Average velocity over an interval

rubecuber
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Homework Statement



The velocity v of blood that flows in a blood vessel with radius R and length l at a distance r from the central axis is v(r), where P is the pressure difference between the ends of the vessel and η is the viscosity of the blood.
v(r) = P/4nl (R^2 - r^2)

a) Find the average velocity vave (with respect to r) over the interval 0 ≤ r ≤ R.
vave =

(b) Compare the average velocity vave with the maximum velocity vmax.




Homework Equations


v(r) = P/4nl (R^2 - r^2)
and
http://www.mediafire.com/imageview.php?quickkey=v2qyuycs2k81812&thumb=6

The Attempt at a Solution


I'm looking at this and trying to work it out and the best I can do now is cry. But seriously, I don't know what's important and what's not. I'll take anything. I know average velocity is 1/(b-a) integral of what you're doing but it doesn't make much sense to me to take the integral of that nasty equation so I'm at a loss.

Thanks
 
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It's not a 'nasty' expression. P, n, l and R are constants. It's just a quadratic in r. Really, integrals don't come much easier. Just try it, ok? Split it into (P/(4nl))R^2-(P/(4nl))*r^2. This first term is just a constant and the second one is a constant time r^2. Oh, and use more parentheses. P/4nl could mean (P/4)*nl, (P/(4n))*l etc etc. They aren't the same.
 
GOT IT! Thanks.
 
For the second part of the problem how do you get the ratio? or find the max velocity to make the ratio
 
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