15. BASIC PHYSICS OF PRESSURE AND FLOW IN FLUIDS Flashcards
1
Q
- What is the Law of Laplace?
A
- it relates the Transmural Pressure
(this is the difference between two sides of a wall) - TO the wall stress
- this law gives the average stress over the wall
2
Q
- In a Cylindrical Vessel, what simple relation exists?
A
- the relation between pressure
- and the circumferential wall stress
3
Q
- What does the Law of Laplace only hold for?
A
- it only holds for Simple Geometries
- it applies to cylindrical and spherical geometries
- regardless of whether the material is linear or
nonlinear - regardless of whether the wall is thin or thick
4
Q
- In which field is the Law of Laplace most often used?
A
- in Hemodynamics
5
Q
- What information does the Law of Laplace give us, with regards to Hemodynamics?
A
- it gives us the relation between:
- pressure within the lumen of a vessel (▵P)
- the tension in the wall (T)
- the vessel radius (R)
LUMEN= cavity or channel within a tube or tubular organ
6
Q
- How do we mathematically write the Law of Laplace?
A
T = ▵P x R
- T = tension in the wall
(a form of stress) - ▵P = pressure within the lumen of a vessel
- R = radius of the cylinder
7
Q
- What is the only Limitation of Laplace’s Law?
A
- it gives the average wall stress
- it cannot give any information on the stress distribution across the wall
8
Q
- What bodily functions does the Law of Laplace help us understand?
A
- Cardiac Function
- Vascular Function
- this law is of great conceptual importance
9
Q
- What is the main determinant of Wall Stress in the heart?
A
- the ratio
(r/h) - the ratio at the left ventricle apex and the base of the heart is the same
- this means that there are similar wall stresses at both of these points
10
Q
- How do the Cardiac Muscle cells increase in thickness during Hypertension?
A
- it builds more contractile proteins in parallel
- this leads to a concentric hypertrophy
11
Q
- What do thicker Cardiac Muscle cells result in?
A
- a thicker wall
- this causes the systolic wall stress to return to normal levels
- EVEN if there is a higher pressure in the systole
12
Q
- What is the Equation of Continuity?
A
- it is a statement of the conservation of mass during flow
- mass cannot be lost without some kind of disruption
13
Q
- When is the Product constant?
PRODUCT = p x A x v
p = density
A= area
v= speed
A
- When a fluid of given density (p)
- moves with an average speed (v)
- in a tube with a cross-sectional area (A)
14
Q
- What do the symbols A x v represent?
A
- the volume flow per unit time
- (m³ / s)
- Av can also be found as Q
15
Q
- What do the symbols pAv represent?
A
- mass per unit time
- kg/m³ x m³/s = kg/s
16
Q
- What can be said about mass and volume when the substance is in a stable state?
A
- the same mass flows into a volume
- the same mass leaves the volume
17
Q
- LOOKING AT THIS IMAGE:
- Suppose that an incompressible fluid fills this pipe
- this fluid flows through the pipe
What can be inferred?
A
- the flow of the incompressible fluid at point A1 is equal to the flow of the incompressible fluid at point A2
- the mass flow rate is the same for point A1 and point A2
18
Q
- Looking at this image, how would we mathematically describe the continuity of the incompressible fluid?
A
- Q = A1.v1
- Q= A2.v2
THEREFORE:
A1.v1 = A2.v2
- v1 is the average fluid speed over A1
- v2 is the average fluid speed over A2
19
Q
- What can be said abut a gas that is moving at a low speed?
A
- the density of the gas remains the same at different positions throughout the container that the gas is found in
20
Q
- What does Bernoulli’s Equation relate?
A
- it relates blood pressure (P)
- AND blood flow velocity (v)
21
Q
- What can the Bernoulli Equation be viewed as?
A
- an Energy Law
- it expresses the conservation of energy in the flowing blood
22
Q
- What does Bernoulli’s equation state when pressure is lost due to friction?
OR when turbulence is neglected
A
- the sum of the fluid mechanical energy, fluid kinetic energy and fluid potential energy stay constant
- FLUID MECHANICAL ENERGY = pressure energy
- FLUID KINETIC ENERGY = ½.p.v²
- FLUID POTENTIAL ENERGY = p.g.h
23
Q
- How can we describe Bernoulli’s Equation mathematically?
A
P + ½p.v² + p.g.h = CONSTANT
- P = pressure energy (flow energy)
- ½p.v² = kinetic energy
- p.g.h = potential energy
24
Q
- With regards to total energy, what can be said about an organ filled with blood?
A
- the total energy is constant
25
Q
- Why can the term p.g.h (Potential energy) be ignored when it comes to a blood vessel in the Supine Human?
