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GCSE level physics exam revision notes all about forces Part 6
Forces and pressure: 6.3
Forces and pressure in liquids - density & depth factors - liquid pressure
calculations using the P = hρg
formula & differences in pressure in liquids compared to solids
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What is the formula for pressure?
What causes
pressure in liquids?
How do you calculate pressure in a liquid?
Sub-index physics notes on 6.
Forces and Pressure in fluids & calculations
This page contains online questions only.
Jot down
your answers and check them against the worked out answers at the end of
the page.
6.3
Pressure in a liquid - density and depth factors - calculations
Density is a measure of how close the
particles are together.
The more compact they are, the greater the density.
As already mentioned, in liquids the density
is uniform throughout and because there is so little space between the particles
the density only slightly decreases with increase in temperature with the
increased kinetic energy of the particles.
However, the volume shows almost no
change with increased pressure (so here you can consider
liquids to be virtually incompressible).
All liquids expand on heating - observe a
mercury or alcohol thermometer.
 The
pressure in a fluid varies AND increases with depth - it
doesn't matter whether you are dealing with gases like the
atmosphere or liquids
like the water of a lake or ocean.
The greater the height/depth of fluid, the greater the weight
of particles that gravity is pulling down, hence the increase in force per unit
area at a particular level, hence the increase in pressure.
The pressure in a fluid acts in all
directions (← → ↑ ↓) because the particles are moving and colliding
with each other, and the sides of the container, at random in all directions.
Liquid pressure significantly increases with depth as
the weight of the column of liquid increases.
A simple experiment can demonstrate this
rule using a tall container with holes in the side. When you fill it with
water, the water gushes out of the holes, but the lower the hole, the
greater the water pressure, the faster the water comes out and travels a
greater distance.
A note on dam construction (e.g. reservoir for
water supply or hydroelectric power plant)
Since water pressure increases with depth, to resist
this increase in pressure, the width of a dam must also be increased
to combat the increased force on the dam wall.
The width of the dam is much greater at its base
compared the top of the dam wall.
The pressure also increases with
increase in density of the fluid
- so air and water differ significantly
for a pressure created at a specific depth of fluid (densities: air density
1.2 kg/m3 and water 1000 kg/m3 at room temperature).
From your own experience you may
have observed:
Sometimes in a car descending or
ascending a few hundred metres on a road can make your ears 'pop'
and hurt slightly because of the change in pressure with height.
BUT, you only have to dive into a
few metres of water to experience the same effect on your ears. As
you suddenly into the water, the pressure is suddenly increased on
your ear drums - the pain comes from the greater external water
pressure than the internal body pressure on the other side of your
ear drum. However, for most people, when under the water at shallow
depths, the pressures become equal quite quickly
You can calculate the pressure at a given
depth created by the
weight of liquid
in the earth's gravitation field using the following formula:
pressure in a liquid = depth of liquid x
density of liquid x gravitational field strength
P = hρg
P, pressure
in pascals (Pa);
h = depth in metres (m); ρ = density (kg/m3),
and the
gravitational field strength =
g = 9.8 N/kg (on the Earth's surface)
Unit connections
Taking the formula P = h
x ρ x g 'apart' in terms of units.
pressure = force per
unit area = height of column of material x density of material x
gravitational constant
N / m2
= m x kg/m3 x 9.8 N/kg
unit analysis: on
the right the kg cancel out, m/m3 = 1/m2, you are
left with N/m2 !!
Note: Upthrust force in fluids and flotation etc. are covered
in
FORCES 7. Pressure & upthrust in liquids, why do
objects float or sink in a fluid?, variation of atmospheric pressure with
height
Examples of liquid pressure situations
Liquid pressure is quietly working behind
the scenes in everything from medicine to engineering - it’s one of those
physics concepts that’s both elegant and incredibly useful. Here are some
standout real-world applications of pressure in liquids:
Engineering and
Infrastructure
- Hydraulic Brakes:
Use incompressible brake fluid to transmit pressure from the pedal to the
brake pads.
