Pressure

Meaning of Pressure

Pressure is defined as:

The force acting per unit area on a surface.

Pressure tells us how concentrated a force is over an area.

Formula for Pressure

Where:

• P = pressure (pascals, Pa)

• F = force (newtons, N)

• A = area over which the force acts (square metres, m²)

Unit definition:

How Force Affects Pressure

• Increasing force (area constant) → pressure increases.

• Decreasing force (area constant) → pressure decreases.

Example: Pressing harder on the ground increases the pressure on the ground.

How Area Affects Pressure (Exam-Critical)

• Smaller area (same force) → greater pressure.

• Larger area (same force) → smaller pressure.

This explains many everyday applications.

[Insert diagram showing the same force acting on small vs large area]

Everyday Applications of Pressure

Sharp Objects

• Knives, needles, pins have small contact areas.

• For the same force, they produce high pressure, making cutting and piercing easier.

[Insert diagram showing knife edge vs blunt surface]

Wide Surfaces to Reduce Pressure

• Snow shoes, camel feet, tractor tyres have large contact areas.

• This reduces pressure and prevents sinking.

[Insert diagram showing camel feet or snow shoes]

High-Heeled Shoes

• High heels have small area of contact.

• They produce high pressure, which can damage floors or soft ground.

Worked Examples (Teaching Core)

Example 1: Calculating Pressure

A force of 100 N acts on an area of 0.5 m².

Calculate the pressure.

Solution

Example 2: Effect of Area Change

A force of 200 N acts on:

• (a) area = 2 m²

• (b) area = 0.5 m²

Solutions

Smaller area → higher pressure.

Example 3: Finding Force

A pressure of 300 Pa acts over an area of 0.2 m².

Calculate the force.

Rearranging:

Visual Aid: Formula Triangle

[Insert formula triangle with P at the top, F and A at the base]

Key Examination Tips (High-Value)

• Always convert area to m².

• Do not confuse pressure (Pa) with force (N).

• State the formula before substituting values.

• Use realistic units and values.

Common Examination Errors (Examiner Insight)

Students often:

• use cm² instead of m² without converting,

• say pressure increases with area (incorrect),

• confuse mass with force,

• omit units in final answers.

Remember: pressure depends on both force and area.

Questions

Question 1

Define pressure.

Question 2

A force of 50 N acts on an area of 0.25 m².

Calculate the pressure.

Question 3

Explain why a sharp knife cuts better than a blunt one.

Question 4

A camel can walk on sand without sinking deeply.

Explain this using pressure concepts.

Solutions

Solution 1

Pressure is the force acting per unit area.

Solution 2

Solution 3

A sharp knife has a smaller contact area, producing higher pressure for the same force.

Solution 4

The camel’s wide feet increase the contact area, reducing pressure on the sand and preventing sinking.

End-of-Objective

A learner who has mastered this objective can:

• define pressure accurately,

• relate pressure to force and area,

• apply $P = \frac{F}{A}$ correctly,
  • explain everyday pressure applications clearly.

Meaning of Atmospheric Pressure

Atmospheric pressure is defined as:

The pressure exerted by the weight of air in the Earth’s atmosphere on all objects on the Earth’s surface.

Air has mass, and due to gravity, it exerts a force. This force acting over an area produces pressure.

Key Characteristics of Atmospheric Pressure

• Acts in all directions (upwards, downwards, and sideways).

• Acts on solids, liquids, and gases.

• Decreases with increase in altitude (height above sea level).

• Normally not noticed because it acts equally in all directions.

Effects of Atmospheric Pressure

(a) Atmospheric Pressure on Liquids

Atmospheric pressure allows liquids to:

• remain in containers,

• rise into straws or syringes when pressure inside is reduced.

Example: Drinking through a straw

• Air pressure inside the straw is reduced when air is sucked out.

• Atmospheric pressure on the liquid surface pushes the liquid up the straw.

[Insert diagram showing liquid rising in a straw due to atmospheric pressure]

(b) Atmospheric Pressure and Containers

Atmospheric pressure can cause containers to:

• collapse if air inside is removed.

Example: Collapsing can

• When air inside a can is removed or cooled, internal pressure decreases.

• External atmospheric pressure pushes the can inward.

