1.9.2Motion, Forces and Energy
Pressure in a Liquid — Cambridge IGCSE Physics 0625 Revision Notes & Topical Questions
5 min read 9 parts Lesson 91 of 91 1 quiz
Lesson summary
1.9.2 Pressure in a Liquid — IGCSE PHYSICS notes: Explain how the pressure in a liquid depends on depth and density and calculate it using p = ρgh (Extended).A liquid has weight, so liquid higher up pushes down on liquid below.Pressure beneath the surface increases with depth bec…
- Column of water
- Depth of 10 m in water
- Total pressure at depth h
- Pressure due to the liquid alone
- Different liquids have different densities
- Submarines and deep-sea vehicles
Part 1 of 7Why pressure increases with depth
A liquid has weight, so liquid higher up pushes down on liquid below.
Pressure beneath the surface increases with depth because more liquid lies above.
A diver feels the pressure increase with depth.
Dam walls are thicker at the bottom than at the top.
Column of water
- Column of water the highest pressure is at the bottom, so a hole near the bottom gives a strong jet and a hole near the top a weak jet.
Part 2 of 7Properties of liquid pressure
1
Pressure acts in all directions at a given depth and at right angles to any surface.
2
Pressure is the same at all points at the same depth in the same liquid.
3
Holes at the same height spurt water the same distance.
4
Pressure increases with depth and with the density of the liquid.
5
Sea water is denser than fresh water, so its pressure is greater at the same depth.
6
Pressure does not depend on the shape or width of the container, only on the depth below the surface.
Part 3 of 7The equation for liquid pressure (Extended)
Equation
- Equation the change in pressure is Δp = ρgΔh, or p = ρgh for the pressure due to the liquid at depth h.
- Δp is the pressure in pascals (Pa).
- ρ is the density in kg/m3; water is about 1000 kg/m3 and sea water about 1030 kg/m3.
- g is the gravitational field strength, 9.8 N/kg.
- h is the vertical depth below the surface in metres.
Origin
- Origin a column of liquid of base area A and height h has weight mg = ρAhg, so the pressure at its base is ρAhg ÷ A = ρgh.
Depth of 10 m in water
- ρgh is about 98 000 Pa, roughly one atmosphere, so every 10 m of water adds about one more atmosphere.
Part 4 of 7Total pressure
1
The surface of an open liquid is under atmospheric pressure, about 100 kPa.
2Total pressure at depth h
Total pressure at depth h atmospheric pressure + ρgh.
3Pressure due to the liquid alone
- Pressure due to the liquid alone subtract atmospheric pressure from the total.
4
Convert kPa to Pa and depths to metres before using the equation.
Part 5 of 7Why depth matters and not shape
1
The pressure at a point is due to the weight of the column of liquid directly above it.
2
A narrow tube and a wide tank of the same depth give the same pressure at the base.
3
In connected vessels of different shapes the liquid rises to the same level in each, so pressure at the same depth is equal.
4
A tall thin column can give a greater pressure than a wide shallow container if its depth is greater.
5Different liquids have different densities
- Different liquids have different densities mercury (about 13 600 kg/m3) gives about 100 kPa at only 0.76 m depth.
6
A mercury barometer is compact, while a water barometer would need to be over 10 m tall.
Part 6 of 7Uses of liquid pressure
Uses of liquid pressure
Dams
- Dams they have thick bases to withstand the greater pressure deep down.
Submarines and deep-sea vehicles
- Submarines and deep-sea vehicles they have strong hulls, and divers must adjust to high pressure.
Hydraulic systems
- Hydraulic systems a liquid is almost incompressible, so pressure applied to one piston is transmitted equally to another.
- With input piston area A1 and output piston area A2, F2 = F1 × (A2 ÷ A1), so a small force produces a large one.
- Hydraulic systems are used in car brakes and jacks.
Manometers
- Manometers the difference in liquid heights in a U-tube measures a pressure difference, Δp = ρgΔh.What the symbols mean: p = pressure due to the liquid (Pa) · ρ = density of the liquid (kg m−3) · g = 9.81 N kg−1 · h = depth (m)
Part 7 of 7More from the specification
More from the specification
Contact forces and sharp surface pressure
- Contact forces and sharp surface pressure concentrated perpendicular forces acting on sharp point geometries generate extremely high localised pressure.
Pressure and Surface Area
- Pressure is defined as force per unit area (p = F/A),
- where force in newtons (N) divided by area in metres squared (m²) yields pressure in pascals (Pa).
High Pressure vs Low Pressure Footwear
- High-heeled shoes exert extreme pressure because body weight is concentrated onto a tiny contact area,
- whereas flat shoes spread weight to reduce pressure.
Hydrostatic Pressure in Liquids
- The pressure exerted at depth h below a liquid surface is given by Δp = ρgh, acting equally in all directions on an immersed object.
Solving Hydrostatic Problems
- When calculating liquid pressure, identify relevant quantities (density ρ, depth h,
- and g = 9.8 N/kg),
- and substitute into equations using coherent SI units.
Newton
- Unit of force, kg m s-2.
Spread
- The extent to which repeated readings differ.
Key terms
| Term | Meaning |
|---|---|
| Pressure in a liquid | Pressure caused by the weight of liquid above; p = ρgh. |
| Density (ρ) | Mass per unit volume, in kg/m³. |
| Depth | Vertical distance below the surface. |
| Atmospheric pressure | Pressure of the air, about 100 kPa. |
| Hydraulic system | Machine using liquid pressure to transmit a force. |
| Incompressible | Cannot be squashed into a smaller volume, as with liquids. |
Avoid these mistakes
1
Using the length of the container or the volume of liquid instead of the vertical depth.
2
Forgetting to use density in kg/m³ — 1 g/cm³ is 1000 kg/m³.
3
Thinking a wide container has a larger pressure at the bottom — only depth and density matter.
4
Forgetting atmospheric pressure when the total pressure is asked for.
5
Thinking pressure is greatest at the surface — it increases with depth.
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