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Flashcards in Materials Deck (63)
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1
Q

How is fluid defined?

A

as any substance that can flow
-normally means liquids and gases however some solids made up of tiny particles can sometimes behave as fluids e.g. an example is the flow of sand through an hourglass

2
Q

How is Density defined?

A

is a measure of the mass per unit volume of a substance
-this is technically called ‘volumic mass’, its value depends on the mass of the particles from which the substance is made, and how closely those particles are packed

3
Q

How is Upthrust defined?

A

-is an upward force on an object cause by the object displacing fluid

4
Q

How is Archimedes’ principle defined?

A

states that the upthrust on an object is equal to the weight of fluid displaced

5
Q

What is a hydrometer?

A

is an instrument used to determine the density of a fluid

6
Q

How do you calculate density?

A

density (kgm^-3) = mass (kg)/ volume (m^3)

p =m/v

7
Q

How is density affected by temperature?

A

as objects expand when they get hotter, the volume depends on the temperature and so the density must also be affected by changes in temperature

8
Q

What is the density of air?

A
  • 1.2 as a gas at sea level, 20°C
9
Q

What is the density of water?

A

-pure, liquid at 4°C, 1000

10
Q

What is the upthrust when an object is completely submerged?

A

if an object is completely submerged the mass of the fluid displaced is equal to the volume of the object multiplied by the density of the fluid

m=Vp

The weight of fluid displaced (i.e. upthrust) is ten found using the relationship W=mg

11
Q

Why do object sink?

A
  • as the upthrust on the object when it is completely submerged is less than it weight
  • therefore the object accelerates downwards within the water until it reached the bottom of the pond, which then exerts an extra upward force (reaction force) to balance the weight so the brick rests stationary on the bottom with zero resultant force
12
Q

How does an object float?

A
  • the instance an object touches the surface of a fluid –> there is no upthrust as no water has been displaced
  • as the object sinks deeper into the fluid it displaces an increasing volume of the fluid, so increasing the upthrust acting on it
  • if a point is reached when the upthrust and weight are balanced exactly, the object will stop sinking further - it will float there,
  • So for an object to float it will have to sink until it has displaced its own weight of fluid
13
Q

How is floating and hydrometer’s linked>

A
  • the idea of floating at different depths is the principles behind the hydrometer, an instrument used to determine the density of a fluid
  • the device has a constant weight, so it will sink lower in a fluids of lesser density
  • this is because a greater volume of a less-dense fluid must be displaced to balance the weight of the hydrometer.
  • Scale markings on the marrow stem of the hydrometer indicates the density of liquids
14
Q

How is the hydrometer used with alcohol?

A
  • comparing the density of alcoholic drinks with that of water gives an indication of the proportion of alcohol they contain
  • the lower the density the greater the alcohol content, as alcohol has a lower density that the water it is mixed with
  • this has long been the basis for the taxation of alcohol
15
Q

How is Laminar flow defined?

A

also known as streamline flow

  • is where a fluid moves with uniform lines in which the velocity is constant over time
  • usually occurs at lower speeds
16
Q

How is Turbulent flow defined ?

A

is here fluid velocity in a particular place changes over time, often in an unpredictable manner
- laminar flow will turn into turbulent flow as the fluid increase past a certain point

17
Q

How are streamlines defined?

A

are lines of laminar flow in which the velocity is constant over time

18
Q

What does a laminar flow look like?

A
  • shape depends on the area of the object in which it flows
  • through a simple pipe it has a bullet sort of shape
  • thinking of water as several concentric cylinder from the central axis outwards to the layer of water in contact with the pipe itself
  • the friction between the outer most layer and the wall causes the layer to move slowly
  • each subsequent layer after it will receive friction from the previous slower-moving layer, which will slow it down
  • however each subsequently layer will receive less friction than the last the most friction is between the outlayer and the pipe wall
  • the inner most cylindrical layer will be moving the fastest
19
Q

What is a Newtonian fluid?