[Insert diagram showing a collapsing can experiment]

(c) Atmospheric Pressure on the Human Body

• Atmospheric pressure acts on the human body at all times.

• The body does not collapse because internal body pressure balances external pressure.

• Changes in pressure can affect the ears (e.g. during climbing or flying).

Example: Ear popping

• Occurs due to pressure difference between the inside and outside of the ear.

(d) Atmospheric Pressure and Weather

Atmospheric pressure influences:

• wind movement,

• weather patterns,

• formation of clouds and rain.

Air moves from regions of high pressure to low pressure, producing wind.

(e) Atmospheric Pressure at High Altitudes

At higher altitudes:

• atmospheric pressure is lower,

• less oxygen is available,

• breathing becomes more difficult.

Examples

• Mountain climbers,

• Aircraft cabins (pressurised).

[Insert diagram showing pressure decreasing with altitude]

Why We Are Not Crushed by Atmospheric Pressure

Although atmospheric pressure is large:

• it acts uniformly in all directions,

• internal pressure inside the body balances it.

Hence, there is no net crushing force.

Summary of Effects (Exam-Ready)

Common Examination Errors (Examiner Insight)

Students often:

• say air has no weight (incorrect),

• think atmospheric pressure acts only downward,

• confuse atmospheric pressure with liquid pressure,

• fail to explain effects clearly.

Always mention air exerts force due to its weight.

Exam-Style Questions (Original)

Question 1

What is meant by atmospheric pressure?

Question 2

Explain why liquid rises when drinking through a straw.

Question 3

Describe what happens when a sealed can is crushed and explain why.

Question 4

Explain why breathing becomes difficult at high altitudes.

Worked Solutions (Beyond Excellent)

Solution 1

Atmospheric pressure is the pressure exerted by the weight of air on objects on the Earth’s surface.

Solution 2

Sucking air from the straw reduces the pressure inside it, so atmospheric pressure on the liquid surface pushes the liquid up the straw.

Solution 3

When the air pressure inside the can decreases, the greater external atmospheric pressure crushes the can inward.

Solution 4

At high altitudes atmospheric pressure is lower, so less oxygen enters the lungs during breathing.

End-of-Objective

A learner who has mastered this objective can:

• define atmospheric pressure correctly,

• describe its effects using real-life examples,

• explain pressure-related phenomena logically,

• answer structured and explanatory exam questions confidently.

What Is a Mercury Barometer?

A mercury barometer is an instrument used to measure atmospheric pressure using a column of mercury supported by the pressure of the atmosphere.

It works on the principle that:

Atmospheric pressure can support a column of liquid.

Construction of a Simple Mercury Barometer

A simple mercury barometer consists of:

• A long glass tube, sealed at one end

• The tube is completely filled with mercury

• A mercury reservoir (trough or container)

• The open end of the tube is placed below the mercury surface in the reservoir

When the tube is inverted:

• Some mercury flows out into the reservoir

• A column of mercury remains in the tube

At the top of the mercury column is a vacuum, called a Torricellian vacuum.

[Insert labelled diagram of a simple mercury barometer]

How the Mercury Barometer Works

• Atmospheric pressure acts on the surface of mercury in the reservoir

• This pressure pushes mercury up the glass tube

• The mercury rises until:
  • the pressure due to the mercury column balances atmospheric pressure

At sea level:

• The height of the mercury column is about 760 mm

This height is a measure of atmospheric pressure.

Relationship Between Mercury Height and Atmospheric Pressure

• High atmospheric pressure → mercury column rises

• Low atmospheric pressure → mercury column falls

Thus:

The height of the mercury column is directly related to atmospheric pressure.

Use of the Mercury Barometer

The mercury barometer is used to:

• measure atmospheric pressure,

• study weather changes,

• predict weather conditions.

Weather indication

• Rising mercury → high pressure → fair weather

• Falling mercury → low pressure → cloudy or rainy weather

Why Mercury Is Used

Mercury is suitable because:

• it has very high density (short column needed),

• it does not wet glass,

• it produces a clear, visible column.

