A common medical problem in today's world is a disease of the arteries that feed our heart muscle (called "coronary arteries") that results in narrowing of the arterial diameter and reduced blood flow to the heart muscle. An interesting additional effect sometimes occurs when the lower pressure in the narrowed portion of the artery (caused by the higher velocity there) results in the collapse of the artery. If that happens, the blood flow through the artery stops, which allows the pressure to increase and the artery to reopen, thus setting the stage for the process to repeat itself. The result is a rapid cycling between an open and closed condition, known as a "flutter" of the artery.
The following values are typical of a narrowed coronary artery:
Average velocity in the artery entrance: 0.50 m/s
Average velocity in the narrowed portion: 4.50 m/s
Time-averaged pressure at the artery entrance: 100 mm Hg (gauge)
Density of blood: 1,060 kg/m³
Answer the following questions based on these conditions:
a. At sea level, what is the absolute pressure at the artery entrance in units of Pa?
b. Neglecting the effects of friction and any height changes, what absolute pressure (Pa) might be expected in the narrowed portion of such an artery?
c. What is the value of the answer to (b) in units of mm Hg (gauge)?