$(35$ POINTS$)$ CH$.13$ You are a medical proressional attemping to expiore the proviem of blood pressure drops in diseased, narrowed arteries. The arteries have approximately circular cross$-$section.

In a section of an artery, the diameter $d_1$ is $0\mathrm{.}00540$ m and the speed $v_1$ of the blood is $0\mathrm{.}493\frac{m}{s}.$ The section narrows into another segment of artery with diameter $d_2=0\mathrm{.}00250$ m $.$ The height relative to the laboratory floor changes as you see. $.)$ The density of this particular blood is $1\mathrm{.}060{10}^{3}k\frac{g}{m^3}.$ NOTE: The diagram below shows dimensions and arrows qualitatively and may not be exactly at scale.

$($a$)(4$ points$)$ What is the circular cross$-$sectional area $A_1$ of the first section of artery?

$($b$)(4$ points$)$ What is the circular cross$-$sectional area $A_2$ of the second section?

$($c$)(10$ points$)$ What is the speed $v_2$ in the narrow section of artery?

$($d$)(14$ points$)$ What is the pressure difference $P_1-P_2$ between the two sections?

$($e$)(3$ points$)$ Short answer in sentence form or math form; just clearly explain your work: It was mentioned in class a drop in pressure could lead to the collapse of the narrow section of artery. Explain. What would be one major consequence of such a collapse?