Units of Atmospheric Pressure (BGCSE Level)

Atmospheric pressure may be expressed as:

• millimetres of mercury (mmHg)

• pascals (Pa) (introduced later)

At sea level:

• Atmospheric pressure ≈ 760 mmHg

Summary of Key Points (Exam-Ready)

Common Examination Errors (Examiner Insight)

Students often:

• say mercury is pulled up by suction (incorrect),

• forget the presence of a vacuum at the top,

• confuse mercury barometer with aneroid barometer,

• fail to relate height change to pressure change.

Always state that atmospheric pressure pushes mercury up.

Questions

Question 1

What is a mercury barometer?

Question 2

Describe the construction of a simple mercury barometer.

Question 3

Explain how a mercury barometer measures atmospheric pressure.

Question 4

State what happens to the mercury column when atmospheric pressure decreases.

Solutions

Solution 1

A mercury barometer is an instrument used to measure atmospheric pressure using a column of mercury.

Solution 2

It consists of a long glass tube filled with mercury, inverted into a mercury reservoir, with a vacuum at the top of the tube.

Solution 3

Atmospheric pressure pushes mercury up the tube until the pressure due to the mercury column balances the atmospheric pressure.

Solution 4

The mercury column falls because the atmospheric pressure supporting it decreases.

End-of-Objective

A learner who has mastered this objective can:

• describe the structure of a mercury barometer,

• explain clearly how it works,

• relate mercury height to atmospheric pressure,

• apply the concept to weather and pressure changes.

Weather Charts and Isobars

A weather chart is a map that shows:

• atmospheric pressure,

• weather conditions over a wide area.

An isobar is defined as:

A line drawn on a weather chart joining points of equal atmospheric pressure.

Isobars are usually labelled in millibars (mb).

[Insert labelled weather chart showing isobars]

Units of Pressure Used on Weather Charts

• Atmospheric pressure on weather charts is measured in millibars (mb).

• Typical sea-level pressure is about 1013 mb.

Pressure values:

• Above 1013 mb → high pressure

• Below 1013 mb → low pressure

High-Pressure Systems (Anticyclones)

A high-pressure area is a region where atmospheric pressure is higher than surrounding areas.

Isobar pattern

• Isobars form closed loops,

• Pressure increases towards the centre,

• Isobars are often widely spaced.

Weather conditions

• Clear skies,

• Dry and sunny weather,

• Light winds.

[Insert diagram showing high-pressure isobar pattern]

Low-Pressure Systems (Depressions)

A low-pressure area is a region where atmospheric pressure is lower than surrounding areas.

Isobar pattern

• Closed loops,

• Pressure decreases towards the centre,

• Isobars often closely spaced.

Weather conditions

• Cloudy skies,

• Rain or storms,

• Strong winds.

[Insert diagram showing low-pressure isobar pattern]

Wind Direction from Isobars

Wind direction depends on pressure differences.

Key rules:

• Wind blows from high pressure to low pressure.

• The greater the pressure difference, the stronger the wind.

• Winds do not move directly across isobars; they tend to flow along curved paths around pressure systems.

Simplified BGCSE rule

Wind blows from regions of high pressure to regions of low pressure.

[Insert diagram showing wind direction relative to isobars]

Wind Strength and Isobar Spacing (Exam-Critical)

• Closely spaced isobars → strong winds

• Widely spaced isobars → weak or gentle winds

This is because:

• Close isobars indicate a large pressure gradient,

• Large pressure gradient produces stronger winds.

[Insert comparison diagram: close vs wide isobars]

Predicting Weather Using Isobars (Step-by-Step)

To predict weather from a chart:

1. Identify pressure values (in mb).

2. Locate high-pressure and low-pressure areas.

3. Observe isobar spacing.

4. Predict:
   • type of weather (clear or rainy),
   • wind strength (strong or weak),
   • general wind direction.

Summary Table (Exam-Ready)

Common Examination Errors (Examiner Insight)

Students often:

• confuse isobars with contour lines,

• say wind blows from low to high pressure (incorrect),

• ignore isobar spacing when describing wind strength,

• forget pressure units (millibars).

Always mention isobar spacing and pressure values.

Questions

Question 1

What is an isobar?

Question 2

Explain how isobar spacing indicates wind strength.

Question 3

Describe the type of weather associated with a low-pressure system.

