Topic 4: Materials
Created 10 March 2026 14:31
Tags Notes
Fluids
Density
Density is a fundamental bulk property of solids, defined as the mass per
unit volume of a substance.
It’s a measure of how tightly packed the atoms or molecules are in a
material.
Density is typically denoted by the symbol ρ (rho).
Usually expressed in units of mass per unit volume, such as grams per
cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).
Formula:
Density(ρ)=mass (m) volume (V)(1)
Liquids and gases expand much more than solids when they are heated, so
a fixed mass of fluid occupies a bigger volume than the solid form and so
its density is reduced.
Liquids are generally considered to be incompressible, but gases are
readily squeezed (try putting your finger over the outlet of a bicycle pump
and pushing in the handle).
Because of this, the pressure needs to be stated in addition to the
temperature when the density of a gas is quoted.
Upthrust
Topic 4: Materials 1
, Upthrust in fluids is a fundamental concept in physics and engineering.
Also known as buoyancy, it’s the upward force exerted by a fluid (such as a
liquid or gas) on an object that’s partially or fully submerged in it.
The magnitude of the upthrust force depends on the:
1. Density of the fluid
2. Volume of the displaced fluid (the amount of fluid pushed out of the
way by the object)
3. Acceleration due to gravity (g)
The buoyancy force is equal to the weight of the displaced fluid. This is
known as Archimedes’ Principle.
Upthrust is responsible for many interesting phenomena, such as:
—Objects floating or sinking in water.
—Shops and boats able to carry heavy loads.
—Submarines diving and surfacing.
—Helium-filled balloons rising in air
Consider a cylinder immersed in a liquid, as shown in Figure 1. The
upthrust is the difference between the force due to water pressure at the
bottom of the cylinder, and that at the top, F1
For a fluid of density ρ:
F1 = p1 A = h1 ρgA
F2 = p2 A = h2 ρgA
U = F2 – F1
U = (h2 –h1 )ρgA
U = (h2 –h1 )Aρg
V = (h2 –h1 )A
So,
Topic 4: Materials 2
, U = V ρg(2)
By equation 1
m
ρ=
V
Vρ = m put in equation 2
U = mg
The upthrust is equal to the weight of the displaced fluid.
Figure 1 Upthrust on a cylinder.
This result is often stated as Archimedes’ principle.
Moving fluids-streamlines and laminar flow
Streamlines and laminar flow are two related concepts in fluid dynamics:
Streamlines:–
Streamlines are imaginary lines that represent the path of fluid particles
in a flow field.– They are used to visualize the direction of fluid motion
and can be obtained experimentally or computationally.– Streamlines are
useful for understanding fluid behaviour, identifying patterns, and
analysing flow structures.
Laminar Flow:–
Laminar flow is a type of fluid flow characterized by smooth, parallel
layers of fluid that slide over each other without mixing.– In laminar flow,
the fluid particles move in straight lines, and the flow is predictable and
stable.– Laminar flow is often associated with low velocities, high
Topic 4: Materials 3
Created 10 March 2026 14:31
Tags Notes
Fluids
Density
Density is a fundamental bulk property of solids, defined as the mass per
unit volume of a substance.
It’s a measure of how tightly packed the atoms or molecules are in a
material.
Density is typically denoted by the symbol ρ (rho).
Usually expressed in units of mass per unit volume, such as grams per
cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).
Formula:
Density(ρ)=mass (m) volume (V)(1)
Liquids and gases expand much more than solids when they are heated, so
a fixed mass of fluid occupies a bigger volume than the solid form and so
its density is reduced.
Liquids are generally considered to be incompressible, but gases are
readily squeezed (try putting your finger over the outlet of a bicycle pump
and pushing in the handle).
Because of this, the pressure needs to be stated in addition to the
temperature when the density of a gas is quoted.
Upthrust
Topic 4: Materials 1
, Upthrust in fluids is a fundamental concept in physics and engineering.
Also known as buoyancy, it’s the upward force exerted by a fluid (such as a
liquid or gas) on an object that’s partially or fully submerged in it.
The magnitude of the upthrust force depends on the:
1. Density of the fluid
2. Volume of the displaced fluid (the amount of fluid pushed out of the
way by the object)
3. Acceleration due to gravity (g)
The buoyancy force is equal to the weight of the displaced fluid. This is
known as Archimedes’ Principle.
Upthrust is responsible for many interesting phenomena, such as:
—Objects floating or sinking in water.
—Shops and boats able to carry heavy loads.
—Submarines diving and surfacing.
—Helium-filled balloons rising in air
Consider a cylinder immersed in a liquid, as shown in Figure 1. The
upthrust is the difference between the force due to water pressure at the
bottom of the cylinder, and that at the top, F1
For a fluid of density ρ:
F1 = p1 A = h1 ρgA
F2 = p2 A = h2 ρgA
U = F2 – F1
U = (h2 –h1 )ρgA
U = (h2 –h1 )Aρg
V = (h2 –h1 )A
So,
Topic 4: Materials 2
, U = V ρg(2)
By equation 1
m
ρ=
V
Vρ = m put in equation 2
U = mg
The upthrust is equal to the weight of the displaced fluid.
Figure 1 Upthrust on a cylinder.
This result is often stated as Archimedes’ principle.
Moving fluids-streamlines and laminar flow
Streamlines and laminar flow are two related concepts in fluid dynamics:
Streamlines:–
Streamlines are imaginary lines that represent the path of fluid particles
in a flow field.– They are used to visualize the direction of fluid motion
and can be obtained experimentally or computationally.– Streamlines are
useful for understanding fluid behaviour, identifying patterns, and
analysing flow structures.
Laminar Flow:–
Laminar flow is a type of fluid flow characterized by smooth, parallel
layers of fluid that slide over each other without mixing.– In laminar flow,
the fluid particles move in straight lines, and the flow is predictable and
stable.– Laminar flow is often associated with low velocities, high
Topic 4: Materials 3
