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)