Question 4

A weather chart shows closely spaced isobars around a low-pressure centre.

Predict the weather conditions and explain your answer.

Solutions

Solution 1

An isobar is a line drawn on a weather chart joining points of equal atmospheric pressure.

Solution 2

Closely spaced isobars show a large pressure difference over a short distance, producing strong winds.

Solution 3

Low-pressure systems are associated with cloudy skies, rainfall, and strong winds.

Solution 4

The weather is likely to be windy and rainy because the closely spaced isobars indicate strong winds and the low-pressure centre causes rising air and cloud formation.

End-of-Objective

A learner who has mastered this objective can:

• interpret isobar patterns confidently,

• use pressure values in millibars correctly,

• predict weather conditions accurately,

• explain wind strength and direction clearly in exam answers.

Pressure in Fluids

Fluids (liquids and gases) exert pressure because:

• they have mass, and

• they are affected by gravity.

In liquids, pressure increases with depth because:

• the deeper you go, the more liquid is above you,

• the weight of this liquid exerts a force.

Factors Affecting Pressure Beneath a Fluid Surface

The pressure at a point beneath a liquid surface depends on:

1. Depth of the liquid (h)

2. Density of the liquid (ρ)

3. Gravitational field strength (g)

It does not depend on:

• the shape of the container,

• the surface area of the liquid.

Formula for Pressure in a Liquid

Where:

• P = pressure (Pa)

• ρ = density of the liquid (kg m³)

• g = gravitational field strength (≈ 10 m s²)

• h = depth below the liquid surface (m)

Interpretation of the Formula (Exam-Critical)

From $P = \rho g h$:

• Increasing depth (h) → pressure increases

• Increasing density (ρ) → pressure increases

• At the surface (h=0) → pressure due to liquid is zero

Visual Concept: Pressure Increasing with Depth

[Insert diagram showing liquid in a container with pressure increasing downward]

Worked Examples (Teaching Core)

Example 1: Effect of Depth

Calculate the pressure due to water at a depth of 5 m.

(Take density of water = 1000 kg m³, $g = 10\,\text{m s}^{2}$.)

Solution

Example 2: Effect of Density

Two liquids have the same depth of 2 m:

• Liquid A: density = 800 kg m³

• Liquid B: density = 1000 kg m³

Calculate the pressure in each liquid.

Solutions

Liquid A:

Liquid B:

Conclusion:

Higher density → higher pressure at the same depth.

Example 3: Finding Depth

A pressure of 30 000 Pa is measured in water.

Find the depth.

Everyday Applications of Liquid Pressure

Dams and Water Tanks

• Dams are thicker at the bottom.

• Pressure is greater at larger depths.

[Insert diagram showing a dam thicker at the bottom]

Divers and Submarines

• Pressure increases as divers go deeper.

• Divers must ascend slowly to avoid injury.

Water Jets from Holes

• Water flows faster from holes at the bottom of a container.

• Lower holes are at greater depth → higher pressure.

[Insert diagram showing water jets from different depths]

Key Examination Tips (High-Value)

• Use metres, not centimetres, for depth.

• Use correct density values (e.g. water ≈ 1000 kg m⁻³).

• Always include units.

• Pressure calculated using ρgh is liquid pressure only, not atmospheric pressure (unless stated).

Common Examination Errors (Examiner Insight)

Students often:

• forget to convert cm to m,

• confuse density with mass,

• use P=AF instead of ρgh,

• say pressure depends on container shape.

Remember: depth and density are the key factors.

Questions

Question 1

State the formula used to calculate pressure beneath a liquid surface.

Question 2

Calculate the pressure at a depth of 4 m in oil of density 900 kg m³.

(Take $g = 10\,\text{m s}^{2}$.)

Question 3

Explain why pressure at the bottom of a swimming pool is greater than near the surface.

Question 4

Explain why dams are built thicker at the bottom than at the top.

Solutions

Solution 1

Solution 2

Solution 3

Pressure increases with depth because more liquid above exerts greater weight and force.

Solution 4

The pressure of water increases with depth, so the bottom of the dam experiences greater pressure and must be stronger.