A
WHEN VELOCITY IS VERY HIGH:
- the pressure is low
- this is because we have to incorporate the effects of
friction and the change in the size of the vessels
- this will make the flow of the blood turbulent
26
Q
- What does Bernoulli’s equation predict with regards to pressure in blood vessels?
A
ACCORDING TO BERNOULLI:
- after the blood vessel narrows:
- the pressure is recovered completely
IN REALITY:
- pressure distal due to stenosis does not recover
completely
- this is due to energy losses by the fluid friction and by
the turbulence
STENOSIS= narrowing
DISTAL = a part of the body that is farther away from the
centre of the body than another part
27
Q
- What does Bernoulli’s Law tell us with regards to fluid particles?
A
WHEN A FLUID PARTICLE DECELERATES:
- the pressure increases
WHEN A FLUID PARTICLE ACCELERATES:
(such as with severe stenosis)
- the pressure drops
- the flow of blood is more turbulent
28
Q
- With regards to Bernoulli’s Equation, what can be said about the energy per unit volume for any two points?
A
29
Q
- In the Supine Human, how can we work out pressure differences using Bernoulli’s Equation?
A
30
Q
- How is Bernoulli’s Equation Clinically applied?
A
- it is used for estimating the severity of aortic valve stenosis
- it is used for estimating the severity of mitral valve stenosis
- it is used for estimating the severity of arterial stenosis and aneurysms
31
Q
- What is the result of stenosis by plaque deposits?
A
- the blood velocity must be increased
- this will result in a decrease in pressure
- this will lead to further narrowing of the artery
- the artery may then close entirely
32
Q
- What happens to the blood flow when the artery is narrowed?
A
- the blood flow will become more turbulent
- the blood flow could possibly damage the arterial wall
- this will damage the elasticity of the arterial wall
33
Q
- What is the result of the arterial wall becoming less elastic?
A
- the wall’s vibrational characteristics will change
- this can lead to resonant vibrations
- these will dislodge the plaque deposits
34
Q
- What is an aneurysm?
A
- it is a localised bulge in the artery
- it is ballon like
35
Q
- What happens when the radius of the Aneurysm increases?
A
- the velocity of the blood flow increases
- the pressure decreases
- the wall of the artery is weakened further
- this increases the chance of the aneurysm rupturing
36
Q
- What does Poiseuille’s Law describe?
A
- the relation between:
- the pressure drop (▵P)
- the fluid flow (Q) - this is all measured under steady conditions
37
Q
- What are the characteristics of the laminar flow of fluids through a tube/vessel?
LAMINAR= a flow that takes place along constant streamlines, without turbulence
A
- each fluid layer will stay at the same constant distance from the centre
- the velocity profile (v.r) is parabolic
38
Q
- What are three factors that flow is strongly dependent on?
A
- the radius of the tube
(this is known as the fourth power) - the pressure drop over the tube length
(▵P / l) - the viscosity of the fluid
(η)
39
Q
- What is the formula that describes the velocity (v) as a function of the radius (r)?
A
v = velocity
▵P =change in pressure
ri = initial radius
r = centre line
= usually equal to zero
= this is the maximum velocity
η = viscosity of the fluid
= fluid coefficient
l = length of the tube
40
Q
- How is Blood Flow (Q) worked out?
A
Q = blood flow
▵P = change in pressure
η = viscosity of fluid
l = length of tube
π = pi
ri = initial radius
NB: this shows how Poiseuille’s Law relates ▵P and
Q to each other
: it does this through a uniform (constant) radius
: and through a stiff blood vessel
41
Q
- How would we work out the Volume Flow Rate?
A
- velocity x surface area
- v x (P . r² / 4)
42
Q
- What are the three major assumptions for Poiseuille’s Law to hold?
A
- the tube is stiff
. it is straight
. it is uniform - the fluid is Newtonian
. meaning that the viscosity is constant - the flow is laminar
. it is steady
. it it not pulsatile (strong regular rhythm)
. the velocity at the wall is zero
43
Q
- What is a more general form of Poiseuille’s Law?
A
- Q = ▵P / R
- R = resistance
44
Q
- How is R (Resistance) calculated?
A
R = Resistance
η = viscosity of fluid
l = length of the tube/vessel
π = pi
ri = initial radius
45
Q
- What is this law used in analogy with?
A
- it is used in analogy to Ohm’s Law of electricity
- this is where the resistance is equal to:
- voltage drop / current - the voltage difference is compared to the pressure drop
- the current is compared to the volume flow
- the resistance can be calculated from pressure and flow measurements
46
Q
- Read through Summary 1.
Does everything make sense?
A
- yes
47
Q
- Read through Summary 2.
Does everything make sense?
A
- yes
48
Q
- Read through Summary 3.
Does everything make sense?
A
- yes
49
Q
- Read through Summary 4.
Does everything make sense?
A
- yes
50
Q
- Read through Summary 5.
Does everything make sense?
A
- yes