A
  • as with most areas of scientific investigation Isaac Newton produced much work on the subject of fluid flow
  • he is created with the development of equations to describe the frictional force between the layers in streamline flow
  • if a liquid follows his formulae ,as most common liquids do, it is known as a Newtonian fluid
20
Q

What is streamlining?

A
  • the lines within a laminar flow are called streamlines
  • at any point any one of these streamlines, the velocity of the flow will be constant over time
  • as velocity is a vector this means hat the water at any point in the pipe will always move in the same direction at the same speed
  • the direction and/or speed may be different in different places, but at any given point place direction and speed must stay the same
21
Q

What are the characteristics of turbulent flow?

A
  • velocity in any given place changes over time
  • the flow becomes chaotic and swirling eddies form
  • any direction
22
Q

why is streamlining important for car manufacturers?

A

-turbulent flow increases the drag of a vehicle and so increases fuel consumption

23
Q

How can you investigate the different types of flow?

A
  • Turbulent flow was first demonstrated by Osborne Reynolds in 1883
  • in an experiment showing colored water flowing into a glass tube
  • you can set up a similar experiment to show turbulent caused by faster fluid flow or by different
  • At most speeds, a smooth curved object will produce less turbulence than a squarer one
24
Q

How is Viscosity defined?

A

is, essentially, the idea of how resistant a fluid is to flowing
- measured in Pascal seconds (Pa s)

25
Q

How is Coefficient of viscosity?

A

is a numerical value given to a fluid to indicate how much it resists flow
-η (eta)

26
Q

How is viscosity linked to the rate of flow of a fluid?

A
  • viscosity determines the friction force acting within a fluid, it has a direct effect on the rate of flow of the fluid
  • the rate of flow of a fluid through a pipe is inversely proportional to the viscosity of the fluid
27
Q

Who is Jean Poiseuille?

A
  • In 1838, the French doctor and physiologist investigated the flow of fluid through pipes and proved the connection between flow rate and viscosity
  • Poiseuille was interest in blood flow through the heart but his law was immensely important in industrial design
  • for example the rate of flow of liquid chocolate through pipes in the manufacture of sweets will vary with the chocolate’s viscosity –> more sugar meant increased viscosity thus less chocolate per sweet
  • viscosity of the liquid chocolate also depended on the temperature, which might have come from something as minor as a change in supplier of cocoa beans
28
Q

How is viscosity affected by temperature?

A
  • viscosity is directly related to fluid temperature
  • in general, liquids have a lower coefficient of viscosity at higher temperature
  • and gases have a higher viscosity when temperature increases
29
Q

How can we investigate the flow rates of fluids?

A
  • by using a constant head apparatus, a capillary tube and a measuring cylinder
    -using a constant pressure, water forced through a narrow pipe will flow at a certain rate, inversely proportional to its viscosity.
    -by varying the height of a water tank (constant head apparatus), you can record measurements of this ‘head of pressure’, h, against the flow rate
    -the gradient of the best line of fit will allow you to calculate the viscosity of water
    -you can plot a graph of the flow rate (F) against height (h) and hence calculate the viscosity of water (η)
    -Poiseuille’s equation tells us that the gradient of the graph is (πpgr^4)/(8ηl)
    where r is the internal radius of the capillary tube, l is the length of the capillary tube, p is the density of water and g= 9.81 N kg^-1
30
Q

How do you investigate how viscosity changes with temperature?

A
  • you can investigate how viscocity changes with temperature using a re-sealable tin or bottle half-fuel of a test fluid e.g. gold syrup
  • the temperature of the liquid is varied with a water bath
  • the viscosity of the liquid will affect the rate at which the tin or bottle rolls down the fixed ramp
31
Q

How is terminal velocity defined?

A

is the velocity of a falling object when its weight is balanced by the sum of the drag and upthrust acting on it

32
Q

how do we calculate the acceleration of something falling towards earth?

