Blood Flow $(2pts).$ When you are resting, your heart typically pumps about $5$ L of blood through your body every minute.

$($a$)$ All of the blood pumped by your heart must go through the aorta. Your aorta has a radius of about $0\mathrm{.}9$ cm $.$ What is the speed of blood flow in your aorta? Support your answer with a derivation of the flow rate entering the aorta from the heart.

$($b$)$ Your lungs are designed with tremendous redundancy; they have far more capillaries than are actually used at any one time. $($The remaining capillaries are collapsed and do not support blood flow.$)$ Each of your $300$ million alveoli is surrounded by an estimated $1000$ tiny capillaries. Each capillary has a radius of approximately $4{10}^{-4}cm,$ and blood flows in a capillary at a speed of about $5{10}^{-4}\frac{m}{s}.$ Estimate the fraction of capillaries in your lung that are actually being used.