15. BASIC PHYSICS OF PRESSURE AND FLOW IN FLUIDS

Question 1

1. What is the Law of Laplace?

Answer 1

• 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

Question 2

2. In a Cylindrical Vessel, what simple relation exists?

Answer 2

• the relation between pressure
• and the circumferential wall stress

Question 3

3. What does the Law of Laplace only hold for?

Answer 3

• 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

Question 4

4. In which field is the Law of Laplace most often used?

Answer 4

• in Hemodynamics

Question 5

5. What information does the Law of Laplace give us, with regards to Hemodynamics?

Answer 5

• 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

Question 6

6. How do we mathematically write the Law of Laplace?

Answer 6

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

Question 7

7. What is the only Limitation of Laplace’s Law?

Answer 7

• it gives the average wall stress
• it cannot give any information on the stress distribution across the wall

Question 8

8. What bodily functions does the Law of Laplace help us understand?

Answer 8

• Cardiac Function
• Vascular Function
• this law is of great conceptual importance

Question 9

9. What is the main determinant of Wall Stress in the heart?

Answer 9

• 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

Question 10

10. How do the Cardiac Muscle cells increase in thickness during Hypertension?

Answer 10

• it builds more contractile proteins in parallel
• this leads to a concentric hypertrophy

Question 11

11. What do thicker Cardiac Muscle cells result in?

Answer 11

• a thicker wall
• this causes the systolic wall stress to return to normal levels
• EVEN if there is a higher pressure in the systole

Question 12

12. What is the Equation of Continuity?

Answer 12

• it is a statement of the conservation of mass during flow
• mass cannot be lost without some kind of disruption

Question 13

13. When is the Product constant?

PRODUCT = p x A x v
p = density
A= area
v= speed

Answer 13

• When a fluid of given density (p)
• moves with an average speed (v)
• in a tube with a cross-sectional area (A)

Question 14

14. What do the symbols A x v represent?

Answer 14

• the volume flow per unit time
• (m³ / s)
• Av can also be found as Q

Question 15

15. What do the symbols pAv represent?

Answer 15

• mass per unit time
• kg/m³ x m³/s = kg/s

Question 16

16. What can be said about mass and volume when the substance is in a stable state?

Answer 16

• the same mass flows into a volume
• the same mass leaves the volume

Question 17

17. LOOKING AT THIS IMAGE:
    
    • Suppose that an incompressible fluid fills this pipe
    • this fluid flows through the pipe

What can be inferred?

Answer 17

• 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

Question 18

18. Looking at this image, how would we mathematically describe the continuity of the incompressible fluid?

Answer 18

• 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

Question 19

19. What can be said abut a gas that is moving at a low speed?

Answer 19

• the density of the gas remains the same at different positions throughout the container that the gas is found in

Question 20

20. What does Bernoulli’s Equation relate?

Answer 20

• it relates blood pressure (P)
• AND blood flow velocity (v)

Question 21

21. What can the Bernoulli Equation be viewed as?

Answer 21

• an Energy Law
• it expresses the conservation of energy in the flowing blood

Question 22

22. What does Bernoulli’s equation state when pressure is lost due to friction?
    OR when turbulence is neglected

Answer 22

• 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

Question 23

23. How can we describe Bernoulli’s Equation mathematically?

Answer 23

P + ½p.v² + p.g.h = CONSTANT

• P = pressure energy (flow energy)
• ½p.v² = kinetic energy
• p.g.h = potential energy

Question 24

24. With regards to total energy, what can be said about an organ filled with blood?

Answer 24

• the total energy is constant

Question 25

25. Why can the term p.g.h (Potential energy) be ignored when it comes to a blood vessel in the Supine Human?

Answer 25

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

Question 26

26. What does Bernoulli's equation predict with regards to pressure in blood vessels?

Answer 26

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

Question 27

27. What does Bernoulli's Law tell us with regards to fluid particles?

Answer 27

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

Question 28

28. With regards to Bernoulli's Equation, what can be said about the energy per unit volume for any two points?

Answer 28

Question 29

29. In the Supine Human, how can we work out pressure differences using Bernoulli's Equation?

Answer 29

Question 30

30. How is Bernoulli's Equation Clinically applied?

Answer 30

- 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

Question 31

31. What is the result of stenosis by plaque deposits?

Answer 31

- 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

Question 32

32. What happens to the blood flow when the artery is narrowed?

Answer 32

- 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

Question 33

33. What is the result of the arterial wall becoming less elastic?

Answer 33

- the wall's vibrational characteristics will change - this can lead to resonant vibrations - these will dislodge the plaque deposits

Question 34

34. What is an aneurysm?

Answer 34

- it is a localised bulge in the artery - it is ballon like

Question 35

35. What happens when the radius of the Aneurysm increases?

Answer 35

- 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

Question 36

36. What does Poiseuille's Law describe?

Answer 36

- the relation between: - the pressure drop (▵P) - the fluid flow (Q) - this is all measured under steady conditions

Question 37

37. 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

Answer 37

- each fluid layer will stay at the same constant distance from the centre - the velocity profile (v.r) is parabolic

Question 38

38. What are three factors that flow is strongly dependent on?

Answer 38

1. the radius of the tube (this is known as the fourth power) 2. the pressure drop over the tube length (▵P / l) 3. the viscosity of the fluid (η)

Question 39

39. What is the formula that describes the velocity (v) as a function of the radius (r)?

Answer 39

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

Question 40

40. How is Blood Flow (Q) worked out?

Answer 40

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

Question 41

41. How would we work out the Volume Flow Rate?

Answer 41

- velocity x surface area - v x (P . r² / 4)

Question 42

42. What are the three major assumptions for Poiseuille's Law to hold?

Answer 42

1. the tube is stiff . it is straight . it is uniform 2. the fluid is Newtonian . meaning that the viscosity is constant 3. the flow is laminar . it is steady . it it not pulsatile (strong regular rhythm) . the velocity at the wall is zero

Question 43

43. What is a more general form of Poiseuille's Law?

Answer 43

- Q = ▵P / R - R = resistance

Question 44

44. How is R (Resistance) calculated?

Answer 44

R = Resistance η = viscosity of fluid l = length of the tube/vessel π = pi ri = initial radius

Question 45

45. What is this law used in analogy with?

Answer 45

- 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

Question 46

46. Read through Summary 1. Does everything make sense?

Answer 46

- yes

Question 47

47. Read through Summary 2. Does everything make sense?

Answer 47

- yes

Question 48

48. Read through Summary 3. Does everything make sense?

Answer 48

- yes

Question 49

49. Read through Summary 4. Does everything make sense?

Answer 49

- yes

Question 50

50. Read through Summary 5. Does everything make sense?

Answer 50

- yes