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Avg Value Of A Function: Word Problem

  1. May 11, 2008 #1
    1. The problem statement, all variables and given/known data
    [​IMG]
    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.

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

    (b)Compare the average velocity v_ave with the maximum velocity v_max.(v_ave/v_max)

    So I need to set the problem up, into an integral form, to find the avg velocity for part A. The integration limits for the integral should be from zero to Big R, multiplied by (1 over big R) to get our average value. Now the problem is, every thing in the equation except the (1/4) is a variable. How would I even begin to integrate this?

    Thanks.
     
  2. jcsd
  3. May 11, 2008 #2

    dx

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    The only variable is r. The rest of those symbols are constants.
     
  4. May 11, 2008 #3
    Ah. Well now I've solved part A, how would go about part B?

    (a) is PR[tex]^{3}[/tex]/6nlR

    I have V_ave, what is V max?
     
  5. May 11, 2008 #4

    dx

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    You have a formula for v as a function of r. At what value of r is it maximum?
     
  6. May 11, 2008 #5
    So if you make the equation v(R) instead of v(r), then the (R[tex]^{2}[/tex]-R[tex]^{2}[/tex]) = equal zero, so V_max is zero?
     
  7. May 11, 2008 #6

    dx

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    Why did you do that? Think of it this way - the velocity at which the fluid flows depends on the distance from the center of the pipe. At a particular value of that distance, the velocity is maximum. Try drawing a picture. Plot v as a function of r. Also, first try to guess what it should be. Where do you think the water is flowing fastest? Near the center? Near the edge? Somewhere in between?
     
    Last edited: May 11, 2008
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