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Fluid mechanics Flashcards

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1
Q

What are ideal fluids

A

Incompressible
Free of internal friction (not viscous)

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1
Q

What does Bernoulli’s theorem apply to?

A

Ideal fluids in stationary and irrotational motion

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2
Q

When is the flow rate constant?

A

When the fluid is incompressible and the glass of the conduit are rigid

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3
Q

What is stationary motion?

A

The speed at the level of a section which is constant in all points of a section

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4
Q

What is irrotational motion?

A

Free of vortexes
No sharp-angled elbows and abrupt section changes in the duct

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5
Q

Is internal friction negligible in real liquid?

A

No they aren’t, they are present and not negligible

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6
Q

Are real liquids smooth?

A

No, they display a degree of viscosity

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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

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8
Q

What do fluids consist of?

A

Liquids and gases

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9
Q

What are fluids?

A

Continuous and deformable bodies with uniform density

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10
Q

Are liquids compressible?

A

No not very

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11
Q

Where are forces between molecules higher, liquids or gas?

A

Liquids

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12
Q

Formula for pressure

A

p=F/S

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13
Q

Unit for pressure

A

N/m^2

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14
Q

What is the flowrate?

A

Volume of a fluid that passes through a section of the duct in the unit of time

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15
Q

What is the flowrate measured in?

A

m^3/s

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16
Q

Formula for flowrate

A

Q=V/t=S*v

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17
Q

2 types of fluid

A

Ideal fluids
Real fluids

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18
Q

What are real fluids?

A

Forces with frictional forces present (viscous)

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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

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20
Q

What is Leonardo’s law?

A

S1v1=S2v2

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21
Q

What is the velocity along the walls in laminar flow?

A

0

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22
Q

What is the velocity along the axis in laminar flow?

A

Maximum

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23
Q

What does the equation for flowrate in real liquids look like?

A

Q=Svm
vm= average velocity (1/2vmax)

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24
Q

What happens to the molecules in a fluid at rest?

A

They are in constant motion

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25
Q

What does Pascal’s principle state?

A

A pressure exerted in one point of an incompressible fluid is transmitted unaltered to every point of the liquid

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26
Q

What does the pressure inside a fluid depend on?

A

The distance from the surface
The pressure at the bottom will be higher

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27
Q

What does Stevin’s law state?

A

p=rohhg+p0
p=pressure

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28
Q

Fw=?

A

mg=rohVg=rohShg

Fw= force weight

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29
Q

Density of water

A

1*10^3 kg/m^3

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30
Q

What does Archimedes’ principle state?

A

A body immersed in a fluid is subjected to an upward force of an intensity equal to the weight of the displaced fluid volume

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31
Q

What is the thrust of Archimedes?

A

Upward force exerted by the surface doesn’t depend on what occupies the volume (body or liquid)

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32
Q

Formula for force acting on a immersed body according to archimedes principle

A

Farch=^ps=Vg*roh(liq)

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33
Q

What does whether a body floats or sinks depend on?

A

Density

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34
Q

Farch?Fw
roh(bod)?roh(liq)
When body floats

A

Farch>Fw
roh(bod)<roh(liq)

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35
Q

Farch?Fw
roh(bod)?roh(liq)
When body stays in the middle

A

Farch=Fw
roh(bod)=roh(liq)

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36
Q

Farch?Fw
roh(bod)?roh(liq)
When body sinks

A

Farch<Fw
roh(bod)>roh(liq)

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37
Q

What does if a body rotates or not depend on?

A

The centre of thrust and center of gravity

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38
Q

What does Bernoulli’s theorem represent?

A

The extension to fluid of the principle of conservation of energy

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39
Q

What does Bernoulli’s theorem allow us to interpret?

A

Important aspects of blood circulation in large blood vessels

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40
Q

When does Bernoulli’s theorem apply?

A

In stationary and irrotational motion

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41
Q

What is stationary motion?

A

Speed at the level of a section is constant in all the points of the section

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42
Q

What is irrotational motion free of?

A

Vortexes

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43
Q

What are the two forces acting on a liquid during motion?

A

Force of gravity
Pressure forces
If fluid I real then friction, if fluid is ideal then no friction

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44
Q

What is the work done by the forces acting on the masses of fluid equal to?

