Physics notes · Chapter 5 of 11
Properties of Matter & Fluids
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What is a Fluid?
- A fluid is any substance that can flow and take the shape of its container: liquids and gases (a solid keeps a fixed shape).
- Solid: fixed shape and fixed volume. Liquid: fixed volume, no fixed shape. Gas: neither.
- Fluid statics studies fluids at rest; fluid dynamics studies fluids in motion.
- States of Matter
| State | Fixed shape | Fixed volume |
|---|---|---|
| Solid | Yes | Yes |
| Liquid | No | Yes |
| Gas | No | No |
Check yourself
Define a fluid
Any substance that can flow and take the shape of its container.
Which states are fluids?
Both liquids and gases; a solid is not, as it keeps a fixed shape.
Solid, liquid, gas — shape and volume
Solid: fixed shape + fixed volume. Liquid: fixed volume, no fixed shape. Gas: neither.
Fluid statics vs fluid dynamics
Statics studies fluids at rest; dynamics studies fluids in motion.
Density and Relative Density
- Density ρ = mass ÷ volume, SI unit kg m⁻³: how tightly matter is packed.
- Water is densest at 4°C: 1.0 × 10³ kg m⁻³ (1 g cm⁻³).
- Relative density = density of a substance ÷ density of water at 4°C: a pure number with no unit. Above 1 a body sinks; below 1 it floats (ice, cork, oil).
- Density and Relative Density
| Substance | Density (kg m⁻³) | Rel. density |
|---|---|---|
| Water (4°C) | 1000 | 1.0 |
| Ice | 917 | 0.92 |
| Aluminium | 2700 | 2.7 |
| Mercury | 13600 | 13.6 |
Check yourself
Define density and its SI unit
ρ = mass ÷ volume; SI unit kg m⁻³. It shows how tightly matter is packed.
Density of water at 4°C
1.0 × 10³ kg m⁻³ (1 g cm⁻³); water is densest at 4°C.
Define relative density
Density of substance ÷ density of water at 4°C — a pure number with no unit.
Relative density > 1 vs < 1
> 1 → the body sinks; < 1 → it floats (ice, cork, oil).
Pressure in Fluids
- Pressure = force acting perpendicular (normal) to a surface ÷ area: P = F ÷ A. A sharp pin pierces easily because a small area concentrates the force.
- Pressure is a scalar, dimensions [M L⁻¹ T⁻²], unit the pascal (after Blaise Pascal): 1 Pa = 1 N m⁻².
- A fluid at rest pushes perpendicular to any surface it touches; its pressure increases with depth (P₂ − P₁ = ρgh) and is equal everywhere at the same level.
Check yourself
Define pressure in a fluid
Force acting perpendicular (normal) to a surface ÷ area; P = F ÷ A.
Why does a sharp pin pierce easily?
A small area concentrates force, so a blunt rod does not.
Dimensional formula of pressure
[M L⁻¹ T⁻²]; named after Blaise Pascal.
Direction of fluid pressure at rest
Always pushes perpendicular (normal) to any surface it touches.
How does pressure change with depth?
It increases with depth; the difference over height h is P₂ − P₁ = ρgh.
Pressure at the same horizontal level
Equal everywhere in a still liquid. Pressure is a scalar; 1 Pa = 1 N m⁻².
Pascal's Law
- Pascal's law: pressure on an enclosed fluid is transmitted undiminished, equally, in all directions, because liquids are nearly incompressible.
- It powers the hydraulic system, a force multiplier: since force = pressure × area, a larger piston gives a much larger force, so a small push lifts a heavy car.
- Uses: hydraulic lift, hydraulic press, hydraulic brakes, the dentist's chair.
Check yourself
State Pascal's Law
Pressure on an enclosed fluid is transmitted undiminished, equally, in all directions.
Why does Pascal's law work?
Because liquids are nearly incompressible, so the push reaches every point.
What does it power?
The hydraulic system, which acts as a force multiplier.
Why does a larger piston give more force?
Since force = pressure × area, a larger piston gives a much larger output force — a small push lifts a heavy car.
Devices using Pascal's law
Hydraulic lift, hydraulic press, hydraulic brakes and the dentist's chair.
Atmospheric Pressure and the Barometer
- Atmospheric pressure: the weight of the air column above a unit area. We are not crushed because it pushes equally from all sides.
- 1 atm = 1.013 × 10⁵ Pa at sea level. It falls with altitude, which is why climbers carry oxygen.
- Torricelli first measured it with the mercury barometer: the column stands about 76 cm (760 mm) at sea level, with the Torricellian vacuum above it.
Check yourself
Define atmospheric pressure
The weight of the air column above a unit area.
Why are we not crushed by it?
The pressure pushes equally from all sides.
Value of 1 atm at sea level
1 atm = 1.013 × 10⁵ Pa.
Why do climbers carry oxygen?
Atmospheric pressure falls with altitude.
Who first measured atmospheric pressure?
Evangelista Torricelli, using the mercury barometer.
Height of the mercury column at sea level
About 76 cm (760 mm); the empty space above is the Torricellian vacuum.
Buoyancy and Archimedes' Principle
- Buoyancy (upthrust): the upward force a fluid exerts on a body in it, which is why things feel lighter in water.
- Archimedes' principle: upthrust = weight of the fluid displaced.
- A body floats if buoyancy ≥ its weight and sinks if its weight is greater. Law of floatation: a floating body displaces fluid equal to its own weight.
- Relative density can be found from the loss of weight of a body in water.
Check yourself
Define buoyancy (upthrust)
The upward force a fluid exerts on a body in it — why an object feels lighter in water.
When does a body float or sink?
If buoyancy ≥ weight it floats; if weight > buoyancy it sinks.
State the law of floatation
A floating body displaces fluid equal to its own weight.
