When blood flows along a blood vessel, the flux f (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius r of the blood vessel:
f=kr4(this is known as poiseuille’s law; ) a partially clogged artery can be expanded by an operation called angioplasty, in which a balloon-tipped catheter is inflated inside the artery in order to widen it and restore the normal blood flow. show that the relative change in f is about four times the relative change in r. how will a 5% increase in the radius affect the flow of blood?

So a 5% relative increase in R would mean a 20% relative increase in F

Step-by-step explanation:

First we need to remind the definition of relative increase of a variable.

For a variable A its relative increase is given by .

Using this, the relative increase in F is and similarly the relative increase in R is given by .

Let's then start by deriving F with respect to R:

thus

.

If we plug the value 5% in we get

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x=half

step-by-step explanation: