Question

Poiseuille's Law states that the volume, V, of blood flowing through an artery in a unit of time at a fixed pressure is directly proportional to the fourth power of the radius of the artery. That is, V=kr4, where r is the radius of the artery y about how much must the radius of the artery be increased to achieve a 55 % increase in the volume of blood flowing through the artery?

Answer 1

Answer:

11.58%

Step-by-step explanation:

The initial volume if blood flowing through the artery is given by

$V=kr^4$

To achieve a new volume of 155% (55% increase) of the initial volume, the new radius must be:

$V'= 1.55V\\1.55V=k(r')^4\\1.55kr^4 = k(r')^4\\(\sqrt[4]{1.55}*r)^4=(r')^4 \\(1.1158*r)^4=(r')^4 \\r'=1.1158*r$

Since the new radius is 1.1158 times larger than the initial radius, the percentage increased is:

$I=(1.1158 - 1)*100\%\\I= 11.58\%$