Week 5 - Flow Through Tubes Flashcards
What drives flow through blood vessels?
A gradient of pressure
- Proportional to the pressure difference between the ends of a vessel
- So the higher the pressure difference, the greater the flow
- Determined by the resistance of the vessel
Define flow
The volume of fluid passing a given point per unit time
- Flow = mean velocity x cross-sectional area
What determines the resistance of a vessel?
- The nature of the fluid
- The vessel itself
Define velocity
The rate of movement of fluid particles along the tube
What is the relationship between flow and velocity?
- Flow must be the same at all points along a vessel
- Velocity can vary along the length if the radius of the tube changes
- At a given flow, velocity is inversely proportional to cross-sectional area
- So vessels with a small cross-sectional area have a high velocity
Describe laminar flow
- There is a gradient of velocity from the middle to the edge of the vessel
- Velocity is highest in the centre
- Fluid is stationary at the edge
- The fluid moves in concentric layers
- The middle layers move faster than the edge layers, so the fluid layers must slide over each other
- In most blood vessels, the flow is laminar
Describe turbulent flow
- As the mean velocity increases, flow becomes turbulent (e.g, if a vessel nips narrowed)
- The velocity gradient breaks down as layers of fluid try to move over each other faster than physics will allow
- The fluid tumbles over, greatly increasing flow resistance
- It generates sound
Define viscosity
The extent to which fluid layers resist sliding over each other
What is the relationship between viscosity and velocity?
- The higher the viscosity the slower the central layers will flow
- So the lower the average velocity
- Viscosity determines the slope of the gradient of velocity
- At a constant gradient, the wider the tube the faster the middle layers move, so the mean velocity is proportional to the cross-sectional area of the tube
What is the relationship between mean velocity and viscosity?
Mean velocity is inversely proportional to viscosity
What is the relationship between mean velocity and cross-sectional area?
Mean velocity is directly proportional to cross-sectional area
What is flow resistance?
Pressure = flow x resistance
- Resistances increases as viscosity increases
- It decreases with the 4th power of the radius (velocity increases as the square of radius, flow = velocity x surface area (increases as radius squared) so flow = r^2 x r^2)
- Hence a very small change in the tube’s radius makes a very big change to resistance
Describe the relationship between pressure, resistance and flow
If flow is fixed
- The higher the resistance, the greater the pressure change from 1 end of the vessel to the other
If pressure is fixed
- The higher the resistance, the lower the flow
What is the effect of combining flow resistance in series?
Resistances add together
What is the effect of combining flow resistance in parallel?
The effective resistance is lower
- As there is more than 1 path for the current to flow down
- For 2 vessels in parallel: the resistance of 1 of the vessels is half of the original, as the blood has 2 parts
How does the flow differ over the whole circulation?
It doesn’t differ: it is the same at all points
What is the resistance and hence pressure drop in arteries?
Low: so the pressure drop over arteries is small
What is the resistance and hence pressure drop in arterioles?
High: so the pressure drop over arterioles to large
What is the resistance and hence pressure drop in capillaries?
Individually they are resistance
- But there are many connected in parallel so the overall resistance is low
- The pressure drop over capillaries is small
What is the resistance and hence pressure drop in venules and veins?
Low: so pressure drop is low