End-of-Objective

A learner who has mastered this objective can:

• relate liquid pressure to depth and density,

• apply P=ρgh correctly,

• apply $P = \rho g h$ correctly,

• solve numerical problems confidently,

• explain real-life applications of fluid pressure clearly.

Where:

• P = pressure difference (Pa)

• ρ (rho) = density of the liquid (kg m³)

• g = gravitational field strength (≈ 10 m s²)

• h = vertical height difference between the liquid columns (m)

Worked Example (Simple)

A manometer contains water of density 1000 kg m⁻³.

The difference in liquid levels is 0.20 m.

Calculate the pressure difference.

Solution

Uses of a Manometer

A manometer is used to:

• measure gas pressure in laboratories,

• check pressure in sealed containers,

• measure pressure differences in ventilation systems,

• demonstrate pressure concepts in physics experiments.

Summary Table (Exam-Ready)

Common Examination Errors (Examiner Insight)

Students often:

• measure height along the tube instead of vertical height,

• forget to convert cm to m,

• confuse manometer with a barometer,

• ignore which side has higher pressure.

Always identify which pressure is greater before explaining.

Exam-Style Questions (Original)

Question 1

What is a manometer?

Question 2

Describe the construction of a simple manometer.

Question 3

Explain how a manometer can be used to measure gas pressure.

Question 4

A manometer shows a liquid height difference of 15 cm.

If the liquid has a density of 1000 kg m⁻³, calculate the pressure difference.

(Take $g = 10\,\text{m s}^{-2}$.)

Worked Solutions (Beyond Excellent)

Solution 1

A manometer is an instrument used to measure pressure or pressure difference using a column of liquid.

Solution 2

It consists of a U-shaped tube partially filled with liquid, with one end connected to a gas source and the other open to the atmosphere.

Solution 3

Gas pressure pushes the liquid down on one side, causing it to rise on the other side. The height difference of the liquid columns indicates the pressure difference.

Solution 4

End-of-Objective

A learner who has mastered this objective can:

• describe the structure and function of a manometer,

• use it to compare pressures accurately,

• apply P=ρgh correctly,

• apply $P = \rho g h$ correctly,

• explain manometer readings confidently in exams.

What Is a Manometer?

A manometer is an instrument used to measure pressure, especially:

• gas pressure,

• pressure difference between a gas and the atmosphere,

• pressure difference between two gases.

It works by comparing pressures using a column of liquid.

Construction of a Simple Manometer

A simple manometer consists of:

• a U-shaped glass tube,

• partially filled with a liquid (commonly mercury or coloured water),

• one end connected to a gas supply,

• the other end open to the atmosphere (or connected to another gas).

[Insert labelled diagram of a U-tube manometer]

https://engineerexcel.com/wp-content/uploads/2024/02/u-tube-manometer-measuring-vacuum-pressure.png

https://www.dubai-sensor.com/product_images/uploaded_images/fig-1.-u-tube-pressure-manometer.png

How a Manometer Works (Principle)

• Pressure applied to one side of the manometer pushes the liquid down on that side.

• The liquid rises on the other side.

• The difference in height of the liquid columns represents the pressure difference.

Key idea:

Greater pressure difference → greater height difference.

Using a Manometer to Measure Pressure

Case 1: Gas Pressure Greater Than Atmospheric Pressure

• Liquid level on the gas side goes down.

• Liquid level on the open side goes up.

• The vertical height difference h is measured.

[Insert diagram showing gas pressure greater than atmospheric pressure]

https://d2vlcm61l7u1fs.cloudfront.net/media%2F747%2F7471ffe3-a4e6-4935-944e-d88603625593%2FphpFJsJzq.png

https://media.nagwa.com/537152706862/en/thumbnail_s.jpeg

Case 2: Gas Pressure Less Than Atmospheric Pressure

• Liquid level on the gas side goes up.

• Liquid level on the open side goes down.

[Insert diagram showing gas pressure less than atmospheric pressure]

https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/887/2015/04/23212003/CNX_Chem_09_01_Manometer1.jpg

https://ecampusontario.pressbooks.pub/app/uploads/sites/25/2016/05/CNX_Chem_09_01_Manometer.jpg

Quantitative Relationship (BGCSE Level)

The pressure difference measured by a manometer is given by: