Fluid mechanics Flashcards
1
Q
What are ideal fluids
A
Incompressible
Free of internal friction (not viscous)
1
Q
What does Bernoulli’s theorem apply to?
A
Ideal fluids in stationary and irrotational motion
2
Q
When is the flow rate constant?
A
When the fluid is incompressible and the glass of the conduit are rigid
3
Q
What is stationary motion?
A
The speed at the level of a section which is constant in all points of a section
4
Q
What is irrotational motion?
A
Free of vortexes
No sharp-angled elbows and abrupt section changes in the duct
5
Q
Is internal friction negligible in real liquid?
A
No they aren’t, they are present and not negligible
6
Q
Are real liquids smooth?
A
No, they display a degree of viscosity
7
Q
Is the kinetic energy theorem valid and applicable to the motion of real liquid?
A
No because non-conservative forces come into play
8
Q
What do fluids consist of?
A
Liquids and gases
9
Q
What are fluids?
A
Continuous and deformable bodies with uniform density
10
Q
Are liquids compressible?
A
No not very
11
Q
Where are forces between molecules higher, liquids or gas?
A
Liquids
12
Q
Formula for pressure
A
p=F/S
13
Q
Unit for pressure
A
N/m^2
14
Q
What is the flowrate?
A
Volume of a fluid that passes through a section of the duct in the unit of time
15
Q
What is the flowrate measured in?
A
m^3/s
16
Q
Formula for flowrate
A
Q=V/t=S*v
17
Q
2 types of fluid
A
Ideal fluids
Real fluids
18
Q
What are real fluids?
A
Forces with frictional forces present (viscous)
19
Q
What does it mean if ideal fluids are in steady motion?
A
Speed is constant in every point of the action of the duct
20
Q
What is Leonardo’s law?
A
S1v1=S2v2
21
Q
What is the velocity along the walls in laminar flow?
A
0
22
Q
What is the velocity along the axis in laminar flow?
A
Maximum
23
Q
What does the equation for flowrate in real liquids look like?
A
Q=Svm
vm= average velocity (1/2vmax)
24
What happens to the molecules in a fluid at rest?
They are in constant motion
25
What does Pascal's principle state?
A pressure exerted in one point of an incompressible fluid is transmitted unaltered to every point of the liquid
26
What does the pressure inside a fluid depend on?
The distance from the surface
The pressure at the bottom will be higher
27
What does Stevin's law state?
p=roh*h*g+p0
p=pressure
28
Fw=?
m*g=roh*V*g=roh*S*h*g
Fw= force weight
29
Density of water
1*10^3 kg/m^3
30
What does Archimedes' principle state?
A body immersed in a fluid is subjected to an upward force of an intensity equal to the weight of the displaced fluid volume
31
What is the thrust of Archimedes?
Upward force exerted by the surface doesn't depend on what occupies the volume (body or liquid)
32
Formula for force acting on a immersed body according to archimedes principle
Farch=^p*s=V*g*roh(liq)
33
What does whether a body floats or sinks depend on?
Density
34
Farch?Fw
roh(bod)?roh(liq)
When body floats
Farch>Fw
roh(bod)
35
Farch?Fw
roh(bod)?roh(liq)
When body stays in the middle
Farch=Fw
roh(bod)=roh(liq)
36
Farch?Fw
roh(bod)?roh(liq)
When body sinks
Farchroh(liq)
37
What does if a body rotates or not depend on?
The centre of thrust and center of gravity
38
What does Bernoulli's theorem represent?
The extension to fluid of the principle of conservation of energy
39
What does Bernoulli's theorem allow us to interpret?
Important aspects of blood circulation in large blood vessels
40
When does Bernoulli's theorem apply?
In stationary and irrotational motion
41
What is stationary motion?
Speed at the level of a section is constant in all the points of the section
42
What is irrotational motion free of?
Vortexes
43
What are the two forces acting on a liquid during motion?
