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Water in a pipe problem

  1. Jun 12, 2009 #1
    1. The problem statement, all variables and given/known data
    Water flowing through a 2.68 cm diameter pipe fill a 284 L bathtub in 8.2 minutes. What is the speed of the water in the pipe?



    2. Relevant equations
    p+pgh +1/2pv^2=p2 +pgh + 1/2pv2^2


    3. The attempt at a solution
    I know that p=pat for both cases but the water does not start from any height and does not end up at any height. I don't know how to start that one. Thank you for your help.
     
  2. jcsd
  3. Jun 12, 2009 #2

    dx

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    If the area of the pipe opening is A, and the speed of the water flowing through it is v, what is the volume of water that flows into the bathtub in 1 second?
     
  4. Jun 12, 2009 #3
    volume=q/a. So is the volume 284 L in this case?
     
  5. Jun 12, 2009 #4
    Also, for the area, would I just consider the cross section since there is no height in this case?
     
  6. Jun 12, 2009 #5

    dx

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    Yes area is the cross section. If the area of the cross section is A, and the speed of flow is v, then a volume Av will flow into the pipe per second. Do you see why?
     
  7. Jun 12, 2009 #6
    No I'm trying but I don't. Could you explain it to me please.
     
  8. Jun 12, 2009 #7
    Also,if that is the case would not velocity be in L/m^2? would I need to solve it for 8.2 minutes?
     
  9. Jun 12, 2009 #8

    dx

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    If the circular opening of the pipe has area A, then a small cylindrical volume of length v(dt) of water will leave in the small time dt. The volume of this small cylinder is A(v)(dt) (area of cross section times length). So dV = A(v)(dt), or dV/dt = Av.
     
  10. Jun 12, 2009 #9

    dx

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    If the rate at which the water is flowing into the bathtub is Av, how much volume will flow into the tub in 8.2 minutes in terms of Av?
     
  11. Jun 12, 2009 #10
    Av*492 s. But wouldn't Av have to be in m/s?
     
  12. Jun 12, 2009 #11

    dx

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    Av will have units of m^3/s. (if you write A in units of m^2, and v in units of m/s)
     
  13. Jun 12, 2009 #12

    dx

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    Now just solve Av(492) = 284.
     
  14. Jun 12, 2009 #13
    How do I find v since it's not given?
     
  15. Jun 12, 2009 #14
    OH I get it! Thank You!
     
  16. Jun 12, 2009 #15
    I solved for V and my units were in m/s but that did not work. Why is it wrong still?
     
  17. Jun 12, 2009 #16

    dx

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    What was your value for A? It should be 5.64 x 10-4 m2.
     
  18. Jun 12, 2009 #17
    OH I got it! I had to convert L into m^3 then the final answer is in m/s. Thank you very much!
     
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