Question

3. 1/2 points | Previous Answers My Notes 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. (a) For a nonsmoker, with blood viscosity of 2.50 x 103 Pa s, normal blood flow requires a pressure difference of 8 mm Hg between the two ends of a certain artery. If this person were to smoke regularly, his blood viscosity could increase to 2.83 x 10-3 Pa-s (a 13% increase), and the diameter of his artery would constrict by 10%, what pressure difference between the ends of the artery would then be needed to maintain the same blood flow rate? 10.1 x mm of Hg (b) Which had a larger effect on the pressure difference needed: the change in viscosity, or the change in the diameter of the artery? the diameter

Answer 1

To maintain same flow rate, the required pressure should also increase with increasing viscosity. Moreover, the reduction of cross sectional area causes a reduction in flow rate. Therefore to match-up with the required flow rate pressure should also increase with decreasing area.

pressure=P, Area=A, Viscosity=V, diameter=d, radius=r

$P \propto \frac{V}{A} \propto \frac{V}{\pi r^2}$

required pressure P is

$\frac{P}{P_1}= \frac{Vr_1^2}{V_1r^2}$

Therefore,

$P=\frac{2.83*r_1^2}{2*0.81r_1^2}P_1 \\ P=13.975 mm Hg$

Diameter has square dependence on pressure and hence has a larger effect.