A
  • acceleration due to gravity in a vacuum is 9.81 ms^-2
  • in reality, in order to calculate an object;s actual acceleration when falling, we need to take account of all the forces acting on it, combine these to find a resultant force and then use Newton’s second law a=F/m to calculate the resulting acceleration
  • e.g. with a skydiving this means we need to include the weight, the upthrust and the viscous drag varies with speed through the fluid, and speed is constantly changing as a result of acceleration
  • usually, we consider the equilibrium situation, in which the weight exactly balanced the sum of upthrust and drag. meaning that the falling velocity remains constant, this constant velocity is the terminal velocity
33
Q

When is the phrase terminal velocity only applicable?

A

when objects falling under gravity with a constant weight
-for similar situation horizontally for example a car using a constant thrust force, an alternative phrase such as ‘maximum velocity’ would be more appropriate

34
Q

Who is Sir George Gabriel Stokes?

A
  • an Irish mathematician and physicist at Cambridge University, investigated fluid dynamics and came up with an equation for the viscous drag (F) on a small sphere at low speeds, this formula is known as Stoke’s law
35
Q

What is Stoke’s law?

A

F=6πrηv

  • r= radius of the sphere (m)
  • v= the velocity of sphere (ms^-1)
  • η = the coefficient of viscosity of the fluid (Pa s)

thus in such a simple situation the drag force is directly proportional to the radius of the sphere, and directly proportional to the velocity, neither of which is necessarily an obvious outcome

36
Q

How do you derive the terminal velocity of a sphere in a fuild?

A
(terminal velocity of the sphere in terms of the force)
-weight = upthrust + Stoke's force
-m(s)g= weight of fluid displaced + 6πrηv(term)
where m(s) is the mass of the sphere

(for the sphere, the mass m(s) is given by):
m(s) = volume x density of sphere = 4/3π^3 x p(s)

(so the weight of the sphere W(s)):
W(s)=m(s)g= 4/3πr^3p(s)g

(for the spgere the upthrust is equal to the weight of fluid displaced, the mass m(f) of fluid displaced is given by):
m(f) = volume x density of fluid = 4/3πr^3 x p(F)

(so the weight of fluid displaced W(f) is given by):
W(f) = m(f)g = 4/3πr^3p(f)g

(overall is):
4/3πr^3p(s)g=4/3πrp(f)g + 6πrηv(term)

Which rearranges to:
v(term) = (4/3πr^3g(p(s)-p(f)))/(6πrη)

Cancelling the π and r and tidying the fraction we get:
v(term) = (2r^2g(p(s)-P(f)))/9η)

37
Q

how do larger spheres fall compared to smaller spheres?

A
  • terminal velocity is proportional to the square of the radius
  • this means that a larger sphere falls faster,
  • furthermore, because the radius is squared, it falls much faster
38
Q

How do you investigate terminal velocity?

A
  • you can investigate the viscosity of a liquid by allowing various differently sized spheres to fall through it and then measure their terminal velocity and radii
  • you can plot a graph of the terminal velocity , v(term), against the sphere’s radius, r^2 ad hence calculate the viscosity of water η.
  • Stoke’s law lets us that the gradient of the graph = (2g(p(s) - p(f)))/9η
  • you may need to do additional experiments to find the densities of the two materials
  • water is usually not viscous enough to give a measurable different terminal velocities in this experiment
  • However if you do use water you can then compare the answer for its viscosity with that found from the Poiseuille flow experiment
39
Q

What is Viscous drag?

A
  • viscous drag is the friction force between a solid and a fluid
  • calculating the fluid friction force can be relatively simple, on the other hand it can be very complicated to calculate for large objects, fast objects, and irregular shaped objects, as the turbulent flow creates an unpredictable situation
  • it must be remembered that the simple slow-falling sphere of Stoke’s law is not a common situation and in most real application the terminal velocity value is a result of more complex calculations. However. the principle that larger object generally fall faster holds true for most objects without a parachute
40
Q

how is tension defined?

