A person has a 5200-N/m^2 gauge pressure of blood flowing at 0.50 m/s inside a 1

Question

A person has a 5200-N/m^2 gauge pressure of blood flowing at 0.50 m/s inside a 1.0-cm-radius main artery. The gauge pressure outside the artery is 3200 N/m^2. When using his stethoscope, a physician hears a fluttering sound farther along the artery. The sound is a sign that the artery is vibrating open and closed., which indicates that there must be a constriction in the artery that has reduced its radius and subsequently reduced the internal blood pressure to less than the external 3200 N/m^2 pressure. What is the maximum artery radius at this construction?

Explanation / Answer

The pressure is given as 5200 N/m2

outside the artery pressure is 3200 N/m2

The difference in pressure,dp= 2000N/m2

The length of the tube is given as ,l=0.01 m

viscosity of blood at 370C,u=3*10-3

Flow rate of the blood,Q=velocity*Area=0.5*1*10-4m=5*10-5 ml/s

dp=8ulQ/pi*r4

r=(8ulQ/pi*dp)1/4

r=8*5*10-5*1*3*10-3)/3.14*2000=0.0037 m

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