Factors Affecting Flow Rate through Tubes

Question 1

Define Pressure (P)

Answer 1

Force exerted per unit area

Question 2

Define Pressure gradient (∆P)

Answer 2

The difference in forces exerted (per unit area) at either side of an object eg. a tube or membrane

Question 3

Define Flow (Q)

Answer 3

The volume of fluid passing a given level of the circulation/airways per unit time - usually measured in ml/s or l/min

Question 4

Define Velocity (v)

Answer 4

The rate of movement of fluid particles along a vessel/airway - measured in cm/s

Question 5

Define Resistance (R)

Answer 5

A force that tends to oppose the flow of a substance

Question 6

What happens in the pulmonary and systemic circulation?

Answer 6

Pulmonary circulation moves blood between the lungs and heart. It is under low pressures and low resistance. Oxygenated blood moves into the left atrium to the left ventricle then to the systemic circulation.

Systemic circulation moves blood between the heart and the rest of the body. It is under high pressure and high resistance. Deoxygenated blood from the body moves from the right atrium to the right ventricle which then goes to lungs to become oxygenated again.

Question 7

How much blood does each side of the heart put out?

Answer 7

5 litres of blood per minute at rest

Question 8

Why is the pressure drop different in different parts of the circulation?

Answer 8

The pressure drop reflects differences in resistance to flow. `Pressure is the highest (100mmHg) in the large arteries –> muscular arteries –> arterioles –> capillaries –> venules –> veins where the pressure is the lowest (0-8mmHg).

Question 9

Where is most of the blood stored?

Answer 9

67% stored in the veins and venules, so the cardiac output can be increased if needed.

Question 10

What is Boyle’s Law?

Answer 10

As the pressure increases, the volume of a container decreases so pressure and volume are inversely proportional.

Question 11

What is the relationship between pressure and flow?

Answer 11

Flow (Q) is generated by a pressure gradient (∆P) since flow is from a high pressure to a low pressure.

Flow is proportional to the pressure difference between the ends of vessels & airways

Other things being equal: flow is proportional to pressure gradient

Question 12

What is the relationship between flow and resistance to flow?

Answer 12

For a given pressure gradient, the flow is determined by the resistance (R) of the vessel / airway.

Pressure gradient = flow x resistance

∆P = QR

Question 13

What does the resistance of a vessel/airway depend on?

Answer 13

The resistance of a vessel/airway depends on its radius

A narrower tube will have higher resistance

Question 14

What is the clinical application of the pressure gradient equation?

Answer 14

Pressure gradient = flow x resistance

Mean arterial pressure = cardiac output x systemic vascular resistance (total peripheral resistance)
MAP = CO x SVR

CO can be increased by increasing fluids.
SVR can be increased with medications that constrict the blood vessels.

Question 15

What is the relationship between flow, velocity and cross-sectional area in connected tubes?

Answer 15

If flow is constant a change in cross-sectional area (related to radius) results in a change in velocity. They are inversely proportional, so an increase in cross-sectional area (radius) results in a decrease in velocity

V= Q/A

This means narrowing of airways reduces the CSA causing an increase in the velocity, which then leads to an increase in turbulence.

Question 16

Describe laminar flow

Answer 16

• Greater width of the tube means more layers of laminar flow can build up and so velocity increases.
• Fluid will not move with the same velocity across the width of a tube.
• Velocity is at its lowest at the edges.
• Velocity is at the highest at the centre of the tube.
• Laminar flow will mean that the width of the tube greatly affects its resistance.

Question 17

When is turbulent flow more likely?

Answer 17

• Velocity is high (e.g. secondary to a narrowed tube)
• Viscosity is low – less adhesions between the layers of flow
• Tube diameter is high

Question 18

When the pressure gradient is constant, what is the relationship between radius and mean velocity?

Answer 18

At a constant pressure gradient - mean velocity is proportional to r^2.
So if the radius decreases, velocity will decrease.