A

is a force acting within a material in a direction that would extend the material
- if a material is made longer the force is called tension however the extra length is called extension

41
Q

how is extension defined?

A

is an increase in size of a material sample caused by a tension force

42
Q

how is compression defined?

A

is a force acting within a material in a direction that would squash the material, Also the decrease in size of a material sample under a compressive force
- the size lost can also be referred to as negative extension

43
Q

How is the limit of proportionality defined?

A

the limit of proportionality is the maximum extension (or strain) that an object (or sample) can exhibit, which is still proportional to the load (or stress applied)

44
Q

How is elastic limit defined?

A

a materials elastic limit is the maximum extension or compression tat material can undergo and still return to its original dimensions when the force is removed

45
Q

How is spring constant defined?

A

the spring constant is the Hooke’s law constant of proportionality, k, for a spring under tension

46
Q

How is hysteresis defined?

A

for the extension of a material sample, hysteresis is where the extension under a certain load will be different depending on its history of past loads and extensions

47
Q

Who has Robert Hooke?

A
  • a contemporary and vigorous rival to Isaac Newton, was an exceptional experimental scientist, his interest were diverse and the law that bears his name is arguably one of his least notable achievements
  • this law being Hooke’s Law
48
Q

What is Hooke’s law?

A
  • the force that is needed to extend a spring is proportional to the extension of the spring, a material only obeys Hooke’s law if i has not passed its limit of proportionality
  • if only a small force is applied to the spring it will deform elastically, but return to the same shape
  • if a force is applied that means the spring goes passed its elastic limit the spring will deform plastically and not return to its original shape and size?
49
Q

How do you calculate Hooke’s Law?

A
force applied (N) = stiffness constant (Nm^-1) x extension (m)
ΔF=kΔx

the stiffness constant for a spring is usually referred to as the spring constant, either phrase refers to in the Hooke’s law equation

50
Q

How do you investigate Hooke’s Law?

A

-by hanging various masses on a spring and measuring the corresponding extensions, you can gather a set results for ΔF and ΔX,
in each case, you could calculate the spring constant from a pair of readings, but you will get more accurate final answer for k if you plot a graph of the results and find its gradient
-in the graph plot the dependent variables on the x-axis (extension) against weight force on the y-axis,
- the gradient gives you the spring constant ΔF/Δx = k

51
Q

What is Elastic strain energy?

A

-the work done in deforming a material sample before it reaches it elastic limit will be stored within the material as elastic strain energy E(el)
- as work done can be calculated by multiplying the force by the distance moved in the direction of the force, it is the same for deforming material too
- but Hooke’s law means that the force value varies at different extensions
if we plot the extension of a spring with increasingly large masses hanging on it , the graph will follow Hooke’s law, to find the work done to extend the spring a certain amount, we must calculate using the average force over the distance of the extension

52
Q

How do you calculate elastic strain energy?

A

ΔE(el) = 1/2FΔx`

53
Q

How do you find work done from force- extension and force compression graphs?

A
  • the work done in deforming a material is calculated by multiplying the extension or compression by an appropriate average force value
  • if the force is varying in a non-linear way, which is common for some materials, finding the average force may not be a straightforward process
  • however, the area below the line on a force-extension graph will give you work done
  • this is easy to calculate as it is a basic area of triangle
  • if the graph is not linear the work done can still be calculated from under the graph
  • if the line is curved you may need to find the area by estimating and counting the squares on the graph` paper, and then multiply them by the elastic energy value (F x Δx) for each individual square
54
Q

What is stress?

A
  • Tensile (or compressive) stress is a measure of the force within a material sample, but it takes account of the cross-sectional area across the sample
  • this allows force comparisons to be made between samples of different sizes, so that they are measured under comparable conditions
55
Q

How do you calculate stress?

