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.

(a) For a nonsmoker, with blood viscosity of 2.5 103 Pa·s, normal blood flow requires a pressure difference of 8.0 mm Hg between the two ends of a certain artery. If this person were to smoke regularly, his blood viscosity would increase to 2.8 103 Pa·s (a 12% 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? Show your work.

______ 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? Support your answer with a quantitative comparison.

The viscosity, the diameter, they both had equal effects, or you can't tell from the information given.

Explanation / Answer

from the poiseullis equation

volume flow rate ofliquid is

dP=((8*n*l)/(pi*r^4))*Q -----(1)

let,

n1=2.5*10^-3 pa.s

n2=2.8*10^-3 pa.S

diameter d2=d1-10%d1

d2=(9/10)*d1

===> r2=9/10*r1

from equation (1)

dp2/dp1=(n2/n1)*(r1/r2)^4

dp2/(8 mm of Hg)=(2.5*10^-3)/(2.8*10^-3)*(10/9)^4

====>

dp2=10.89 mm of Hg -----is answer

b)

here,

both ,changne in viscosity and diameter of the artery effects on the pressure difference

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