Fluid mechanics Flashcards
What are ideal fluids
Incompressible
Free of internal friction (not viscous)
What does Bernoulli’s theorem apply to?
Ideal fluids in stationary and irrotational motion
When is the flow rate constant?
When the fluid is incompressible and the glass of the conduit are rigid
What is stationary motion?
The speed at the level of a section which is constant in all points of a section
What is irrotational motion?
Free of vortexes
No sharp-angled elbows and abrupt section changes in the duct
Is internal friction negligible in real liquid?
No they aren’t, they are present and not negligible
Are real liquids smooth?
No, they display a degree of viscosity
Is the kinetic energy theorem valid and applicable to the motion of real liquid?
No because non-conservative forces come into play
What do fluids consist of?
Liquids and gases
What are fluids?
Continuous and deformable bodies with uniform density
Are liquids compressible?
No not very
Where are forces between molecules higher, liquids or gas?
Liquids
Formula for pressure
p=F/S
Unit for pressure
N/m^2
What is the flowrate?
Volume of a fluid that passes through a section of the duct in the unit of time
What is the flowrate measured in?
m^3/s
Formula for flowrate
Q=V/t=S*v
2 types of fluid
Ideal fluids
Real fluids
What are real fluids?
Forces with frictional forces present (viscous)
What does it mean if ideal fluids are in steady motion?
Speed is constant in every point of the action of the duct
What is Leonardo’s law?
S1v1=S2v2
What is the velocity along the walls in laminar flow?
0
What is the velocity along the axis in laminar flow?
Maximum
What does the equation for flowrate in real liquids look like?
Q=Svm
vm= average velocity (1/2vmax)
What happens to the molecules in a fluid at rest?
They are in constant motion
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
What does the pressure inside a fluid depend on?
The distance from the surface
The pressure at the bottom will be higher
What does Stevin’s law state?
p=rohhg+p0
p=pressure
Fw=?
mg=rohVg=rohShg
Fw= force weight
Density of water
1*10^3 kg/m^3
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
What is the thrust of Archimedes?
Upward force exerted by the surface doesn’t depend on what occupies the volume (body or liquid)
Formula for force acting on a immersed body according to archimedes principle
Farch=^ps=Vg*roh(liq)
What does whether a body floats or sinks depend on?
Density
Farch?Fw
roh(bod)?roh(liq)
When body floats
Farch>Fw
roh(bod)<roh(liq)
Farch?Fw
roh(bod)?roh(liq)
When body stays in the middle
Farch=Fw
roh(bod)=roh(liq)
Farch?Fw
roh(bod)?roh(liq)
When body sinks
Farch<Fw
roh(bod)>roh(liq)
What does if a body rotates or not depend on?
The centre of thrust and center of gravity
What does Bernoulli’s theorem represent?
The extension to fluid of the principle of conservation of energy
What does Bernoulli’s theorem allow us to interpret?
Important aspects of blood circulation in large blood vessels
When does Bernoulli’s theorem apply?
In stationary and irrotational motion
What is stationary motion?
Speed at the level of a section is constant in all the points of the section
What is irrotational motion free of?
Vortexes
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
What is the work done by the forces acting on the masses of fluid equal to?
The change of kinetic energy (kinetic energy theorem)
Is the mass in ideal fluids variable?
No because they are incompressible
What is Bernoullis’ equation?
Constan=h+p/(roh*g)+v^2/(2g)
Wtot=^Ec
Bernoullis’
h1+p1/(rohg)+v1^2/2g=h2+p2/(rohg)+v2^2/2g
What is stenosis?
When vessels shrinks
What is an aneurysm?
When vessels increase
When considering Leonardo’s law what happens during stenosis?
Velocity is greater and the surface smaller than normal
When considering Leonardo’s law what happens during aneurysm?
Velocity is smaller and the surface greater than normal
What happens in Bernoulli’s theorem during stenosis?
Pressure decreases and volume goes up
What happens in Bernoulli’s theorem during aneurysm?
Pressure increases and volume goes down
Formula for Stevino’s law
p2=p1+rohhg
When does Stevino’s law apply?
When fluid is at rest in a container
Formula for Torricelli’s theorem
h1=v2^2/2g
v2=sqrt 2gh1
Where does friction intervene in real liquids?
Between the molecules during their flow and the contact between molecules and the walls
What isn’t valid in non-conservative forces?
