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
Pressure at depth h in a fluid of density ρ under gravity g
Upward force = weight of fluid displaced (Archimedes' principle)
Density of object < density of fluid — upthrust equals weight
~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
🔬 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?
⭐ How Well Do You Understand This Topic?
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