Pressure in Fluids

This lesson covers pressure, including pressure in solids and fluids (liquids and gases), upthrust and atmospheric pressure — as required by the Edexcel GCSE Physics specification (1PH0), Topic 2: Motion and Forces. You need to know the equations for pressure, understand how pressure varies with depth, and explain floating and sinking.

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What Is Pressure?

Pressure is the force applied per unit area. It describes how concentrated a force is — the smaller the area, the greater the pressure for the same force.

Pressure = Force ÷ Area

P = F / A

Quantity	Symbol	Unit
Pressure	P	Pascals (Pa)
Force	F	Newtons (N)
Area	A	Square metres (m²)

1 Pa = 1 N/m² — a pressure of one pascal means a force of one newton is spread over one square metre.

Rearranging the Equation

• F = P × A (to find force)
• A = F ÷ P (to find area)

Exam Tip: Make sure you convert units correctly. Areas should be in m² — if given in cm², divide by 10,000 (since 1 m² = 10,000 cm²). This is a very common source of errors.

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Worked Examples: P = F / A

Worked Example 1

A box weighs 600 N and has a base area of 2 m². What pressure does it exert on the floor?

P = F / A = 600 / 2 = 300 Pa

Worked Example 2

A woman weighing 600 N stands in high-heeled shoes. The total area of both heels in contact with the ground is 0.0002 m². What pressure do the heels exert?

P = F / A = 600 / 0.0002 = 3,000,000 Pa (3 MPa)

This is much greater than the pressure from flat shoes (perhaps 30,000 Pa) — which explains why high heels can damage soft floors.

Worked Example 3

A hydraulic press needs to exert a pressure of 500,000 Pa. If the piston has an area of 0.04 m², what force is produced?

F = P × A = 500,000 × 0.04 = 20,000 N

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Pressure in Liquids

Pressure in a liquid increases with depth and depends on the density of the liquid. The equation is:

Pressure = Density × Gravitational Field Strength × Height (depth)

P = ρ g h

Quantity	Symbol	Unit
Pressure	P	Pascals (Pa)
Density	ρ (rho)	Kilograms per cubic metre (kg/m³)
Gravitational field strength	g	Newtons per kilogram (N/kg) — use 9.8 N/kg
Height (depth) of liquid	h	Metres (m)

Key Points About Pressure in Liquids

• Pressure in a liquid acts equally in all directions at a given depth.
• Pressure increases with depth — the deeper you go, the greater the weight of liquid above you.
• Pressure depends on the density of the liquid — a denser liquid (e.g. mercury) creates more pressure at the same depth than a less dense liquid (e.g. water).
• Pressure does not depend on the shape or width of the container — only on the depth and density.

Worked Example 4

Calculate the pressure at a depth of 25 m in the sea. The density of seawater is 1025 kg/m³ and g = 9.8 N/kg.

P = ρgh = 1025 × 9.8 × 25 = 251,125 Pa ≈ 251 kPa

Worked Example 5

A diver descends to a depth where the water pressure is 196,000 Pa. The density of the water is 1000 kg/m³. What is the depth?

h = P / (ρg) = 196,000 / (1000 × 9.8) = 20 m

Exam Tip: Remember that P = ρgh gives the pressure due to the liquid only. The total pressure on a diver includes atmospheric pressure (about 101,325 Pa) plus the water pressure. Read the question carefully to see if it asks for total pressure or just the pressure from the liquid.

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Atmospheric Pressure

Atmospheric pressure is the pressure exerted by the weight of air in the Earth's atmosphere above us.

Key Facts

• At sea level, atmospheric pressure is approximately 101,325 Pa (about 101 kPa or 1 atm).
• Atmospheric pressure is caused by air molecules colliding with surfaces.
• Atmospheric pressure decreases with altitude — as you go higher, there is less air above you, so there is less weight of air pushing down.

Why Atmospheric Pressure Decreases with Altitude

Altitude	Atmospheric Pressure	Reason
Sea level	~101 kPa	Maximum column of air above
Top of a mountain	~70 kPa	Less air above, fewer collisions
Edge of atmosphere	~0 kPa	Almost no air above

• The atmosphere has no clear boundary — it just gets thinner and thinner.
• At higher altitudes, the air is less dense (fewer molecules per unit volume), so there are fewer collisions with surfaces and the pressure is lower.

graph TD
    A["Atmospheric Pressure"] --> B["Caused by the weight<br/>of air above a surface"]
    A --> C["Acts in all directions"]
    A --> D["Decreases with<br/>increasing altitude"]
    D --> E["Less air above<br/>= less weight<br/>= lower pressure"]

    style A fill:#2c3e50,color:#fff
    style B fill:#2980b9,color:#fff
    style C fill:#27ae60,color:#fff
    style D fill:#e67e22,color:#fff
    style E fill:#c0392b,color:#fff

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Upthrust and Archimedes' Principle

When an object is placed in a fluid (liquid or gas), the fluid exerts an upward force on the object called upthrust (or buoyant force).

What Causes Upthrust?

• Pressure in a fluid increases with depth.
• The bottom of a submerged object is at a greater depth than the top.
• Therefore, the pressure on the bottom is greater than the pressure on the top.
• This pressure difference creates a net upward force — the upthrust.

Archimedes' Principle

The upthrust on an object is equal to the weight of fluid displaced by the object.

If an object displaces 0.5 m³ of water (density 1000 kg/m³):

• Mass of displaced water = 1000 × 0.5 = 500 kg
• Weight of displaced water = 500 × 9.8 = 4900 N
• Upthrust = 4900 N

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