How can relative density be found?
From the loss of weight of a body in water.
State Archimedes' Principle
Upthrust = weight of the fluid displaced by the body.
Floating Ice and Melting (Key Exam Cases)
- Ice floats because its density (≈917 kg m⁻³) is less than water's.
Ice contracts on melting, because water is denser than ice.
Floating ice holding a stone: the level falls after melting.
Check yourself
Ice melts in a brim-full beaker — what happens?
The water level stays the same (no overflow).
Why does the level not change?
The melted water exactly fills the volume that was displaced.
Does ice expand or contract on melting?
It contracts (volume decreases) because water is denser than ice.
Why does ice float?
Its density (≈917 kg m⁻³) is less than water.
Floating ice holding a stone — level after melting?
The level falls after melting.
Anomalous Expansion of Water
- Anomalous expansion: from 0°C to 4°C water contracts on heating instead of expanding; above 4°C it expands normally.
- Water is densest at 4°C (maximum density, minimum volume).
- So ice forms on top of a lake while the water below stays liquid, with the densest 4°C water at the bottom: aquatic life survives.
Check yourself
What is anomalous expansion of water?
Water shows unusual expansion between 0°C and 4°C.
Heating water from 0°C to 4°C does what?
Water contracts instead of expanding; above 4°C it expands normally.
Where is water densest?
At 4°C — maximum density and minimum volume.
How does this let aquatic life survive?
Ice forms on top while water below stays liquid; the warmest, densest water at 4°C settles at the bottom of frozen lakes.
Viscosity
- Viscosity: a fluid's internal friction, resisting flow between its layers. High: honey, glycerine, tar; low: water and air.
- SI unit of the coefficient of viscosity: Pa·s (poise in CGS).
- Viscosity causes drag on a body moving through a fluid, like a stone falling in oil.
- Viscosity of Common Fluids
| Fluid | Viscosity |
|---|---|
| Glycerine / honey | Very high |
| Oil | Moderate |
| Water | Low |
| Air / gases | Very low |
Check yourself
Define viscosity
A fluid's internal friction resisting flow between its layers.
Which fluids have high vs low viscosity?
Honey, glycerine, tar have high viscosity; water and air have low.
SI unit of coefficient of viscosity
Pa·s (or poise in CGS).
Viscosity of liquids vs gases with temperature
Liquids: viscosity decreases as temperature rises. Gases: viscosity increases.
What does viscosity cause?
Drag on a body moving through a fluid, like a stone falling in oil.
Surface Tension and Capillarity
- Surface tension makes a liquid surface behave like a stretched elastic film; it comes from the cohesive force pulling molecules inward.
- It makes small drops spherical and lets insects walk on water. It decreases with rising temperature and with soap or detergent.
- Capillarity: the rise or fall of a liquid in a thin tube.
Check yourself
Define surface tension
Makes a liquid surface behave like a stretched elastic film.
What causes surface tension?
The cohesive force between molecules pulling inward.
Two effects of surface tension
Makes small drops spherical; lets insects walk on water.
Define capillarity
The rise or fall of a liquid in a thin tube.
Water rises but mercury falls — why?
Water rises in glass (adhesion); mercury falls (cohesion dominates).
What decreases surface tension?
Rising temperature and soap or detergent.
Fluids in Motion (Streamline, Bernoulli)
- Streamline (laminar) flow is smooth and orderly along fixed paths; turbulent flow is irregular, with eddies and swirls.
- Equation of continuity: a fluid speeds up where the pipe narrows (Av = constant).
- Bernoulli's principle: where a fluid's speed is higher, its pressure is lower. It explains aeroplane lift (faster air over the wing, lower pressure above), the swing of a spinning ball (Magnus effect) and the sprayer.
Check yourself
Streamline vs turbulent flow
Streamline (laminar) is smooth, orderly flow along fixed paths; turbulent is irregular and disordered, with eddies and swirls.
State the equation of continuity
A fluid speeds up where the pipe narrows (Av = constant).
State Bernoulli's principle
Where fluid speed is higher, its pressure is lower.
How does Bernoulli explain aeroplane lift?
Faster air over the wing gives lower pressure above.
What else does Bernoulli explain?
The spin of a ball (Magnus effect) and the action of a sprayer.
Wind, Salinity and Triple Point (PYQ Facts)
- Wind speed: anemometer; wind direction: wind vane.
- Halocline: a salinity gradient in water, salt concentration varying with depth.
- Triple point: where solid, liquid and gas of a substance coexist; for water 273.16 K (0.01°C), at low pressure.
- Atmospheric pressure is read from the height of the liquid column in a barometer.
- Quantities and How They're Measured
| Quantity | Measured / value |
|---|---|
| Wind speed | Anemometer |
| Atmospheric pressure | Barometer |
| Salinity gradient | Halocline |
| Triple point of water | 273.16 K |
Check yourself
Wind speed vs wind direction instruments
Speed → anemometer; direction → wind vane.
What is a halocline?
A water salinity gradient — varying salt concentration with depth.
Define the triple point
Where solid, liquid and gas of a substance coexist together.
Triple point of water
273.16 K (0.01°C) and low pressure.
Which quantities have no unit?
Relative density and strain.
Atmospheric pressure is read from…
The height of the liquid column in a barometer.
All 11 chapters of Physics notes
- Units, Measurement & Physical Quantities11 sections
- Motion, Laws of Motion & Forces13 sections
- Gravitation11 sections
- Work, Power, Energy & Conservation13 sections
- Properties of Matter & Fluids12 sections
- Heat & Thermodynamics12 sections
- Waves & Sound11 sections
- Light & Optics15 sections
- Current Electricity13 sections
- Magnetism & Electromagnetism15 sections
- Modern & Nuclear Physics16 sections