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Pipe Radius

  1. Jun 12, 2016 #1
    1. The problem statement, all variables and given/known data
    The following image shows the parts A and B of a pipe where the middle part goes under a hill the length of both parts A and B is 30m and the diameter of them each is 2cm where as the middle part has a length of 110m to determine the middle part's diameter one engineer decided to push water in the pipe with a speed of 2.50 m\s in part A he dropped a small coin in the flow and noticed that it took 88.8 seconds for it to start from A and exit from B.
    1)calculate the diameter of the middle pipe

    2. Relevant equations

    v=d\s
    A1*v1=A2*v2. (Continuity equation)
    A=pi*r^2



    3. The attempt at a solution
    Finding the area of a and b:
    0.02^2*pi=0.00125m^2
    Finding the time it would take to travel through A and B (not including mid pipe)
    2.50=30/s
    s=12
    So for a and b it would take 24 seconds
    For mid part it would take 88.8-24=64.8
    Mid part speed
    110/64.8=1.697m\s
    So
    0.00125*2.50=1.697*A2
    Area=0.001841
    0.0018141=pi*r^2
    R=0.024m
    Answer sheet says that the diameter is 3.60cm
    help!
     

    Attached Files:

  2. jcsd
  3. Jun 12, 2016 #2

    Simon Bridge

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    ... the diameter of the pipe is 2cm.

    Note: you do not have to compute the area ...
    You can express: ##A_1v_1 = A_2v_2## in terms of the two diameters ##d_1## and ##d_2## using ##A=\pi d^2/4##.
     
  4. Jun 12, 2016 #3

    Simon Bridge

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    Now I've had a chance to check.
    Assuming the coin travels at the same (average) speed as the water - it travels 60m at u=2.5m/s, this takes 60/2.5=24s
    Total travel time is 88.8s to time through the entire length, so the time spent in the middle section is 88.8-24=64.8s
    This gives an average speed through that section as v=110/64.8 = 1.6975m/s = 169.75cm/s
    Volume flow rate is a constant for incompressible flow: we want to find hidden diameter d, given revealed diameter, u, and v
    ##\pi (d^2/4)v = \pi (2^2/4)u \implies d = 2\sqrt{2.5/1.6975} = 2.43##cm (2dp)
    ... in agreement with your answer. (notice I did not need to convert the units of diameter to meters.)

    The model answer says d=3.60cm.
    This suggests the model answer is incorrect, or uses a different model.
    You can work out what the time through the entire pipe would be if the middle section were 3.6cm in diameter.
     
  5. Jun 13, 2016 #4
    Thank you very much but I made a mistake 2cm is the radius not the diameter thanks!
     
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