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Air Flow Problem

  1. Oct 27, 2005 #1
    See attachment for piping system setup.

    Question: How much FORCE will the block feel from the air flowing through the two holes in the lower pipe?

    I have no idea how to calculate this. Does Bernoulli's equation apply anywhere here?
     

    Attached Files:

  2. jcsd
  3. Oct 28, 2005 #2
    it looks just like a problem straight out of my fluid mechanics textbook
    bernoulli's should apply
    and conservation of masses
    mass of all inputs - mass of output = total mass change in the system
    and for this system
    mass in = mass out
     
  4. Oct 28, 2005 #3
    So you have 4 inlets & 1 outlet...

    Conservation of mass??:

    A1v1+A2v2+A3v3+A4v4 = A5v5

    unknowns: v1, v2, v3, v4

    A=area
    v=velocity

    Bernoulli??:

    P1+P2+P3+P4+(1/2)p(v1^2+v2^2+v3^2+v4^2)+pg(z1+z2+z3+z4) = P5+(1/2)p(v5^2)+pg(z5)

    P=pressure
    v = velocity
    p = density
    g = acceleration due to gravity
    z = height

    Assumptions: P1=P2=P3=P4=atmospheric pressure

    unknowns: v1, v2, v3, v4

    2 equations, 4 unknowns.......How can this be solved?

    How can I use this to get the force on the block?
     
  5. Oct 29, 2005 #4

    FredGarvin

    User Avatar
    Science Advisor

    You're not going to be able to cover the entire network in one swoop. Start at the node where the two pipes meet and apply the continuity equation: [tex]Q = Q_1 + Q_2[/tex] where the total flow is the flow from the fan. That will give you the two flow rates (a function of the diameters). Now that you have the flow rate at that node, you can now go to Bernoulli and continue back up the pipe to calculate the pressure drop around those holes.

    Just out of curiosity, when you say "force on the block" you are referring to a lower pressure that will (I hate to use this term) "suck" on the block? In other words, you want to know if you'll have enough flow to pick up the block?
     
  6. Oct 29, 2005 #5
    Just out of curiosity, when you say "force on the block" you are referring to a lower pressure that will (I hate to use this term) "suck" on the block? In other words, you want to know if you'll have enough flow to pick up the block?

    Yes
     
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