- Hydraulic Lifts & Jacks:
Apply Pascal’s Law to lift heavy vehicles or machinery with minimal input
force.
- Dams:
Built thicker at the base to withstand higher water pressure at greater
depths - crucial for structural integrity and hydroelectric power generation
- Water Supply Systems:
Elevated tanks use gravity and liquid pressure to ensure consistent water
flow to homes.
Medical
Applications
- Syringes:
Rely on pressure differences to draw in or inject fluids.
- IV Drips:
Hung above the patient to use gravity-driven liquid pressure for controlled
flow.
- Blood Pressure Monitors:
Use inflatable cuffs to match and measure arterial pressure.
Automotive Systems
- Cooling Systems:
Circulate coolant under pressure to regulate engine temperature and prevent
overheating.
- Hydraulic Suspension:
Adjusts ride height and comfort using fluid pressure.
Industrial and
Domestic Uses
- Pressure Washers:
Use high-pressure water jets to clean surfaces efficiently.
- Rubber Suckers:
Create a vacuum seal using pressure differences - think bathroom hooks or
shop signs.
- Straws:
Atmospheric pressure pushes liquid up when internal pressure is reduced by
sucking.
Exploration and Recreation
- Submarines:
Designed to withstand extreme liquid pressure at depth - crucial for
deep-sea missions.
- Water Slides & Guns:
Use liquid pressure for propulsion and fun.
- Scuba Diving:
Equipment must regulate pressure to match depth and avoid decompression
sickness.
Comparing pressure in solids and fluids (liquids and gases)
The concept of pressure applies across
all states of matter, but the way it's generated, distributed, and
experienced differs significantly between solids, liquids, and
gases. Here's a breakdown:
Pressure in Solids
- Formula:
p = F / A
where ( F ) is the force (usually weight) and ( A ) is the
contact area.
- Direction:
Acts perpendicularly to the surface in contact.
- Distribution:
Localised - only affects the area directly beneath the object.
- Example:
A standing block or a drawing pin - smaller contact area leads to higher
pressure.
Pressure in Liquids
- Formula:
p = hρg
where ( h ) is depth, ( \rho
) is density, and ( g ) is gravitational field strength.
- Direction:
Acts in all directions at a
given depth.
- Distribution: Uniform at a given depth
- pressure
increases with depth.
- Example: Water pressure at the bottom of a tank
increases with depth.
Pressure in Gases
- Cause: Due to collisions of gas particles
with container walls.
- Distribution: Uniform throughout the container (if
sealed).
- Affected by:
- Temperature (higher temp → more collisions → higher pressure)
- Volume (smaller volume → more collisions → higher pressure)
- Number of particles (more particles → higher pressure)
- Example: Air pressure in a balloon or atmosphere.
Key Differences Summary
| Property |
Solids |
Liquids |
Gases |
| Formula |
p = F/A |
p = hρg ) |
From gas laws (e.g. PV = constant x T) |
| Direction |
Perpendicular to surface |
All directions at depth |
All directions in container |
| Distribution |
Localised |
Uniform at depth |
Uniform throughout container |
| Compressibility |
Very low |
Low |
High |
| Particle Motion |
Vibrations only |
Flow past each other |
Free, random motion |
Example calculations involving liquid
pressure
(the gravitational field effect is taken as 9.8 kg/N in these questions).
Q1 Divers have to be
careful when working at depth in water and need to carefully control the
dissolving of gases in their blood stream.
(a) Calculate the
pressure created by a 30 m depth of water given the density of water is 1000
kg/m3
(b) Comment on the
dangers when diving at great depths and how to avoid dangerous problems.
Worked out
ANSWERS to the pressure in liquid questions
Q2 The density of sea water
is ~1025 kg/m3, the maximum depth of the Atlantic ocean is ~8500 m
(8.5 km).
(a) Calculate the water
pressure at this depth.
(b) By what factor is
the pressure greater at these depths compared to the ocean surface?