Kinetic energy theorem
Bernoulli’s theorem
2 types of flow
Laminar
Turbulent
What is laminar flow?
Flow where speed vectors are parallel to each other
What is turbulent flow?
Flow where speed vectors are irregular
What does the maximum speed correspond with in laminar flow?
The axis of the duct
What does the slowest speed correspond with in laminar flow?
The velocity of the molecules in direct contact with the walls
Flow rate definition in laminar flow
Q=Svm= S0.5*vmax
Formula for frictional forces in laminar flow
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
How are temperature and viscosity proportional?
Inversely (the higher the temp the less viscosity)
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
How do we determine the resistance in real fluids?
R=^p/Q
Q=flowrate
What is hematocrit?
Percentage by volume of red blood cells in your blood
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
How much does a 10% radius increase, increase the flowrate?
40%
What is the formula for Poiseuille’s law?
Q=^p/R
What does the blood viscosity depend on?
Concentration of erythrocytes
What does increased viscosity of blood result in?
Increased need for motor work by the heart required to maintain the circulation
How can the resistance in the ducts be calculated?
Same way as electric circuits.
Total resistance?resistance of the single ducts
Total resistance<resistance of the single ducts
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)
What does blood velocity depend on?
The section of the vessels
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
Is poiseuille’s law valid in turbulent flow?
No
Formula for critical speed from where laminar switches to turbulent regime
vc=R* (n/(roh*r))
R= Reynolds number
When do you use Bernoulli’s equation?
When the diameter of the duct is large enough to not consider the resistance
When do you use turbulent flow?
At the exit of the heart resistance
When do we use Poiseuille’s equation?
When we have to consider resistance
Which equation do you use when you have to consider resistance?
Poiseuille
Where in the blood vessels do erythrocytes tend to concentrate?
Along the axis, reduced concentration near the walls
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
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
Where does the maximum pressure drop occur in the vessels?
At level of the arterioles
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
What are the 4 phases in heart rate?
Filling of the ventricle
Constant volume contraction
Ejection of blood
Contraction of ventricle ceases
Formula to calculate the work of the heart
W=pv*^V
pv= mean ventricular pressure
How is the mean ventricular pressure determined experimentally?
Measuring the pressure at the level of the aorta and applying the theorem of Bernoulli
How does the work done by the right ventricle in each heartbeat compare to that of the left?
It is only about 1/5
What is the total work done by the heart for each beat roughly?
1 Joule
What is the measure of blood pressure relative to?
The atmospheric pressure
It is the difference between the outside and inside pressure
What is the maximum pressure of the heart?
Systolic pressure
What is the minimum pressure of the heart?
Diastolic pressure
What are cohesion forces?
Attraction forces between equal molecules
Present in all bodies
What are adhesion forces?
Attraction forces between different molecular species
What are the cohesive forces in solids?
Strong, they prevent solids from moving, giving them their own volume and shape
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
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
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
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)
What are surface molecules?
Molecules that are less than the radius of action away from the surface of the liquid
What has to be done to bring a molecule to the surface that is inside the liquid?
Work against the cohesion forces
Which molecules have greater potential energy?
Surface molecules
Which form do liquids tend to take?
The form that minimises the free surface
Surface tension coefficient=?
^W/^S=F/2l
l= length of the edge of the free surface
What happens to surface tension when temperatures increase?
They decrease
What 2 things does the surface tension depend on?
The homogeneity of the liquid
The nature of the contact medium (liquid, solid or gas)
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
What molecules increases the surface tension?
Mineral salts
What molecules decreases the surface tension?
Organic solutes
What do surfactants (fatty acids, proteins, alcohols) do to the surface tension?
Significantly lower the surface tension
What are cationic surfactants?
Surfactants with the polar group positively charged
What are anionic surfactants?
Surfactants with the polar group negatively charged
What are non-ionic surfactants?
Surfactants with the polar group with no net polar charge
What does Laplace’s law state?
That there is a positive pressure inside a spherical drop due to surface tension
What can gas bubbles in vessels lead to?
Gas embolies, arrested circulation
What is velocity in laminar flow?
Parabolic
Thus average velocity= 1/2Vmax
What kind of flow when Reynolds number <500?
Laminar
What kind of flow when Reynolds number is between 500 and 1999?
It is transitioning
What kind of flow when Reynolds number >2000?
Turbulent
