Answer:
1.18
Explanation:
The flow rate of blood is proportional to the fourth power of its radius as given the Poiseuille's law.
The law is :
[tex]$Q \propto r^4$[/tex]
It is given here that the flood flow rate is been reduced to half its normal value. Therefore, [tex]$Q_1 = \frac{1}{2}Q_2$[/tex]
So, for the radius [tex]$r_1$[/tex] and [tex]$r_2$[/tex], the ratios of their flow rates are :
[tex]$\frac{Q_1}{Q_2}=\frac{r_1^4}{r_2^4}$[/tex]
It is given that the flow rate is reduced to half. So we have,
[tex]$\frac{Q_1}{2Q_1}=\frac{r_1^4}{r_2^4}$[/tex]
or [tex]$r_2=2^{1/4}{r_1}$[/tex]
[tex]$r_2=1.18 \ r_1}$[/tex]
So the radius changes by a factor of 1.18
