Pressure in a Fluid | Physics

📖 In-Depth Theory

Pressure in Fluids

PRESSURE in a fluid acts in ALL DIRECTIONS at any given point — not just downward.

PRESSURE EQUATION:

P = F ÷ A

P = pressure (pascals, Pa)

F = force (newtons, N)

A = area (m²)

1 Pa = 1 N/m²

PRESSURE INCREASES WITH DEPTH:

As depth increases → more fluid above → greater weight → greater pressure.

EQUATION FOR FLUID PRESSURE:

P = h × ρ × g

P = pressure (Pa)

h = depth (m)

ρ = density of fluid (kg/m³)

g = gravitational field strength (N/kg)

EXAMPLE:

Pressure at 10 m depth in seawater (ρ = 1025 kg/m³, g = 9.8 N/kg):

P = 10 × 1025 × 9.8 = 100,450 Pa ≈ 100 kPa

Atmospheric Pressure

ATMOSPHERIC PRESSURE is caused by the weight of the air column above any point.

At sea level: approximately 101,325 Pa (about 100 kPa or 1 atm).

Atmospheric pressure DECREASES with altitude — less air above.

WHY ATMOSPHERIC PRESSURE EXISTS:

The Earth's atmosphere has mass → gravity pulls it down.

At any point, the pressure equals the weight of the air column above per unit area.

EFFECTS OF ATMOSPHERIC PRESSURE:

Suction cups: press cup against smooth surface, remove air → atmospheric pressure holds it on.

Drinking through a straw: lungs create lower pressure → atmospheric pressure pushes drink up.

Barometer: mercury column supported by atmospheric pressure.

Weather: high pressure = fair weather; low pressure = storms.

VARIATION WITH ALTITUDE:

At 5500 m: pressure is approximately half sea-level.

At 10,000 m (cruising altitude): ~26 kPa → aircraft cabins pressurised.

Upthrust and Floating

UPTHRUST (buoyancy force): upward force on an object submerged in a fluid.

ARCHIMEDES' PRINCIPLE:

Upthrust = weight of fluid displaced.

FLOATING CONDITION:

Object floats when: upthrust = weight.

Object sinks when: weight > upthrust.

PHYSICAL EXPLANATION:

Pressure at the bottom of a submerged object > pressure at the top.

Net upward force = pressure difference × area = weight of displaced fluid.

EXAMPLES:

Ship: large volume of water displaced → large upthrust, even though ship is made of steel.

Hot air balloon: buoyancy in air — hot (less dense) air displaces cooler air → upthrust > weight → rises.

Diver with wetsuit: carefully balanced to achieve neutral buoyancy.

DENSITY AND FLOATING:

Object floats if density < fluid density.

Object sinks if density > fluid density.

Example: ice (917 kg/m³) floats on water (1000 kg/m³).

⚠️ Common Mistake

Pressure in a fluid acts in ALL DIRECTIONS — not just downwards. P = hρg gives the ADDITIONAL pressure due to the fluid depth — total pressure at depth includes atmospheric pressure too. Upthrust equals the weight of DISPLACED fluid — not the weight of the whole object.

📐 Variables

PPressure (P) is measured in pascals (Pa)

FForce (F) is measured in newtons (N)

AArea (A) is measured in m² (m²)

hDepth (h) is measured in metres (m)

ρDensity (ρ) is measured in kg/m³ (kg/m³)

📐 Key Equations

P = F ÷ A

P = h × ρ × g (pressure at depth in a fluid)

📌 Key Note

P = F/A. P = hρg — pressure increases with depth, density and g. Atmospheric pressure ~100 kPa at sea level, decreases with altitude. Upthrust = weight of displaced fluid (Archimedes). Float when upthrust ≥ weight. Float if density < fluid density.

🎯 Matching Activity — Pressure in Fluids

Match each scenario to the correct pressure concept. — drag the symbols on the right to match the component names on the left.

P = hρg

Drop here

Atmospheric pressure

Drop here

Upthrust

Drop here

Object floats

Drop here

Upward force = weight of fluid displaced (Archimedes' principle)

Density of object < density of fluid — upthrust equals weight

Pressure at depth h in a fluid of density ρ under gravity g

~100 kPa at sea level — weight of air column above unit area

⚽ FIFA Worked Examples

Fluid Pressure

Calculate the pressure at 5 m depth in fresh water (ρ = 1000 kg/m³, g = 9.8 N/kg).

F

P = h × ρ × g

I

h = 5 m, ρ = 1000 kg/m³, g = 9.8 N/kg

F

P = 5 × 1000 × 9.8 = 49,000

A

P = 49,000 Pa = 49 kPa

⭐ Higher Tier Only

Calculate pressure at depth: P = hρg. Calculate upthrust: F = ρVg. Apply Archimedes' principle to determine whether objects float or sink. Calculate the fraction of a floating object submerged. Solve problems involving pressure differences in fluids.

🔬 Triple Science Only

Pressure in a fluid (physics only) — not in Combined Science.

🎯 Test Yourself

Question 1 of 2

1. Why does pressure in a fluid increase with depth?

2. A steel ship floats in water even though steel is denser than water. Why?

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⚡ Pressure in a Fluid

Pressure in Fluids

Atmospheric Pressure

Upthrust and Floating

Mr. Badmus AI