Flashcards in Materials Deck (75):
What is laminar flow?
Flow in layers with no mixing between the layers (streamlines do not cross). Occurs when a fluid flows in parallel layers with no disruption between the layers.
What is turbulent flow?
Chaotic flow with lots of mixing of layers, eddies and vortices are formed
What is the definition of a strong material?
One which can withstand a large stress before breaking. The strength of a material is the maximum stress that can be applied before the sample goes on to break
What is the definition of a brittle material?
Materials that break with little or no plastic deformation (e.g. glass, concrete)
What is the definition of a tough material?
Materials which deform plastically and and absorb a lot of energy before breaking. Can withstand impact forces
What is the definition of a ductile material?
One that can be pilled (drawn) into threads or wires; materials show a lot of plastic deformation under tensions (e.g. copper)
What is the definition of a malleable material?
Material that can be 'beaten' into shape; materials show a lot of plastic deformation under compression
What is the definition of a hard material?
Material that resists plastic deformation by surface indentation or scratching
What is Hooke's Law?
Force is directly proportional to extension up to the limit of proportionality
What is elastic deformation?
Bonds between atoms are stretched but not broken; sample returns to its original length when load is removed
What is plastic deformation?
Bonds between atoms are broken, layers of atoms slide over each other; material is permanently deformed and does not return to its original length when load is removed
What is the limit of proportionality of a material?
The point up until which force is directly proportional to extension and Hooke's Law is obeyed
What is the elastic limit of a material?
Up until this limit the material behaves elastically and will return to its original length when the load is removed. Between this point and the yield point the material will shorten when the load is removed but not return to its original length
What is the yield point of a material?
The point where the material shows a large increase in strain for a small increase in stress (gradient of graph decreases greatly but is not horizontal). Beyond this limit the material behaves plastically and will not shorten when the load is removed as the deformation is permanent
What is the ultimate tensile strength?
The highest point in the graph - the maximum stress that can be applied for the sample breaks
What is a fluid?
A substance which continually deforms under an applied shear stress. All liquids and gases are fluids
How is a distinction made between a solid and a fluid?
Liquids form a free surface and gases do not, but the distinction between fluids and solids is usually made by evaluating the viscosity of the substance
What is viscosity?
The viscosity of a liquid is its resistance to flow and may be though of as a measure of fluid friction
What are the properties of a fluid?
Not resisting deformation or resisting it lightly (viscous fluids) and having the ability to flow (or ability to take on the shape of a container)
What is a smart material?
One which is able to respond to its environment - one that is sensitive
How do fluids exert a drag?
- Due to a momentum change caused by the object moving through a fluid and changing its direction and speed
- Through the fluid viscosity which drags on the fluid and the object
Why does an unstreamlined object experience a greater change in momentum therefore a greater drag?
The fluid has to move a greater distance so there is a larger change in momentum and therefore a greater force (change in momentum / time = force)
What is density and why is it especially important in fluids?
The density of a body is the measure of how tightly the matter within it is packed together, and is given by the ratio of mass to volume. Different materials usually have different densities which allows them to have different buoyancies
What is used to measure density?
How does pressure in a liquid change with depth and why?
The deeper you go, the greater the pressure you would experience. This is due to the force applied by the liquid (weight of the liquid) above, as the deeper you go then the greater the volume of liquid above you which exerts a force
Derive the equation for pressure in a liquid (due to the liquid alone)
Weight = mass of fluid x g
= volume of fluid x density x g
= area of fluid x depth x density x g
so pressure beneath the column at depth h
= force / area = weight / area = ρ x g x h
What is pressure directly proportional to?
Depth and density. If the density or depth is doubled then the pressure will double
What is the equation for absolute pressure in a liquid?
P = Patm + ρgh
(Patm= atmospheric pressure )
What is the absolute pressure of a liquid?
The pressure at a given depth in a static liquid is a result of the weight of the liquid acting on a unit area at that depth plus any pressure acting on the surface of the liquid
How does upthrust occur?
Pressure in a liquid acts in all directions, and liquid pushes on all surfaces that are in contact with it, but because pressure increases with depth, the pressure on the bottom of the object is greater than that on the top. The difference in pressure creates a buoyancy force which pushes upwards on the block, which is upthrust
Derive the equation for upthrust
Considering an object of area A in a fluid of density ρ.
