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Average velocity over an interval

  1. Sep 13, 2010 #1
    1. The problem statement, all variables and given/known data

    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.




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

    3. 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
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 13, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
  4. Sep 14, 2010 #3
    GOT IT! Thanks.
     
  5. Jan 25, 2011 #4
    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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