Question

There are two carotid arteries that feed blood to the brain, one on each side of the neck and head. One patient's carotid arteries are each 11.2 cm long and have an inside diameter of 5 3 mm Near the middle of the left artery however is 2.0-cm-long stenosis, a section of the artery with a smaller diameter of 3.2 mm. For the same blood flow late, what is the ratio of the pressure drop along the patient's left carotid artery to the drop along his artery? Express your answer using two significant figures.

Answer 1

Rate flow = pressure drop / flow resistance

(Flow resistance)_left=   $\frac{8\eta(9.2x10^{-2})}{\pi(2.65x10^{-3})^4}+\frac{8\eta(2x10^{-2})}{\pi(1.6x10^{-3})^4}$

(Flow resistance)right=   $\frac{8\eta(11.2x10^{-2})}{\pi(2.65x10^{-3})^4}$

For the same flow rate

$\frac{\Delta P_{left}}{\Delta P_{right}}=\frac{ \frac{9.2}{(2.65)^4}+ \frac{2}{(1.6)^4}}{\frac{11.2}{(2.65)^4}}$

$\frac{\Delta P_{left}}{\Delta P_{right}}=2.17$