# Pressure difference to maintain blood flow

hey guys.. i need a bit of help on this question...

For a non-smoker, with blood viscosity of 2.5x10-3Pa's, 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 2.7x10-3 Pa's, and the arterial diameter would constrict to 90% of its normal value. What pressure difference would be needed to maintain the same blood flow?

any help here would be greatly appreciated!!

cheers
KC

tiny-tim
Homework Helper
For a non-smoker, with blood viscosity of 2.5x10-3Pa's, 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 2.7x10-3 Pa's, and the arterial diameter would constrict to 90% of its normal value. What pressure difference would be needed to maintain the same blood flow?

Hi KC!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

ok, this is what i had so far... not sure if i am on the right track or not though...

non smoker:2.5 x 10^-3 Pa.s
smoker: 2.7 x 10^-3 Pa.s

density of blood @ 1 atm: 1060 kg/m3

normal blood flow: $$\Delta$$ 8.0 mmHg

pressure difference:
smoker - nonsmoker = 2 x 10^-4

pressure difference: ________________________________

that's where i am not sure about what to do.

i tried: 8.0 mmHg / 2 x 10^-4 = 40,000 mmHg or 4.0 x 10^-3......
but i know that that's not the answer coz i havent taken into account for the 10% constriction of the artery.

any clues or nudges in the right direction would be GREAT!!

tiny-tim
Homework Helper
ok, this is what i had so far... not sure if i am on the right track or not though...

non smoker:2.5 x 10^-3 Pa.s
smoker: 2.7 x 10^-3 Pa.s

density of blood @ 1 atm: 1060 kg/m3

normal blood flow: $$\Delta$$ 8.0 mmHg

pressure difference:
smoker - nonsmoker = 2 x 10^-4

pressure difference: ________________________________

that's where i am not sure about what to do.

i tried: 8.0 mmHg / 2 x 10^-4 = 40,000 mmHg or 4.0 x 10^-3......
but i know that that's not the answer coz i havent taken into account for the 10% constriction of the artery.

any clues or nudges in the right direction would be GREAT!!

Hi twiztdlogik!

I have to confess I only know about non-viscous flow.

But this looks to me like a dimensions question … y'know, of the "if three men take two days to paint a cube, how long do seven men take to paint a cube with twice the radius and with brushes half as small and paint twice as thin" sort.

So what equation do you know relating pressure to viscosity and diameter and flow?

erm.. are you thinking of the poiseuilles equation...?
i think that would work if i can transpose it to get the right formula for this situation

thanks any ways!