Force of gravity
Pressure forces
If fluid I real then friction, if fluid is ideal then no friction
44
What is the work done by the forces acting on the masses of fluid equal to?
The change of kinetic energy (kinetic energy theorem)
45
Is the mass in ideal fluids variable?
No because they are incompressible
46
What is Bernoullis' equation?
Constan=h+p/(roh*g)+v^2/(2g)
47
Wtot=^Ec
Bernoullis'
h1+p1/(roh*g)+v1^2/2g=h2+p2/(roh*g)+v2^2/2g
48
What is stenosis?
When vessels shrinks
49
What is an aneurysm?
When vessels increase
50
When considering Leonardo's law what happens during stenosis?
Velocity is greater and the surface smaller than normal
51
When considering Leonardo's law what happens during aneurysm?
Velocity is smaller and the surface greater than normal
52
What happens in Bernoulli's theorem during stenosis?
Pressure decreases and volume goes up
53
What happens in Bernoulli's theorem during aneurysm?
Pressure increases and volume goes down
54
Formula for Stevino's law
p2=p1+roh*h*g
55
When does Stevino's law apply?
When fluid is at rest in a container
56
Formula for Torricelli's theorem
h1=v2^2/2g
v2=sqrt 2*g*h1
57
Where does friction intervene in real liquids?
Between the molecules during their flow and the contact between molecules and the walls
58
What isn't valid in non-conservative forces?
Kinetic energy theorem
Bernoulli's theorem
59
2 types of flow
Laminar
Turbulent
60
What is laminar flow?
Flow where speed vectors are parallel to each other
61
What is turbulent flow?
Flow where speed vectors are irregular
62
What does the maximum speed correspond with in laminar flow?
The axis of the duct
63
What does the slowest speed correspond with in laminar flow?
The velocity of the molecules in direct contact with the walls
64
Flow rate definition in laminar flow
Q=S*vm= S*0.5*vmax
65
Formula for frictional forces in laminar flow
Fa=n*A* ^v/r
n= viscosity coefficient (or internal friction)
A=contact surface area between 2 laminae
^v= speed difference between the 2 laminae
r= radius of the lamina
66
How are temperature and viscosity proportional?
Inversely (the higher the temp the less viscosity)
67
Can Bernoulli's theorem be applied to real fluids? why?
No because the non-conservative forces (friction) are involved. Part of the mechanical energy is transformed into thermal energy
68
How do we determine the resistance in real fluids?
R=^p/Q
Q=flowrate
69
What is hematocrit?
Percentage by volume of red blood cells in your blood
70
What does an increase in hematocrits cause? (3 things)
Increase in viscosity
Increase in resistance
Increase in heart job to push the blood towards the duct
71
How much does a 10% radius increase, increase the flowrate?
40%
72
What is the formula for Poiseuille's law?
Q=^p/R
73
What does the blood viscosity depend on?
Concentration of erythrocytes
74
What does increased viscosity of blood result in?
Increased need for motor work by the heart required to maintain the circulation
75
How can the resistance in the ducts be calculated?
Same way as electric circuits.
76
Total resistance?resistance of the single ducts
Total resistance
77
What effect does it have that the circulatory system is in parallel?
It limits the increase in resistance while giving an increase in the total area of the section (capillaries)
78
What does blood velocity depend on?
The section of the vessels
79
When do molecules have turbulent flow?
When the speed is too high, creates a presence of macroscopic vortices which mix the liquids between the axial zone and the periphery
80
Is poiseuille's law valid in turbulent flow?
No
81
Formula for critical speed from where laminar switches to turbulent regime
vc=R* (n/(roh*r))
R= Reynolds number
82
When do you use Bernoulli's equation?
When the diameter of the duct is large enough to not consider the resistance
83
When do you use turbulent flow?
At the exit of the heart resistance
84
When do we use Poiseuille's equation?
When we have to consider resistance
85
Which equation do you use when you have to consider resistance?
Poiseuille
86
Where in the blood vessels do erythrocytes tend to concentrate?
