1.8 Liquid Pressure & Measuring Instruments
Master the physics of pressure beneath liquids and the instruments that measure it
The Hook: Why Do Submarines Have Thick Walls?
Imagine you're in a submarine diving into the ocean. At 10 meters deep, you feel fine. At 100 meters, the hull starts creaking. At 500 meters, only the strongest military submarines survive. Why? Because liquid pressure increases with depth, and understanding this relationship can mean the difference between life and death underwater.
This same principle explains why dams are thicker at the bottom, why your ears pop when you dive into a pool, and how we measure atmospheric pressure with a simple tube of mercury.
Baby Steps: Understanding Liquid Pressure
Step 1: What Creates Pressure in Liquids?
Unlike gases that can be compressed, liquids have weight. Every layer of liquid above you pushes down on you. The deeper you go, the more liquid is stacked above you, creating more pressure.
Step 2: The Three Key Factors
Liquid pressure depends on exactly three things:
- Depth (h): How far below the surface you are (in meters)
- Density (ρ): How tightly packed the liquid's molecules are (in kg/m³)
- Gravitational field strength (g): How strongly gravity pulls (10 N/kg on Earth)
Step 3: The Critical Insight
Here's what surprises most students: The shape of the container doesn't matter! A thin tube and a wide tank both have the same pressure at the same depth. It's only about how much liquid is stacked vertically above you.
Visual Clarification: How Depth Affects Pressure
Notice how the three containers have completely different shapes and volumes, yet points at the same depth experience identical pressure. This is the fundamental principle of hydrostatic pressure.
Deep Theory (Extended): The Formula
Δp = ρg Δh
(Change in Pressure = Density × Gravitational Field Strength × Change in Depth)
Δp (Change in Pressure)
Measured in Pascals (Pa) or N/m²
How much extra pressure you experience
ρ (Rho - Density)
Measured in kg/m³
Water = 1000 kg/m³, Mercury = 13600 kg/m³
g (Gravitational Field)
10 N/kg on Earth
Could be different on Moon or Mars
Δh (Change in Depth)
Measured in meters (m)
Always measure from the surface downward
🎯 Mark Scheme Keywords:
- ✓ "Pressure increases with depth"
- ✓ "Pressure is directly proportional to depth"
- ✓ "Denser liquids exert greater pressure at same depth"
- ✓ "Pressure acts equally in all directions"
- ✓ "Shape of container is irrelevant"
Virtual Lab 1: The Deep Sea Calculator
Drag the submarine to different depths and change the liquid density to see how pressure changes. Watch the real-time calculation!
CALCULATION STEPS:
Δp = ρ × g × Δh
Δp = 1000 × 10 × 20
Δp = 200,000 Pa
What This Means:
At 20m depth in liquid with density 1000 kg/m³, the pressure increases by 200.0 kPa compared to the surface.
💡 EXAMINER'S INSIGHT:
In calculations, always use Δh (change in depth), not absolute position. If moving from 5m to 15m depth, Δh = 10m, not 15m.
Virtual Lab 2: The Mercury Barometer
The mercury barometer measures atmospheric pressure. The atmosphere pushes down on the mercury reservoir, forcing mercury up the tube. At sea level, it reaches 760 mm height. Take it up a mountain and watch what happens!
READING:
760 mm Hg
≈ 101.3 kPa
How It Works:
1. The tube is closed at the top (creating a vacuum)
2. Atmospheric pressure pushes on the mercury reservoir
3. This pressure forces mercury up the tube
4. Mercury rises until its weight balances atmospheric pressure
🎓 EXAM TIP:
Standard atmospheric pressure at sea level = 760 mm Hg = 101 325 Pa = 101.3 kPa
Virtual Lab 3: The U-Tube Manometer
A manometer measures gas pressure by comparing it to atmospheric pressure. The difference in liquid height tells us the excess pressure of the gas supply.
HEIGHT DIFFERENCE:
Δh = 5.0 cm
= 0.050 m
EXCESS PRESSURE CALCULATION:
Δp = ρ × g × Δh
Δp = 1000 × 10 × 0.050
Δp = 500 Pa
Understanding the Reading:
Why is one side higher?
The gas supply pushes down on the left side with greater force than atmospheric pressure on the right side. This extra pressure forces the liquid down on the gas side and up on the open side.
The Measurement:
The vertical height difference (Δh) tells us the excess pressure above atmospheric pressure.
🎯 MARK SCHEME KEYWORDS:
- ✓ "Measure the vertical height difference"
- ✓ "Gas pressure exceeds atmospheric pressure"
- ✓ "Use Δp = ρgΔh to calculate excess pressure"
Examiner's Traps: Common Mistakes
TRAP 1: Confusing Absolute Pressure with Change in Pressure
❌ Wrong: "The pressure at 10m depth is 100,000 Pa"
✓ Correct: "The pressure increases by 100,000 Pa at 10m depth (plus atmospheric pressure at surface)"
TRAP 2: Thinking Container Shape Matters
❌ Wrong: "A wider container has more pressure at the same depth"
✓ Correct: "Pressure depends only on depth, density, and g - not shape or volume"
TRAP 3: Forgetting Units in Calculations
❌ Wrong: Using h = 50 cm directly in formula
✓ Correct: Convert to meters first: h = 0.5 m, then calculate Δp = ρgΔh
TRAP 4: Barometer vs Manometer Confusion
❌ Wrong: "A manometer measures atmospheric pressure"
✓ Correct: "A barometer measures atmospheric pressure; a manometer measures gas supply pressure relative to atmospheric pressure"
TRAP 5: Using Wrong Value for g
❌ Wrong: Using g = 9.8 m/s² when the question says to use g = 10 N/kg
✓ Correct: Always use the value specified in the question (typically 10 N/kg for IGCSE)
Syllabus Coverage Checklist
CORE CONTENT
Define pressure as force per unit area (p = F/A)
Describe how pressure varies with force and area
Describe qualitatively how pressure beneath a liquid changes with depth and density
EXTENDED (SUPPLEMENT) CONTENT
Recall and use the equation Δp = ρgΔh
Describe the simple mercury barometer and its use in measuring atmospheric pressure
Use and describe the use of a manometer
This lesson comprehensively covers Extended syllabus section 1.8 (Pressure) with interactive simulations demonstrating all required concepts and calculations.
Quick Recall Summary
The Formula
Δp = ρgΔh
Change in pressure equals density times gravitational field strength times change in depth
Barometer
Mercury column at sea level: 760 mm
Measures atmospheric pressure. Height decreases with altitude.
Manometer
U-tube measures excess pressure
Height difference shows gas pressure above atmospheric pressure.
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