Pressure: Revision Notes

Condensed for the final weeks. For the full explanation, use the Pressure study guide.

The two equations

PRESSURE FROM A FORCE
p = F / A            p in pascals (Pa), F in N, A in m2
                     1 Pa = 1 N/m2

PRESSURE IN A LIQUID (at depth h)
p = rho g h          rho = density (kg/m3), g ≈ 9.8 N/kg on Earth
                     h = DEPTH below the surface

Note what p = ρgh does not contain: area, shape or total volume. Pressure at a depth depends only on depth, density and g.

Pressure from a force

Same force, smaller area → greater pressure. This explains:

• Sharp knives and drawing pins — tiny area, high pressure, cuts easily.
• Skis and tractor tyres — large area, low pressure, prevents sinking.
• Camels’ wide feet — spread weight over soft sand.

The force from pressure always acts perpendicular to the surface — shown experimentally with a thistle funnel and manometer: rotating the funnel’s open end while holding it at the same depth gives the same manometer reading whichever way it faces, since the liquid pushes at right angles to the membrane regardless of its orientation.

Pressure in liquids

Key facts:

• Increases with depth.
• Acts equally in all directions at a given depth.
• Independent of the shape or width of the container.
• Greater for a denser liquid.

This is why dam walls are thicker at the base — pressure is greatest there.

Atmospheric pressure

Caused by the weight of air above. Roughly 100 000 Pa (1 × 10⁵ Pa) at sea level, decreasing with altitude as there is less air above.

Mercury barometer: the height of the mercury column is supported by atmospheric pressure. At sea level ≈ 760 mm Hg.

Mercury is used rather than water because its high density keeps the column a manageable height — a water barometer would need to be over 10 m tall.

Manometer: a U-tube measuring the pressure of a gas supply; the difference in the two levels gives the excess pressure over atmospheric.

Worked example

A tank holds water 2.5 m deep. Find the pressure at the bottom. (ρ = 1000 kg/m³, g = 9.8 N/kg)

p = rho g h = 1000 x 9.8 x 2.5 = 24 500 Pa

Total pressure including atmosphere:
24 500 + 100 000 = 124 500 Pa

Read the question carefully — “pressure due to the water” excludes atmospheric; “total pressure” includes it.

Hydraulic systems (Pascal’s principle) — background, not examinable

Beyond the O Level Physics 5054 syllabus: the pressure subtopic does not include an outcome on hydraulic systems or transmission of pressure. The following is background reading only.

Pressure applied to an enclosed liquid is transmitted equally throughout the fluid, so a small force on a small piston produces a large force on a larger piston:

p = F / A  (same p throughout)   so   F(output) = p x A(output)

Worked example. A force of 40 N is applied to a piston of area 0.0004 m². The output piston has area 0.0060 m². Find the output force.

p = F / A = 40 / 0.0004 = 100 000 Pa
F(output) = p x A(output) = 100 000 x 0.0060 = 600 N

Liquids are used rather than gases because liquids are virtually incompressible, so pressure is transmitted immediately; a gas would compress first, delaying the output force.

Exam traps

• Use depth in p = ρgh, not the height of the container or the length of a slope.
• Area must be in m² — convert from cm² by dividing by 10 000.
• Pressure in a liquid does not depend on the container’s shape or the volume of liquid.
• Distinguish pressure due to the liquid from total pressure including atmospheric.
• Mercury is chosen for its density, not its colour or toxicity.
• The force from pressure acts perpendicular to the surface, whatever the surface’s orientation.
• In a hydraulic system, it is the pressure that stays equal throughout, not the force. (Background — hydraulic systems are not on the 5054 syllabus.)

Self-test

1. A 600 N person stands on one foot of area 0.015 m². Find the pressure.
2. Why are dam walls thicker at the bottom?
3. State two factors affecting pressure at a point in a liquid.
4. Why is mercury used in a barometer rather than water?
5. Does pressure at 3 m depth differ between a narrow tube and a wide tank?
6. In which direction does the force from pressure act on a submerged surface?
7. (Background, not examinable.) A hydraulic system has an input piston of area 0.0004 m² (force 40 N) and an output piston of area 0.0060 m². Find the output force, and explain why the system uses a liquid rather than a gas.

Answers: 1. p = 600/0.015 = 40 000 Pa. 2. Pressure increases with depth, so the force on the wall is greatest at the base and more material is needed to withstand it. 3. Depth below the surface and the density of the liquid (and g). 4. Mercury is about 13.6 times denser than water, so the supported column is around 760 mm rather than over 10 m — a practical instrument height. 5. No — pressure depends only on depth, density and g, not on the container’s width or shape. 6. Perpendicular to the surface, regardless of the surface’s orientation. 7. p = 40 ÷ 0.0004 = 100 000 Pa; F(output) = 100 000 × 0.0060 = 600 N. A liquid is used because it is virtually incompressible, so pressure is transmitted immediately and in full; a gas would compress first, delaying the output force.