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Fluid Mechanics Velocity at Outlet

  1. Feb 6, 2016 #1
    1. The problem statement, all variables and given/known data
    Water flows through a 1.5 [in] diameter pipe. In a 1.5 [ft] section of the pipe water is injected through the porous walls into the pipe at a velocity of 3 [in/s]. What is the average velocity at the exit if the inlet velocity is 6 [ft/s]?

    2. Relevant equations


    3. The attempt at a solution
    I used 62.4 lb/ft3 for the density of water.
    I calculated the area of the pipe to be
    A=πR2=0.01227 ft3
    m1=ρAv=(62.4)(0.01227)(6)=4.59 lb/s

    Aw=DL=(1.5/12)(1.5)=0.1875 ft^2 I'm not super confident that this area is correct...
    mw=ρAwvw=(62.4)(0.1875)(3/12)=2.925 lb/s

    Then I used the conservation of mass...
    m1+mw=m2
    (4.59)+(2.925)=m2
    m2=7.25 lb/s

    Now just plug into formula to get vout
    vout=(m2)/(ρA)=(7.52)/(62.4*0.01227)
    vout=9.82 ft/s

    Which is wrong.... My options are 7 ft/s, 18 ft/s, 28 ft/s, and 150 ft/s.
    I'm not sure what I did wrong!
     

    Attached Files:

  2. jcsd
  3. Feb 6, 2016 #2

    SteamKing

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    This calculation seems to be OK.
    Is the circumference of a circular pipe equal to its diameter? Or is it equal to something else?
     
  4. Feb 6, 2016 #3
    Haha I knew that area couldn't be right... I got thrown off because I was given the length of the porous wall. So is that length L just useless information?
     
  5. Feb 6, 2016 #4

    SteamKing

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    No, it's not the length that's the problem with the calculation.

    I mentioned specifically the circumference of the pipe and how you calculated it.
     
  6. Feb 6, 2016 #5
    Oops sorry. That makes more sense. Circumference=2πr*h=0.0625ft2. Thanks!!!
     
  7. Feb 6, 2016 #6

    SteamKing

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    What's h supposed to be?
     
  8. Feb 6, 2016 #7
    Oops, that's the length L!
     
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