A

The change of kinetic energy (kinetic energy theorem)

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45
Q

Is the mass in ideal fluids variable?

A

No because they are incompressible

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46
Q

What is Bernoullis’ equation?

A

Constan=h+p/(roh*g)+v^2/(2g)

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47
Q

Wtot=^Ec
Bernoullis’

A

h1+p1/(rohg)+v1^2/2g=h2+p2/(rohg)+v2^2/2g

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48
Q

What is stenosis?

A

When vessels shrinks

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49
Q

What is an aneurysm?

A

When vessels increase

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50
Q

When considering Leonardo’s law what happens during stenosis?

A

Velocity is greater and the surface smaller than normal

51
Q

When considering Leonardo’s law what happens during aneurysm?

A

Velocity is smaller and the surface greater than normal

52
Q

What happens in Bernoulli’s theorem during stenosis?

A

Pressure decreases and volume goes up

53
Q

What happens in Bernoulli’s theorem during aneurysm?

A

Pressure increases and volume goes down

54
Q

Formula for Stevino’s law

A

p2=p1+rohhg

55
Q

When does Stevino’s law apply?

A

When fluid is at rest in a container

56
Q

Formula for Torricelli’s theorem

A

h1=v2^2/2g
v2=sqrt 2gh1

57
Q

Where does friction intervene in real liquids?

A

Between the molecules during their flow and the contact between molecules and the walls

58
Q

What isn’t valid in non-conservative forces?

A

Kinetic energy theorem
Bernoulli’s theorem

59
Q

2 types of flow

A

Laminar
Turbulent

60
Q

What is laminar flow?

A

Flow where speed vectors are parallel to each other

61
Q

What is turbulent flow?

A

Flow where speed vectors are irregular

62
Q

What does the maximum speed correspond with in laminar flow?

A

The axis of the duct

63
Q

What does the slowest speed correspond with in laminar flow?

A

The velocity of the molecules in direct contact with the walls

64
Q

Flow rate definition in laminar flow

A

Q=Svm= S0.5*vmax

65
Q

Formula for frictional forces in laminar flow

A

Fa=nA ^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
Q

How are temperature and viscosity proportional?

A

Inversely (the higher the temp the less viscosity)

67
Q

Can Bernoulli’s theorem be applied to real fluids? why?

A

No because the non-conservative forces (friction) are involved. Part of the mechanical energy is transformed into thermal energy

68
Q

How do we determine the resistance in real fluids?

A

R=^p/Q

Q=flowrate

69
Q

What is hematocrit?

A

Percentage by volume of red blood cells in your blood

70
Q

What does an increase in hematocrits cause? (3 things)

A

Increase in viscosity
Increase in resistance
Increase in heart job to push the blood towards the duct

71
Q

How much does a 10% radius increase, increase the flowrate?

A

40%

72
Q

What is the formula for Poiseuille’s law?

A

Q=^p/R

73
Q

What does the blood viscosity depend on?

A

Concentration of erythrocytes

74
Q

What does increased viscosity of blood result in?

A

Increased need for motor work by the heart required to maintain the circulation

75
Q

How can the resistance in the ducts be calculated?

A

Same way as electric circuits.

76
Q

Total resistance?resistance of the single ducts

A

Total resistance<resistance of the single ducts

77
Q

What effect does it have that the circulatory system is in parallel?

A

It limits the increase in resistance while giving an increase in the total area of the section (capillaries)

78
Q

What does blood velocity depend on?

A

The section of the vessels

79
Q

When do molecules have turbulent flow?

A

When the speed is too high, creates a presence of macroscopic vortices which mix the liquids between the axial zone and the periphery

80
Q

Is poiseuille’s law valid in turbulent flow?

A

No

81
Q

Formula for critical speed from where laminar switches to turbulent regime

A

vc=R* (n/(roh*r))

R= Reynolds number

82
Q

When do you use Bernoulli’s equation?

A

When the diameter of the duct is large enough to not consider the resistance

83
Q

When do you use turbulent flow?

A

At the exit of the heart resistance

84
Q

When do we use Poiseuille’s equation?

A

When we have to consider resistance

85
Q

Which equation do you use when you have to consider resistance?

A

Poiseuille

86
Q

Where in the blood vessels do erythrocytes tend to concentrate?

