Smoking tobacco is bad for your circulatory health. In an attempt to maintain th

Question

Smoking tobacco is bad for your circulatory health. In an attempt to maintain the blood's capacity to deliver oxygen, the body increases its red blood cell production, and this increases the viscosity of the blood. In addition, nicotine from tobacco causes arteries to constrict. For a nonsmoker, with blood viscosity of 2.5×103Pas, normal blood flow requires a pressure difference of 8.0 mm of Hg between the two ends of an artery. If this person were to smoke regularly, his blood viscosity would increase to 2.7×103Pas, and the arterial diameter would constrict to 90 % of its normal value. What pressure difference would be needed to maintain the same blood flow?

Explanation / Answer

The viscosity increases from 2.5 × 10 ^–3 Pa·s to 2.7 × 10^ –3 Pa·s,

So the pressure difference is increased by a factor of (2.7/2.5) = 1.08.

In addition, if the diameter constricts by 90%, this means that the radius also constricts by 90%;

in other words, the radius is multiplied by 0.1.

Therefore, the pressure difference is multiplied by a factor of 1/(0.1)+ 4/(0.9) = 14.44.

Combining both of these factors, the new pressure difference is (8.0 mm Hg)(1.08)(14.44)

= 124.762 mm Hg.

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