Worked out
ANSWERS to the pressure in liquid questions
Q3 At what depth in water
is the increased pressure five times greater than atmospheric pressure (101
kPa)?
Worked out
ANSWERS to the pressure in liquid questions
Q4 At a depth of 12.5 m of
a chemical solvent the pressure at the bottom of the storage tank due to the
solvent was 306 kPa
Calculate density of the
solvent.
Index physics Forces notes 6. Forces & pressure in
fluids, calculations
Key points
about
forces in fluids - calculations and differences in pressure between liquid and
solid situations
Information
sources for Doc Brown's key points: IGCSE-GCSE physics are based on
textbooks & syllabus-specifications for students taking the UK AQA, Edexcel,
OCR 21st Century Science, OCR Gateway science suite, WJEC, CCEA and CIE GCSE
physics 9-1 level science examinations
A comprehensive set of summary revision notes on
pressure in liquids,
tailored to the major UK GCSE/IGCSE physics exam boards: WJEC, CCEA,
CIE, AQA, Edexcel, and OCR. It includes definitions, key formulas,
influencing factors, board-specific content, and student tips.
Pressure in Liquids: Core Concept
- Definition:
Pressure in a liquid is the force exerted per unit area due
to the weight of the liquid above a point.
- Formula:
p = h ρ g
where:
- p = pressure (Pa)
- h = depth of liquid (m)
- ρ = density of liquid (kg/m³)
- g = gravitational field strength
(N/kg)
Factors Affecting Liquid Pressure
| Factor |
Effect on Pressure |
| Depth (h) |
Greater depth → higher pressure |
| Density (ρ) |
Denser liquid → higher pressure |
| Gravity (g) |
Stronger gravity → higher pressure |
| Shape of Container |
No effect - pressure depends only on
depth |
| Atmospheric Pressure |
Adds to total pressure at depth |
Applications and Examples of pressure in
liquids
- Water tanks:
Pressure increases with depth - bottom outlet has strongest flow.
- Dams:
Built thicker at the base to withstand higher pressure.
- Submarines:
Must withstand increasing pressure with depth.
- Hydraulic systems:
Use incompressible liquids to transmit pressure.
Typical Exam Board-Specific Syllabus Content
- Covers pressure-depth relationship,
density, and
hydraulics
- Includes kinetic theory
and fluid particle motion
- Emphasises pressure differences
and upthrust
- Focus on calculating pressure
and practical applications
- Includes manometers,
barometers, and
pressure in fluids
- Strong emphasis on
experimental methods
- Detailed treatment of pressure in
liquids, upthrust, and
hydraulics
- Requires understanding of pressure
differences and
floating/sinking
- Includes worked examples
and depth-density relationships
- Triple science includes pressure
in liquids, upthrust, and
hydraulics
- Focus on pressure-depth formula
and density
- Higher tier includes pressure
comparisons and
submerged objects
- Covers pressure in fluids,
atmospheric pressure, and
hydraulic systems
- Emphasises pressure calculations
and force transmission
- Includes floating/sinking
and upthrust
- Includes pressure in liquids,
upthrust, and
density
- Focus on
pressure variation with depth
- Higher tier includes pressure
differences and
buoyancy
Student Tips for Exam Success
- Memorise the formula:
( p = h ρ g )
- Use correct units:
Pa, m, kg/m³, N/kg
- Convert units carefully:
cm → m, g/cm³ → kg/m³
- Draw diagrams
to visualise pressure gradients
- Understand particle model
for liquids
- Practice calculations
with different liquids and depths
- Revise upthrust and buoyancy
alongside pressure
- Use past papers
to identify common question formats
Keywords, phrases and learning objectives for forces involving
pressure situations
Be able to solve problems and answer calculation
questions on the forces and creating pressure in liquids - be able
to do calculations using the formulae P = F/A and P = hρg
with the appropriate units.
Know how, and explain why, pressure in a liquid
increases with increase in density or increase in depth.
Be able to describe a simple experiment that shows
variation in liquid pressure with depth.