A

Along the axis, reduced concentration near the walls

87
Q

What does the axial accumulation of red blood cells cause?

A

Less friction/decrease in viscosity near the vessel walls
Greater friction/increase in viscosity near the axis

88
Q

What is the sigma (Fahraeus-Linqvist) effect?

A

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
Q

Where does the maximum pressure drop occur in the vessels?

A

At level of the arterioles

90
Q

What is vasocontranction and vasodilation and what does it allow for?

A

Contractions in the arterial walls
Allow a change in flowrate, implying a notable increase or decrease in cardiac effort

91
Q

What are the 4 phases in heart rate?

A

Filling of the ventricle
Constant volume contraction
Ejection of blood
Contraction of ventricle ceases

92
Q

Formula to calculate the work of the heart

A

W=pv*^V

pv= mean ventricular pressure

93
Q

How is the mean ventricular pressure determined experimentally?

A

Measuring the pressure at the level of the aorta and applying the theorem of Bernoulli

94
Q

How does the work done by the right ventricle in each heartbeat compare to that of the left?

A

It is only about 1/5

95
Q

What is the total work done by the heart for each beat roughly?

A

1 Joule

96
Q

What is the measure of blood pressure relative to?

A

The atmospheric pressure
It is the difference between the outside and inside pressure

97
Q

What is the maximum pressure of the heart?

A

Systolic pressure

98
Q

What is the minimum pressure of the heart?

A

Diastolic pressure

99
Q

What are cohesion forces?

A

Attraction forces between equal molecules
Present in all bodies

100
Q

What are adhesion forces?

A

Attraction forces between different molecular species

101
Q

What are the cohesive forces in solids?

A

Strong, they prevent solids from moving, giving them their own volume and shape

102
Q

What are the cohesive forces in gasses?

A

Weak, molecules are free to move with uniform motion until they collide with other molecules, have neither shape nor volume

103
Q

What are the cohesive forces in liquids?

A

Not strong enough to prevent motion but stronger than in gasses. They have the liquid take the shape of the container

104
Q

What is the resultant of all cohesive forces equal to when the molecule is totally immersed in the liquid?

A

0, cohesion forces are all in the same direction

105
Q

What happens when molecules are located near the surface of liquid?

A

They interact with both he underlying liquid molecules and overlying vapour molecules (but liquid molecules are stronger)

106
Q

What are surface molecules?

A

Molecules that are less than the radius of action away from the surface of the liquid

107
Q

What has to be done to bring a molecule to the surface that is inside the liquid?

A

Work against the cohesion forces

108
Q

Which molecules have greater potential energy?

A

Surface molecules

109
Q

Which form do liquids tend to take?

A

The form that minimises the free surface

110
Q

Surface tension coefficient=?

A

^W/^S=F/2l

l= length of the edge of the free surface

111
Q

What happens to surface tension when temperatures increase?

A

They decrease

112
Q

What 2 things does the surface tension depend on?

A

The homogeneity of the liquid
The nature of the contact medium (liquid, solid or gas)

113
Q

2 things about the forces of surface tension

A

Tends to contract the surface of the liquid
Is tangental to the surface and perpendicular to the edge

114
Q

What molecules increases the surface tension?

A

Mineral salts

115
Q

What molecules decreases the surface tension?

A

Organic solutes

116
Q

What do surfactants (fatty acids, proteins, alcohols) do to the surface tension?

A

Significantly lower the surface tension

117
Q

What are cationic surfactants?

A

Surfactants with the polar group positively charged

118
Q

What are anionic surfactants?

A

Surfactants with the polar group negatively charged

119
Q

What are non-ionic surfactants?

A

Surfactants with the polar group with no net polar charge

120
Q

What does Laplace’s law state?

A

That there is a positive pressure inside a spherical drop due to surface tension

121
Q

What can gas bubbles in vessels lead to?

A

Gas embolies, arrested circulation

122
Q

What is velocity in laminar flow?

A

Parabolic
Thus average velocity= 1/2Vmax

123
Q

What kind of flow when Reynolds number <500?

A

Laminar

124
Q

What kind of flow when Reynolds number is between 500 and 1999?

A

It is transitioning

125
Q

What kind of flow when Reynolds number >2000?

A

Turbulent

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