Flow 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 end/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

Do the pressures and resistance tend to be lower or higher in the pulmonary circulation?

Answer 6

Lower pressures, lower resistance

Question 7

Do the pressures and resistance tend to be lower or higher in the systemic circulation?

Answer 7

Higher pressures, high resistance

Question 8

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

Answer 8

Reflects differences in resistance to flow

Question 9

What is the relationship between pressure and flow?

Answer 9

Flow (Q) is generated by a pressure gradient (∆P)

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

Other things being equal: flow is proportional to pressure gradient

Question 10

What is the relationship between flow and resistance to flow?

Answer 10

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

Question 11

What is the equation between pressure gradient, flow and resistance

Answer 11

Pressure gradient = flow x resistance

∆P = QR

Question 12

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

Answer 12

The resistance of a vessel/airway depends on its radius

A narrower tube will have higher resistance

Question 13

What is the clinical application of the pressure gradient equation?

Answer 13

Pressure gradient = flow x resistance

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

MAP = CO x SVR

Question 14

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

Answer 14

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

Question 15

What is the equation between velocity, flow and cross-sectional area when the flow is constant

Answer 15

At a given flow…

v=Q/A

Question 16

Describe laminar flow

Answer 16

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

Answer 17

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

Question 18

What factors determine resistance in a tube?

Answer 18

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

Resistance = 8nl/π(r^4)

Question 19

What is Poiseulle’s law?

Answer 19

Q = ∆Pπ(r^4)/8nl

Therefore flow is directly proportional to the fourth power of the radius of the tube!!

Question 20

Describe turbulent flow

Answer 20

In turbulent flow the layers (laminae) are not flowing in parallel. 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 21

When is turbulent flow more likely?

Answer 21

• 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 22

What are some causes of turbulent flow in the airways?

Answer 22

• Where airways branch
• Where velocity increases due to airways becoming narrower, e.g. bronchospasm in asthma
• When ventilation increases

Question 23

What are some causes of turbulent flow in the blood vessels?

Answer 23

• Where large arteries branch
• Increase in velocity due to arrowed vascular segments, e.g. atherosclerotic plaques, stenotic heart valves
• Low blood viscosity, e.g. anaemia due to reduced haematocrit

Question 24

What is the effect of branching on resistance?

Answer 24

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.
Overall resistance is relatively low in:
- Lower parts of tracheobronchial tree
- Capillaries

Question 25

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

Answer 25

For vessels/airways in series, resistances add.

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

Question 26

How do you calculate transmural pressure?

Answer 26

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

If transmural pressure is positive, the vessel will distend.

Question 27

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

Answer 27

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.

Question 28

What is capacitance?

Answer 28

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.