Then F1 = P1 x A = h1 x ρ x g x A
and F2 = P2 x A = h2 x ρ x g x A
Upthrust = F2 - F1
= (h2 - h1) x A x ρ x g
= V x ρ x g (= weight)
The upthrust on an object is equal to the weight of the fluid displaced. This general rule is often called the Archimedes' principle and works for an object of any shape
What causes an object to float?
When the upthrust caused by the pressure of the water on the object balances the weight of the object. An object will sink if the upthrust is less as there will be a resultant downwards force on the object
Explain the shape of smoke from a snuffed candle.
Initially the flow is laminar and there is no mixing between the fluid layers, but the flow becomes turbulent, where there is mixing between the layers and eddies and vortices are created, causing the smoke to become less structured and will disappear
At what point is the transition from laminar flow to turbulent flow made?
At low speeds the flow is laminar (smooth, though may involve vortices on a large scale) but as the speed increases, the flow will change to turbulent flow.
What happens to a lift force when the fluid flow around an object changes?
Laminar flow often remains attached to a body and allows a pressure difference between faster and slower regions of flow (faster streamlines = lower pressure) which give rise to a lift force. If the flow becomes turbulent or separated from the body then the pressure difference disappears and so does the lift force
How is turbulence caused around a body and how can it be reduced?
Turbulence is caused when flow has to make sharp changes around a body, which causes it to become separated from the body and will cause large swirls of flow. By altering the shape and making a body more streamlined the turbulence can be reduced and so air resistance will also be reduced
Why does increased turbulence cause drag?
Turbulent flow has more kinetic energy, and, because of the law of conservation of energy, this kinetic energy has to come from the object and the object then loses speed as energy is lost/transferred to turbulence
Laminar flow in pipes
At low speeds, the fluid nearest the wall of the pipe is dragged back by friction against the wall and so it moves the slowest. This layer then drags on the next fluid layer and so on, meaning that the fastest layer is that which is furthest away from the wall (i.e. the centre), and because there is no movement between the layers there is no 'diffusion' of fluid velocity.
Laminar flow is often also called Poiseulle Flow
Turbulent flow in pipes
If the volume rate is increased then flow may become turbulent and so the mixing of fluid layers causes fluid layers from near the wall to mix with layers from the centre so the fluid moves with a uniform velocity
What is the equation for laminar flow in pipes / Poisuelle flow?
ΔP = 8ηLQ / πr^4
Pressure required increases with the length of the pipe but decreases enormously with pipe radius; pressure increases as the fluid becomes more viscous
What is Stokes' Law?
An expression for viscous drag force exerted on spherical objects when the movement relative to the fluid is laminar (so for small spheres or ones at very slow speeds)
Fd = 6πηrv
Drag force is directly proportional to the speed and radius to the sphere
What forces is a sphere subjected to when it falls freely in a fluid?
Weight, upthrust and viscous drag
Derive the equation for terminal velocity of a sphere free falling through a liquid
Weight = Fg (mg)
Upthrust = Fu (Vρg)
Viscous drag = Fd (6πηrv)
Resultant force = Fg - Fd - Fu = mg - 6πηrv - Vρg
When object reaches terminal velocity, the resultant force is 0 so
Vterminal = mg - Vρg / 6πηr
How does viscosity of a liquid change with temperature?
An increase in temperature causes a decrease in viscosity
How does viscosity of a gas change with temperature?
An increase in temperature causes an increase in velocity
Derive an alternative formula for terminal velocity of a sphere free falling through a liquid using the volume of a sphere
mg = Vρg = 4/3πr^3 x ρs x g
Vt = 4/3πr^3 x ρs x g - 4/3πr^3 x ρ x g / 6πηr
= 2r^2g(ρs - ρ) / 9η
What is a composite material?
A material made up of more than 1 substance, such as carbon fibre
What is a mechanical property?
How a material behaves when subject to forces. When it is subject to external forces then internal forces are set up in the material which oppose the internal forces
What happens to a material when it is under tension?
When 2 forces extend a material, it is under tension. External forces pull against the attractive forces acting between atoms/molecules within the material
What happens to a material when it compressed?
When 2 forces squeeze a material, the compressive force are opposed by repulsive forces between the atoms/molecules
What happens when a material is bent?
One part of the material is under tension and another part is compressed
What are shear forces?
If 2 forces are applied to a body which cause it to twist then they are shear forces
What is the region of elastic deformation on a force extension graph?
This is the region in which, if the tension is removed, the spring will return to its original length
What is the region of plastic deformation on a force extension graph?
