Problem

The average radius of a carotid artery is $0\mathrm{.}6cm.$ Plaque buildup in a patient causes the radius to reduce to $0\mathrm{.}3cm,$ which requires surgical intervention

Area of a circle $=r^2$

Poiseuille's Equation $Q=\frac{r^{4}P}{8l}$ or $P=\frac{128lQ}{D^4}$

Where, $l=$ length of artery; $=$ blood viscosity, $P=$ pressure, $Q=$ Flow rate

Resistance $(R)=$ Pressure$/$fluid flow

$Q=\frac{P}{R}$;$R=\frac{8L}{r^4}$

a$.$ What is the cross section of the healthy artery? $($Use the equations provided above, answer in $m{m}^2)$

b$.$ What is the cross section of the blocked carotid artery? $($Use the equations provided above, answer in $m{m}^2)$

c$.$ Assuming the pressure drop across the artery $($from one end to the other$)$ remains the same, calculate the ratio of the blood flow rate in the blocked artery vs$.$ the healthy artery, Qblocked $\frac{?}{Q_{\text{h}\text{e}\text{o}\text{l}\text{t}\text{h}\text{y}\text{.}In\text{o}\text{t}\text{h}\text{e}\text{r}\text{w}\text{o}\text{r}\text{d}\text{s}\text{,}\text{t}\text{h}\text{e}\text{f}\text{l}\text{o}\text{w}\text{r}\text{a}\text{t}\text{e}in\text{t}\text{h}\text{e}\text{b}\text{l}\text{o}\text{c}\text{k}\text{e}\text{d}}}$ artery is what percentage of the flow rate in the open artery?