### Video Transcript

Angioplasty is a technique in which
arteries partially blocked with plaque are dilated to increase blood flow. By what factor must the radius of
an artery be increased to increase blood flow by a factor of 7.0?

In this situation, if we imagine
that the artery initially has a radius π sub one and after the operation has a
radius π sub two, then we want to figure out what is π two divided by π one. We can recall that, for a liquid,
the flow rate of that liquid equals the cross-sectional area of the tube or pipe it
passes through multiplied by the speed of the liquid. In this scenario, we can assume
that the speed of the blood flow in the original artery is the same as the blood
flow speed in the extended artery. This means we can write that π΄
two, the cross-sectional area of the dilated artery, times π£ is equal to 7.0 times
π΄ one times π£. The fluid flow speed π£ cancels
out. And if we assume that the artery
has a circular cross section, we can write that π times π two squared is equal to
7.0 times π times π one squared. We see the factors of π cancel
out.

If we divide both sides by π one
squared and take the square root of both sides, we see that π two over π one
equals the square root of 7.0, or to two significant figures 2.6. Thatβs the factor by which the
artery radius must be dilated in order to increase the flow rate by a factor of 7.0.