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Homework Help: Flow Rate Problem -

  1. Apr 7, 2010 #1
    Flow Rate Problem - Please Help!

    1. The problem statement, all variables and given/known data:

    SAE no. 10 oil has a viscosity of 0.2 Pa· s. How long (in sec) would it take to pour 6 liters of oil through a funnel with a neck 12 cm long and 2.6 cm in diameter. Assume that it is poured in such a way that the oil level is kept just above the top of the tube.

    Hint: The specific gravity (= ratio of its density to that of water) of the oil is 0.70.

    2. Relevant equations

    The pressure difference is given by
    Dp = rgL

    1000 liter = 1 m^3 = 10^6 cm^3

    The flow rate is given by Poiseuille's law:

    Q = p * r^4 * Dp / 8*h*L

    3. The attempt at a solution

    You can calculate the pressure difference:
    Dp = rgL
    Dp = (700 kg/m^3)(9.81 m/s^2)(0.0012 m)
    Dp = 82.4 Pa

    And the time it takes for the oil to flow through is the volume of the oil divided by the flow rate:

    t = V / Q = 8 * V * h * L / (p * r^4 * Dp)
    t = 8 (0.006 m^3)*(0.2)*(0.012 m) / p * (0.5)*(0.013 m)^4 * (82.4 Pa)
    t = 8.97 X 10^-9

    But I know that can't be right. Can someone please help me with where I went wrong? And try to explain it to me?
     
    Last edited: Apr 7, 2010
  2. jcsd
  3. Apr 8, 2010 #2

    Redbelly98

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    Re: Flow Rate Problem - Please Help!

    I found two errors.
    12 cm is not 0.0012 m.

    I agree with the next-to-last line here, except for the pressure which you must recalculate based on my earlier comment. Even so, something went really wrong in calculating that final value for t here. Everything to the right of the "/" here is in the denominator, i.e. you must divide by all of those values. Technically, those terms should be enclosed in a pair of parantheses, so that you have
    t = 8 (0.006 m^3)*(0.2)*(0.012 m) / (p * (0.5)*(0.013 m)^4 * (82.4 Pa))
    It's encouraging that you thought about your answer and realized something is wrong :smile:
     
  4. Apr 11, 2010 #3
    Re: Flow Rate Problem - Please Help!

    "You can calculate the pressure difference:
    Dp = rgL
    Dp = (700 kg/m^3)(9.81 m/s^2)(0.0012 m)
    Dp = 82.4 Pa"

    => r = 700 kg/m^3 ???? I'm confused ???
     
  5. Apr 11, 2010 #4

    Redbelly98

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    Re: Flow Rate Problem - Please Help!

    The density of the oil is 0.70 times that of water, which is 1000 kg/m^3.
     
  6. Apr 11, 2010 #5
    Re: Flow Rate Problem - Please Help!

    I don't know what "p" is. Help?
     
  7. Apr 12, 2010 #6

    Redbelly98

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    Re: Flow Rate Problem - Please Help!

    p is π here, 3.14159...
     
  8. Apr 12, 2010 #7
    Re: Flow Rate Problem - Please Help!

    So I calculated the equation using pi:

    t = V / Q = 8 * V * h * L / (p * r^4 * Dp)
    t = 8 (0.006 m^3)*(0.2)*(0.012 m) / [ pi * (0.5)*(0.013 m)^4 * (82.4 Pa) ]
    t = 1.9492 sec

    But it is still incorrect... Any ideas?
     
  9. Apr 12, 2010 #8

    Redbelly98

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    Re: Flow Rate Problem - Please Help!

    Dp is not 82.4 Pa. See post #2.
     
  10. Apr 12, 2010 #9
    Re: Flow Rate Problem - Please Help!

    You can calculate the pressure difference:
    Dp = rgL
    Dp = (700 kg/m^3)(9.81 m/s^2)(0.12 m)
    Dp = 824 Pa

    And the time it takes for the oil to flow through is the volume of the oil divided by the flow rate:

    t = V / Q = 8 * V * h * L / (pi * r^4 * Dp)
    t = 8 (0.006 m^3)*(0.2)*(0.012 m) / (pi * (0.5)*(0.013 m)^4 * (824 Pa))
    t = 0.1949 sec

    It is still incorrect.
     
  11. Apr 12, 2010 #10

    Redbelly98

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    Re: Flow Rate Problem - Please Help!

    Hmm, now that I look more carefully I am seeing several problems with the calculation.

    1. The numbers you have do not give 0.1949 s
    2. 12 cm is not equal to 0.012 m.
    3. Where does the (0.5) come from?
     
  12. Apr 12, 2010 #11
    Re: Flow Rate Problem - Please Help!

    So if I recalculate, fixing my errors and taking out 0.5:

    t = V / Q = 8 * V * h * L / (pi * r^4 * Dp)
    t = 8 (0.006 m^3)*(0.2)*(0.12 m) / (pi * (0.026 m)^4 * (824 Pa))
    t = 0.974 sec

    Still wrong.
     
    Last edited: Apr 12, 2010
  13. Apr 13, 2010 #12

    Redbelly98

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    Re: Flow Rate Problem - Please Help!

    1 more try: 0.026 m is the diameter; the radius is 0.013 m. Use the radius here.
     
    Last edited: Apr 13, 2010
  14. Apr 13, 2010 #13
    Re: Flow Rate Problem - Please Help!

    You were right! Thank you for helping me out!
     
  15. Apr 13, 2010 #14

    Redbelly98

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    Re: Flow Rate Problem - Please Help!

    You're welcome :smile:
     
  16. Apr 13, 2010 #15
    Re: Flow Rate Problem - Please Help!

    Could you please check out my question on Height of Blood Transfusion? Thanks.
     
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