When blood flows along a blood vessel, the volume of blood flowing past a given

Question

When blood flows along a blood vessel, the volume of blood flowing past a given point per unit time (the flux) is proportional to the fourth power of the radius R of the blood vessel, that is F = kR4 , for a constant k depending on the blood pressure, length of the vessel, and blood viscosity. This relationship is called Poiseuille’s Law. An angioplasty can expand a partially clogged artery widening it near the blockage. If an angioplasty increases the radius of a blood vessel by 5%, what will be the approximate relative increase (as a percentage) in blood flow?

Explanation / Answer

f = k*R^4

Increases the radius by 5%

So, R becomes 1.05R

So,
f = kR^4

And f' = k(1.05R)^4 = 1.21550625kR^4

The relative change is :
(f' - f)/f * 100

(1.21550625kR^4 - kR^4) / (kR^4) * 100

21.550625 % ----> ANS

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