Above the elastic limit, the spring's behaviour is plastic, and it deforms permanently, so when the tension is removed the extension will not return to 0.
What are the key points on a force extension graph?
Proportional limit, elastic limit (elastic deformation up until this point), failure
What are the key points of Hooke's Law?
Force is proportional to extension, if the extension is elastic then if forces are removed then the material returns to its original length, the deformation is reversible and elastic energy stored in the material may be recovered as it is released
What is the Hooke's Law equation?
F ∝ Δx, or F = -k Δx
What does k represent in the Hooke's Law equation?
k is the constant of proportionality and represents the stiffness of the material. The higher the value of k the steeper the force extension curve and the stiffer the material. For a spring, k is the spring constant, and the negative sign indicates that the force exerted by the spring is in the opposite direction to the extension (spring tries to push back up against the load)
Materials with which properties absorb the most energy?
A ductile material will often absorb lots of energy before it fails, and much more than a brittle material of equal strength and stiffness. On a stress strain graph the area under the curve of a ductile material is much greater as it requires more energy to break
Derive the equation for energy stored in a material behaving elastically
F ∝ Δx
Work done = area under graph = 1/2 x base x height = 1/2 Fx
F=kx so energy stored = 1/2kx x x = 1/2 kx^2
k is positive because the force on the spring is being considered, not the force exerted by the spring.
x is in m, k is in N/m so energy is stored in J
Force extension graphs for materials such as rubber
Have one curve for loading and one curve for unloading - hysteresis. There is a greater area under the loading curve than under the unloading curve, which shows there is a difference in energy taken in vs energy released when load is released; some energy is stored in the material (and it gets hot). Area under the graph would be the amount of energy that is transferred to KE
Apparatus for investigating the force extension properties of a wire?
- G-clamp to clamp the wire
- Ruler to measure extension
- Tape to allow the extension to be measured easily
- Masses to provide tension
- Micrometer to measure diameter of wire and calculate area
* Long length of wire to ensure a measurable extension
Why are stress and strain useful to work out?
They are quantities based on force and extension that take into account the material dimensions which allows the mechanical properties of different materials to ve compared without having to consider their particular dimensions
What is tensile stress?
Tension / cross sectional area (σ = F/A)
Units are the same as pressure - Nm^-2 or Pa
What is tensile strain?
Extension / original length (ε = Δx / x or ε = Δx / L)
Strain accounts for the fact that samples strain in proportion to their lengths so it has no units
What is the Young modulus of a material?
A measure of the stiffness of an elastic material and a stiff material has a high Young modulus.
Young modulus = stress / strain = σ / ε = E
Gradient of a stress against strain graph
Derive an alternative formula for Young modulus
E = σ / ε = F/A ÷ Δx/L
= F x L / Δx x A
Why does a longer sample give a greater extension?
There are more atoms in the longer sample and each one moves apart from the next when extended. A longer sample then gives a greater total extension due to the larger number of atoms
Why are stress strain graphs useful?
They are the standard way of comparing the mechanical properties of different materials under tension. If a material obeys Hooke's law then the stress strain is a scaled version of a tension extension graph, but, beyond the elastic limit, the stress strain graph gives a much clearer picture of the material's properties as they yield.
What are the key points on a stress strain graph?
Limit of proportionality (where Hooke's law is n longer obeyed and where the graph is no longer linear)
Elastic limit (where the material starts behaving plastically)
Yield point (material shows large increase in strain for small increase in stress)
Ultimate tensile strength (point at which plastic deformation becomes unstable and a neck forms in the sample, which then increases the stress in this region. Maximum value of stress the material can endure before it breaks)
Fracture stress (the stress where the fracture occurs)
Properties of metals
Relatively high stiffness and strength, can be ductile and malleable and have high thermal and electrical conductivities. Properties can be improved by alloying
Properties of polymers
Classified as thermoplastics or thermosets. Thermoplastics become soft when heated and are generally flexible and relatively soft. Thermosets do not soften when heated by decompose and are rigid and hard. Polymers have low electrical and thermal conductivity and properties are temperature dependent
Properties of elastomers
Elastomers are polymers which the property of elasticity. They are soft and deformable and their force extension graphs show a non-linear hysteresis curve which shows some energy is stored in the material increasing its temperature
Properties of ceramics
Crystalline, but glass is an example of a non-crystalline form of ceramic. Brittle, relatively stiff. stronger in compression than tension, hard, chemically inert and bad conductors of electricity and heat