Physics $131$

Written Homework Problems: Week $13$

Problem $1$: Atherosclerosis

Atherosclerosis

Donald's aorta is $8$ cm long and, in the absence of any plaque buildup, has a radius of $1$ cm $.$ The viscosity of blood is $10$mPa$*s.$

A$.$ The pressure drop across the artery with no plaque buildup is $20$ Pa $.$ What is the flow rate of blood through the artery?

B$.$ As a result of plaque buildup, the radius of the artery is reduced to $25\%$ of its original value $(0\mathrm{.}25cm).$ What is the new flow through the artery with the constriction, assuming the same pressure drop as before the plaque clog?

C$.$ What would the new pressure drop across this section of artery need to be to bring the flow rate back to the original level? Give your answer in mmHg $.$

Donald's blood pressure before the plaque buildup was a healthy $110$ mmHg $.$ The contribution of the artery to the blood pressure before the plaque buildup was a negligible $20Pa=0\mathrm{.}15mmHg.$ After the plaque buildup, the artery adds the amount computed in part C to Donald's blood pressure, brining him up to Stage $1$ hypertension! Note: Prehypertension is above $120$ mmHg $,$ hypertension stage $1$ is above $140$ mmHg $,$ stage $2$ is $160mmHg+,$ and $180+$ is hypertensive crisis.