A

stress (pascals, Pa, or Nm^-2) = force (N)/cross-sectional (m^2)
-σ = F/A

56
Q

What is strain?

A

Tensile (or compressive) strain in a measure of the extension (or compression) of a material sample but it takes account of the original length of the sample.
-this allows extension comparisons to be made between samples of different sizes so that they are measures under comparable conditions

57
Q

How do you calculate strain?

A

strain (no units) = extension (m)/original length (m)
ε=Δx/x
as strain is a ratio, it has no units, However it is often expressed as a percentage by multiplying the ratio by 100%

58
Q

What is Young Modulus?

A
  • if a material is deformed elastically, stress will be proportional to strain, with a constant of proportionality that is a measure of the stiffness of the material - how much it deforms under a certain stress
  • the stiffness constant is called the Young Modulus
  • Thus the young modulus is a measure of the stiffness of a material, which takes account of the shape and size of the sample, so that different samples of the same material will all have the same value for the Young Modulus
  • the idea of stiffness is a measure of how much the material deforms when forces are applied to it
  • the definition for Young Modulus also includes the fact that the material must be undergoing elastic deformation, beyond the limit of proportionality, the equation will no longer work to calculate the stiffness of the material
59
Q

How do you calculate Young Modulus?

A

Young Modulus (Pa) = stress (Pa)/strain (no units)
-E=σ/ε
or
-Fx/AΔx
the stiffness constant k, from Hook’e law relates to a particular object such as a spring
-for material, the Young modulus, E, is the stiffness constant for the material in general regardless of sample size

60
Q

How can you analyse stress and strain?

A
  • when stress is proportional to strain we should get a straight line graph if we plot stress against strain –> only for small stresses
  • once the limit of proportionality is passed the internal structure of the material starts to behave differently, and this means that the graph starts to curve
  • depending on the material the graph will go through various phases as the molecular substructure of the specific material determines its response to increasing stress
61
Q

What are the different stages of a general Stress Strain graph?

A

1– straight line part –> the metal extends elastically, and will return to its original size and shape when the force is removed, the gradient of the straight-line portion of the graph is equal to the Young modulus for metal
2– then it hits the limit of proportionality, slightly beyond this point, the metal may still behave elastically, but it cannot be relied upon to increase strain in proportion to the stress
3– then it hits the elastic limit, beyond this point the material is permanently deformed and will not return to its original size and shape, even when the stress is completely released
4– the next point is the yield, beyond which the material undergoes a sudden increase in extension as it atomic substructure is significantly reorganised, the metal ‘gives’ (graph drops) just beyond its yield point as the realignment - slip - of the metal’s atoms reduce the internal stresses
5– after that the graph hits a point where it is at the highest ever value that the stress can ever attain within the material, this is called the Ultimate Tensile Stress, or UTS, σ(U)
6– after is the fracture stress, or breaking stress, it is the value that the stress will be in the material when the sample breaks

62
Q

what is a common trait for stress strain graphs?

A

it is quite common for the limit of proportionality, the elastic limit and the yield point to be in same place on the graph

63
Q

How can we investigate the stress-strain relationship for metals?

A
  • using a metal load,a safe landing pad, clamp-on pulley, a ruler, G-clamp and a thin wire
  • the original length and diameter of the wire must be measured first
  • then, using increasing forces as the independent variable, you will need to take measurements of the extension corresponding to each force
  • There will be some readings during the wire’s elastic deformation region which will increase uniformly
  • beyond,the elastic limit, it will increase with greater extensions for each increase in the load force until, eventually, the fracture stress will be reached and wire will snap.
  • Safety goggles must be worn during this experiment, as wire that snap under tension pose a significant hazard to the eyes
  • the plot stress against strain with the gradient is the stiffness constant or Young modulus: Δy/Δx =stress/strain = E
  • usually you would put the independent variable (stress) on the x-axis however the graph is usual to draw a graph with a curve and the find the gradient of the straight line portion