Question 19

Describe turbulent flow

Answer 19

In turbulent flow, the layers (laminae) are not flowing in parallel, they break up and the flow becomes disordered. The direction, velocity and pressure within the flow become chaotic. Fluid moves in eddies and whirls instead of parallel to the wall of the tube. Resistance to flow is increased. If flow becomes turbulent the pressure gradient required to maintain flow needs to be increased, which in turn increases turbulence.

Question 20

What causes turbulent flow to be more likely?

Answer 20

• High velocity due to a narrowed tube due to narrowed vascular segments, e.g. atherosclerotic plaques, stenotic heart valves, asthma
• Low viscosity which means there is less adhesion between layers of laminar flow, so they are more likely to be disrupted e.g. anaemia due to reduced haematocrit
• High tube diameter which makes it hard to maintain laminar flow
• Tube or large arteries branching or an irregular surface

Question 21

What can turbulent flow cause clinically?

Answer 21

In turbulent flow, the resistance to flow is increased. It can result in damage to the endothelium.

• Bruits
• Murmurs
• Wheeze
• Stridor

Question 22

What factors determine resistance in a tube?

Answer 22

The resistance of a vessel depends on its radius, its length and the viscosity of the fluid

Resistance = 8nl/π(r^4)

n- viscosity
l- length
r- radius

Resistance is inversely proportional to r^4.

Question 23

What is Poiseulle’s law?

Answer 23

Q=P/R

R=8nl/π(r^4)

Therefore, Q = ∆Pπ(r^4)/8nl

Therefore flow is directly proportional to the fourth power of the radius of the tube. If we double the radius, the flow increases by 16 times.

Question 24

How can this equation be clinically applied?

Answer 24

IV cannulas - flow rate depends on size of the cannula
Endotracheal tube - adequate diameter so sufficient flow is administered
Asthma - breathe harder and faster to increase pressure gradient to overcome increase in resistance
Cardiovascular system - heart pumps harder to overcome resistance

Question 25

Define viscosity

Answer 25

This is the extent to which fluid opposes flow - it is the internal slipperiness between fluid layers.

Question 26

How do particulates affect flow?

Answer 26

• Blood composition affects the viscosity and thus flow
• The result of laminar flow is that red cells are borne along in the most rapidly moving streams in the centre of blood vessels.
• Blood vessels can be altered by physiological and pathological conditions.
• In blood, hematocrits are the main determinant of viscosity

Question 27

What is the effect of branching on resistance?

Answer 27

Expectation is that smaller vessels/airways will have a higher resistance than large ones – for individual vessels/airways this is true.
But when many tubes arranged in parallel effective cross-sectional area is much larger, reducing overall volume
Overall resistance is relatively low in:
- Lower parts of tracheobronchial tree
- Capillaries

Question 28

How do you combine resistances in series vs. resistances in parallel?

Answer 28

For vessels/airways in series, resistances add.

For vessels/airways in parallel, the overall resistance is reduced. r = 1/(1/r1 + 1/r2)

Question 29

What are arteries and arterioles known as?

Answer 29

The resistance vessels. These tend to be in series. An increase in resistance will cause an increase the overall pressure gradient to maintain the same flow. Stroke work would need to increase, so the heart needs to work harder to create a greater pressure gradient.

Question 30

How do you calculate transmural pressure?

Answer 30

Transmural pressure = P(intravascular) - P(extravascular)

If transmural pressure is positive, the vessel will distend, especially veins.

Question 31

How does the distensibility of tubes affect the relationship between flow and pressure?

Answer 31

With a rigid tube, resistance is constant.
With a distensible tube, an increase in pressure stretches walls lowering resistance.
There is a tendency for resistance to fall with increasing pressure.
With a low intravascular pressure, the vessels may collapse and flow may cease.

Question 32

What is capacitance?

Answer 32

This distensibility of blood vessels gives them capacitance.
As vessels widen with increasing pressure, transiently more blood will flow in than out.
The distensible vessel will store blood – the more compliant, the more blood will be stored.
Veins are particularly compliant and hold ~67% of the circulating blood volume.