Revision notes on forces & pressure in
liquids, explaining density & depth factors based on the syllabus-specifications
for students taking IGCSE/GCSE level physics examinations, summary
revision notes and key points on forces & pressure in liquids,
explaining density & depth factors for students taking the AQA
igcse/gcse physics notes on forces & pressure in liquids, explaining density &
depth factors, Edexcel gcse
physics notes on forces & pressure in liquids, explaining density &
depth factors, OCR 21st century GCSE
physics notes on forces & pressure in liquids, explaining density &
depth factors, OCR gateway
GCSE physics notes on forces & pressure in liquids, explaining
density & depth factors, WJEC gcse physics notes on forces &
pressure in liquids, explaining density & depth factors, CCEA
gcse physics notes on forces & pressure in liquids, explaining density &
depth factors for students taking CIE Cambridge igcse
physics, exam revision notes on
forces & pressure in liquids, explaining density & depth factors, useful for US grade 9-10 physics courses,
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Index physics Forces notes 6. Forces & pressure in fluids, calculations
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Worked out
ANSWERS to the pressure in liquid calculations
Example calculations involving liquid
pressure
(the gravitational field effect is taken as 9.8 kg/N in these questions).
Q1 Divers have to be
careful when working at depth in water and need to carefully control the
dissolving of gases in their blood stream.
(a) Calculate the
pressure created by a 30 m depth of water given the density of water is 1000
kg/m3 and gravity 9.8 N/kg.
P = hρg
P = 30 x 1000 x 9.8 =
294 000 Pa (2.94 x 105 Pa, 294 kPa)
(b) Comment on the
dangers when diving at great depths and how to avoid dangerous problems.
Atmospheric
pressure is about 101 kPa, so a diver at these depths will experience a
much greater pressure than on the surface of the water
Increase in pressure causes more
gases to dissolve in the blood stream (this is a general rule for gases in
contact with a liquid that can act as a solvent).
This can have serious consequences if
time isn't allowed for the body pressure to adjust to the new external
pressure, particularly when returning back to the surface.
The bends, also known as decompression sickness disease, occurs in
divers when dissolved gases (mainly nitrogen) come out of solution in
bubbles and can affect any body area including joints, lung, heart, skin and
brain.
The effects can be fatal
unless time is allowed for the body to adjust in a decompression chamber.
Q2 The density of sea water
is ~1025 kg/m3, the maximum depth of the Atlantic ocean is ~8500 m
(8.5 km).
(a) Calculate the water
pressure at this depth.
P = hρg
P = 8500 x 1025 x
9.8 =
85 400 000 Pa (to 3 sf, 85.4 MPa, 85400 kPa, 8.54 x 107 Pa, 8.54 x
104 kPa)
(b) By what factor is
the pressure greater at these depths compared to the ocean surface?
Atmospheric pressure
is ~101 kPa
Pressure at bottom
of ocean
÷ pressure at surface = 85400 ÷ 101 =
846 (3 sf).
Note: This extraordinary increase in
pressure mean to explore this 'alien' world you need a very strong
submersible craft. However, evolution has allowed all sorts of creatures
to live down at these depths, all fully pressure adjusted over time! If
you (theoretically) brought any such creatures rapidly to the surface
and exposed them to normal pressure, it would kill them!
Q3 At what depth in water
is the increased pressure five times greater than atmospheric pressure (101
kPa)?
5 x 101 = 505 kPa,
505000 Pa, density of water 1000 kg/m3
P = hρg,
rearranging gives h = P/ρg
= 505000/(1000 x 9.8) = 51.5 m
Note: The pressure
increase in water increases by about the value of atmospheric pressure for
every 10 m.
Q4 At a depth of 12.5 m of
a chemical solvent the pressure at the bottom of the storage tank due to the
solvent was 306 kPa
Calculate density of the
solvent.
P = hρg,
rearranging gives ρ = P/hg
= 306000/(12.5 x 9.8) = 2498
kg/m3
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