Flow Rate & Bernoulli: Solving Artery Blockage

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SUMMARY

The discussion focuses on calculating the reduction in the radius of an artery due to a blood clot, given that the flow rate has decreased to 10% of its normal value and the pressure difference has increased by 20%. The relevant equation mentioned is D=sqrt(4Q/πv), where D is the diameter, Q is the volumetric flow rate, and v is the velocity. Participants suggest combining this equation with Bernoulli's equation to derive the factor by which the radius has been reduced.

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  • Understanding of Bernoulli's equation
  • Knowledge of fluid dynamics principles
  • Familiarity with volumetric flow rate calculations
  • Basic algebra and manipulation of equations
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Medical students, biomedical engineers, and anyone involved in cardiovascular research or fluid dynamics will benefit from this discussion.

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Homework Statement



When physicians diagnose arterial blockages, they quote the reduction in flow rate. If the flow rate in the artery has been reduced to 10% of its normal value by a blood clot and the average pressure difference has increased by 20% by what factor has the clot reduced the radius of the artery.

Homework Equations





The Attempt at a Solution


Totally lost on how to start this one, I kind of think that the following equation has something to do with it, bu not sure

D=sqrt(4Q/piv) where v= velocity Q = volumetric flow rate
 
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slksrkhrr said:
When physicians diagnose arterial blockages, they quote the reduction in flow rate. If the flow rate in the artery has been reduced to 10% of its normal value by a blood clot and the average pressure difference has increased by 20% by what factor has the clot reduced the radius of the artery.
…
D=sqrt(4Q/piv) where v= velocity Q = volumetric flow rate

ok, now combine that with Bernoulli's equation …

what do you get? :smile:
 

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