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Homework Help: Continuity: Constant mass flow rate

  1. Jan 16, 2008 #1
    1. The problem statement, all variables and given/known data

    The aorta carries blood away from the heart at a speed of about 40 cm/s and has a radius of approx. 1.1cm. The aorta branches eventually into a large number of tiny capillaries that distribute the blood to the various body organs. In a capillary, the blood speed is approx. 0.07 cm/s, and the radius is about 6 x 10 -4 cm. Treat the blood as an incompressible flulid and use these data to determine the approx number of capillaries in the human body.



    2. Relevant equations

    I think: A1 x V1 = A2 x V2 and A = pi (r)^2


    A = cross sectional area of tube
    V= velocity




    3. The attempt at a solution

    I have figured out the areas of the cross sections of the capillary and the aorta.

    I have labeled them: Ac and Aa respectively.

    Ac= 1.13097 x 10^-6 cm^2

    Aa= 3.8013 cm^2



    I cannot figure out where to go with this information. It seems like I need to know a volume or a length of some sort.

    Can anybody help me out please?

    Thanks!
     
    Last edited: Jan 16, 2008
  2. jcsd
  3. Jan 16, 2008 #2

    stewartcs

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    Science Advisor

    Hint: The flow rate in must equal the flow rate out. The flow rate in is [tex] A_1 \cdot V_1 [/tex] or about [tex]152.05 \frac{cm^3}{s}[/tex].

    The flow rate out must equal this, no matter how many paths it takes. Therefore [tex] A_2 \cdot V_2 \cdot N[/tex] must equal 152.05, where N is the number of capillaries.

    CS
     
  4. Jan 16, 2008 #3
    Thank you very much Stewartcs!
     
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