How is it that the flow of blood through a vessel is proportional to the radius to the 4th power?

[m25]

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How is it that the flow of blood through a vessel is proportional to the radius to the 4th power? (this is according to my TBR book) I thought it would be proportional to radius to the 3rd power because volume is proportional to radius^3.

 

[Cawolf]

Poiseuille's Law

Source: http://hyperphysics.phy-astr.gsu.edu/hbase/ppois.html

 

[m25]

Poiseuille's Law

Source: http://hyperphysics.phy-astr.gsu.edu/hbase/ppois.html

Oooh I see! Are we expected to know this equation for MCAT?

 

[Cawolf]

I don't think so - I bet it would be given.

I just know it from mechanics.

 

[azor ahai]

it's because the radius impacts Q in two ways:

1. Q is proportional to cross-sectional area or r^2
2. Q is inversely proportional to viscosity which is inversely proportional to area or r^2

so you have r^2 twice in the numerator of the poiseulle's law to give you r^4.

generally, you can use ideal flow to characterize arterial flow but for everything else with blood treat it as a real fluid.

 

[Mad Jack]

This is an important law to understand. It will continue to haunt you for years and really helps you understand hemodynamics and pulmonary physiology.

 

[azor ahai]

This is an important law to understand. It will continue to haunt you for years and really helps you understand hemodynamics and pulmonary physiology.

Your location in the 4th dimension makes your comment apropos.

 

[Mad Jack]

Your location in the 4th dimension makes your comment apropos.

Your three dimensional physical laws are like children's toys to me