PressureCambridge IGCSE Physics: Revision notes

Pressure is defined as the force acting perpendicular to a surface per unit area. It is a scalar quantity measured in pascals (Pa), where 1 Pa = 1 N/m².

The fundamental equation is:

p = F/A

Where:

• p = pressure in pascals (Pa) or N/m²
• F = force in newtons (N)
• A = area in square metres (m²)

This equation shows that pressure is directly proportional to force and inversely proportional to area. A larger force creates greater pressure, while spreading a force over a larger area reduces pressure.

Pressure changes dramatically depending on how force is applied:

Effect of increasing force:

• Increasing the force acting on a surface increases pressure proportionally (p ∝ F)
• A heavier person standing on a floor exerts greater pressure than a lighter person on the same surface area

Effect of increasing area:

• Increasing the area over which a force is applied decreases pressure proportionally (p ∝ 1/A)
• A force spread over a larger area produces less pressure
• Conversely, concentrating a force into a smaller area produces much greater pressure

Everyday examples:

This principle explains why sharp objects cut easily (high pressure) and why shoes with heels sink into soft ground more than flat shoes.

Pressure beneath the surface of a liquid increases with depth due to the weight of liquid above pressing down.

Key observations:

• At the surface of a liquid, pressure equals atmospheric pressure (approximately 101,000 Pa)
• As you go deeper, the increasing column of liquid adds to the pressure
• Pressure acts equally in all directions at any given depth (Pascal's principle)
• The change in pressure depends only on depth and the properties of the liquid, not on the shape of the container

Qualitative description:

• A small increase in depth produces a measurable increase in pressure
• Doubling the depth approximately doubles the additional pressure from the liquid
• Denser liquids exert greater pressure at the same depth than less dense liquids
• This is why submarines experience greater force at greater depths, and why dam walls are thicker at the bottom

The pressure change caused by a column of liquid is given by:

Δp = ρgΔh

Where:

• Δp = change in pressure in pascals (Pa)
• ρ = density of the liquid in kilograms per cubic metre (kg/m³)
• g = gravitational field strength, approximately 9.8 m/s² (or 10 m/s² for approximations)
• Δh = change in depth in metres (m)

Deriving the equation:

Pressure is defined as force per area. The force exerted by a liquid column is its weight:

• Weight = mass × g
• Mass = density × volume
• For a column of uniform cross-section: Volume = area × height
• Therefore: Pressure = (ρ × A × Δh × g) / A = ρgΔh

Important points:

• This equation only gives the additional pressure caused by the liquid
• Total pressure at depth = atmospheric pressure + ρgΔh
• The equation is linear: doubling depth doubles the pressure increase
• It applies to any incompressible fluid

The density of a liquid directly controls how much pressure increases with depth:

Relationship between density and pressure:

• From Δp = ρgΔh, pressure change is directly proportional to density (Δp ∝ ρ)
• At the same depth, a denser liquid exerts greater pressure than a less dense liquid
• Doubling the density doubles the pressure increase at any given depth

Comparative examples:

Mercury creates vastly higher pressure at the same depth because it is much denser than water. This is why barometers using mercury can be much shorter than water-based pressure measuring devices.

Practical implications:

• Oil rigs must design equipment differently depending on the density of fluids involved
• Marine organisms experience different pressures in different ocean depths and salinity zones
• Industrial processes involving dense liquids require stronger containment vessels at greater depths