Pressure in Fluids
Year 10 (IGCSE) 🚀 Forces & Motion Apply P = ρgh; explain atmospheric pressure and hydraulics.
💧 Pressure in Liquids: P = ρgh
The pressure in a fluid depends on the fluid's density, gravitational field strength, and depth.
💧 Fluid Pressure
$$P = \rho g h$$
$\rho$ = density of fluid (kg/m³) · $g$ = 10 N/kg · $h$ = depth below surface (m)
🌊 Example: Pressure at 10 m depth in seawater (ρ = 1025 kg/m³):
P = 1025 × 10 × 10 = 102,500 Pa ≈ 1 atmosphere extra
P = 1025 × 10 × 10 = 102,500 Pa ≈ 1 atmosphere extra
Every 10 m deeper in the ocean adds roughly 1 atmosphere (100,000 Pa) of pressure. At 100 m depth, pressure is about 11 atmospheres!
🔧 Hydraulic Systems
Hydraulics use Pascal's principle: pressure applied to a fluid in a closed system is transmitted equally throughout.
🔧 Pascal's Principle
$$P_1 = P_2 \rightarrow \frac{F_1}{A_1} = \frac{F_2}{A_2} \rightarrow F_2 = F_1 \times \frac{A_2}{A_1}$$🚗 Car brakes: A small force on the brake pedal (small piston, area 2 cm²) creates a large braking force at the wheel (large piston, area 20 cm²).
Force is multiplied by 10! This is why hydraulic brakes work so well.
Force is multiplied by 10! This is why hydraulic brakes work so well.
🌍 Atmospheric Pressure
The atmosphere is a layer of gas about 100 km thick, pressing down on everything at the surface.
🌍 Atmospheric Pressure
$$P_{\text{atm}} \approx 101,000 \text{ Pa} \approx 1 \text{ atmosphere} \approx 76 \text{ cm Hg}$$| 📍 Location | 📊 Pressure |
|---|---|
| Sea level | 101,325 Pa |
| Top of Everest (8848 m) | ≈ 33,000 Pa (1/3 of sea level) |
| Commercial aircraft (12,000 m) | ≈ 20,000 Pa (cabin pressurised) |
A drinking straw works because you lower the air pressure inside it — atmospheric pressure on the liquid surface then pushes the drink up into your mouth!
Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
💧 Fluid Pressure Calculator (P = ρgh)
g = 10 N/kg | Water density = 1000 kg/m³