g = 9.8 N/kg. Calculate the pressure at the bottom. (3 marks)
p = h ρ g = 1.2 × 1000 × 9.8 = 11 760 Pa (about 1.2 × 10⁴ Pa)
Explain why liquid reaches the same level in every tube when connected tubes of different shapes are filled. (2 marks)
The liquid is connected, so the pressure at the bottom is the same everywhere. Pressure depends only on the height of liquid above (p = h ρ g), not on the shape or width of the tube, so the liquid rises to the same height in each one.
A force of 50 N acts on a piston of area 5 cm². Calculate the pressure.
A = 5 ÷ 10 000 = 0.0005 m². p = F ÷ A = 50 ÷ 0.0005 = 100 000 Pa
Explain why atmospheric pressure is greatest at the Earth's surface, and why p = h ρ g can't be used for the whole atmosphere. (3 marks)
At the surface there is the greatest height of air above, so the greatest weight of air pressing down: the greatest pressure. Higher up there's less air above, so the density falls. Because the density is not constant, there is no single ρ to use in p = h ρ g.
✅ Check your answer
Formula written out first · h is the height of fluid above the point, in m · area in m² · "greater height above → greater weight → greater pressure" in that order · answer in Pa.
📘 Now do it in your workbook
Both pressure equations in words and symbols with your own calculation for each, the swimming-pool and atmosphere explanations, then the three diagrams and an exam-style question.
AQA GCSE Physics Workbook · FORCES · page 9✅ Can you do it? Tick as you go
0% complete🎉 Nice work! You've ticked off every objective for this topic.
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Prefer to watch? Here's the whole thing
Video walkthrough — coming soon
Both pressure equations, the three experiments and the swimming-pool answer explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it.
Both pressure equations, the three experiments and the swimming-pool answer explained out loud — useful for a last-minute recap, or if you'd rather hear it than read it. The video is on its way.
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Video coming soon
The walkthrough for this lesson is being filmed and will appear right here. Until then, the notes and the free workbook page above cover every mark.
Now put it into practice
Page 9 of the Forces workbook is free: both pressure equations, the explanations, and the three experiments to draw and match.
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