Flow through tubes Flashcards
Define Pressure (P)
Force exerted per unit area
Define Pressure gradient (∆P)
The difference in forces exerted (per unit area) at either end/side of an object eg. a tube or membrane
Define Flow (Q)
The volume of fluid passing a given level of the circulation/airways per unit time - usually measured in ml/s or l/min
Define Velocity (v)
The rate of movement of fluid particles along a vessel/airway - measured in cm/s
Define Resistance (R)
A force that tends to oppose the flow of a substance
Do the pressures and resistance tend to be lower or higher in the pulmonary circulation?
Lower pressures, lower resistance
Do the pressures and resistance tend to be lower or higher in the systemic circulation?
Higher pressures, high resistance
Why is the pressure drop different in different parts of the circulation?
Reflects differences in resistance to flow
What is the relationship between pressure and flow?
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
What is the relationship between flow and resistance to flow?
For a given pressure gradient, the flow is determined by the resistance (R) of the vessel / airway
What is the equation between pressure gradient, flow and resistance
Pressure gradient = flow x resistance
∆P = QR
What does the resistance of a vessel/airway depend on?
The resistance of a vessel/airway depends on its radius
A narrower tube will have higher resistance
What is the clinical application of the pressure gradient equation?
Pressure gradient = flow x resistance
Mean arterial pressure = cardiac output x systemic vascular resistance (total peripheral resistance)
MAP = CO x SVR
What is the relationship between flow, velocity and cross-sectional area in connected tubes?
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
What is the equation between velocity, flow and cross-sectional area when the flow is constant
At a given flow…
v=Q/A
Describe laminar flow
- 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.
When the pressure gradient is constant, what is the relationship between radius and mean velocity?
At a constant pressure gradient - mean velocity is proportional to r^2.
So if the radius decreases, velocity will decrease.
What factors determine resistance in a tube?
The resistance of a vessel depends on its radius, its length and the viscosity of the fluid
Resistance = 8nl/π(r^4)
What is Poiseulle’s law?
Q = ∆Pπ(r^4)/8nl
Therefore flow is directly proportional to the fourth power of the radius of the tube!!
Describe turbulent flow
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.
When is turbulent flow more likely?
- Velocity is high (e.g. secondary to a narrowed tube)
- Viscosity is low – less adhesions between the layers of flow
- Tube diameter is high
What are some causes of turbulent flow in the airways?
- Where airways branch
- Where velocity increases due to airways becoming narrower, e.g. bronchospasm in asthma
- When ventilation increases
What are some causes of turbulent flow in the blood vessels?
- 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
What is the effect of branching on resistance?
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
How do you combine resistances in series vs. resistances in parallel?
For vessels/airways in series, resistances add.
For vessels/airways in parallel, the overall resistance is reduced. r = r1.r2/(r1 + r2)
How do you calculate transmural pressure?
Transmural pressure = P(intravascular) - P(extravascular)
If transmural pressure is positive, the vessel will distend.
How does the distensibility of tubes affect the relationship between flow and pressure?
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.
What is capacitance?
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.