Along the axis, reduced concentration near the walls
87
What does the axial accumulation of red blood cells cause?
Less friction/decrease in viscosity near the vessel walls
Greater friction/increase in viscosity near the axis
88
What is the sigma (Fahraeus-Linqvist) effect?
When radius of the vessel is in order of a few hundred micrometers the blood motion cannot be described as laminar motion
The relative viscosity the lower and therefor poiseuilles law is no longer valid
89
Where does the maximum pressure drop occur in the vessels?
At level of the arterioles
90
What is vasocontranction and vasodilation and what does it allow for?
Contractions in the arterial walls
Allow a change in flowrate, implying a notable increase or decrease in cardiac effort
91
What are the 4 phases in heart rate?
Filling of the ventricle
Constant volume contraction
Ejection of blood
Contraction of ventricle ceases
92
Formula to calculate the work of the heart
W=pv*^V
pv= mean ventricular pressure
93
How is the mean ventricular pressure determined experimentally?
Measuring the pressure at the level of the aorta and applying the theorem of Bernoulli
94
How does the work done by the right ventricle in each heartbeat compare to that of the left?
It is only about 1/5
95
What is the total work done by the heart for each beat roughly?
1 Joule
96
What is the measure of blood pressure relative to?
The atmospheric pressure
It is the difference between the outside and inside pressure
97
What is the maximum pressure of the heart?
Systolic pressure
98
What is the minimum pressure of the heart?
Diastolic pressure
99
What are cohesion forces?
Attraction forces between equal molecules
Present in all bodies
100
What are adhesion forces?
Attraction forces between different molecular species
101
What are the cohesive forces in solids?
Strong, they prevent solids from moving, giving them their own volume and shape
102
What are the cohesive forces in gasses?
Weak, molecules are free to move with uniform motion until they collide with other molecules, have neither shape nor volume
103
What are the cohesive forces in liquids?
Not strong enough to prevent motion but stronger than in gasses. They have the liquid take the shape of the container
104
What is the resultant of all cohesive forces equal to when the molecule is totally immersed in the liquid?
0, cohesion forces are all in the same direction
105
What happens when molecules are located near the surface of liquid?
They interact with both he underlying liquid molecules and overlying vapour molecules (but liquid molecules are stronger)
106
What are surface molecules?
Molecules that are less than the radius of action away from the surface of the liquid
107
What has to be done to bring a molecule to the surface that is inside the liquid?
Work against the cohesion forces
108
Which molecules have greater potential energy?
Surface molecules
109
Which form do liquids tend to take?
The form that minimises the free surface
110
Surface tension coefficient=?
^W/^S=F/2l
l= length of the edge of the free surface
111
What happens to surface tension when temperatures increase?
They decrease
112
What 2 things does the surface tension depend on?
The homogeneity of the liquid
The nature of the contact medium (liquid, solid or gas)
113
2 things about the forces of surface tension
Tends to contract the surface of the liquid
Is tangental to the surface and perpendicular to the edge
114
What molecules increases the surface tension?
Mineral salts
115
What molecules decreases the surface tension?
Organic solutes
116
What do surfactants (fatty acids, proteins, alcohols) do to the surface tension?
Significantly lower the surface tension
117
What are cationic surfactants?
Surfactants with the polar group positively charged
118
What are anionic surfactants?
Surfactants with the polar group negatively charged
119
What are non-ionic surfactants?
Surfactants with the polar group with no net polar charge
120
What does Laplace's law state?
That there is a positive pressure inside a spherical drop due to surface tension
121
What can gas bubbles in vessels lead to?
Gas embolies, arrested circulation
122
What is velocity in laminar flow?
Parabolic
Thus average velocity= 1/2Vmax
123
What kind of flow when Reynolds number <500?
Laminar
124
What kind of flow when Reynolds number is between 500 and 1999?
It is transitioning
125
What kind of flow when Reynolds number >2000?
Turbulent
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