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Fluids Cons of Momentum

  1. May 23, 2009 #1
    1. The problem statement, all variables and given/known data

    Picture1-35.png

    2. Relevant equations
    [tex]\sum(\dot{m}\vec{v})_{exit}-\sum(\dot{m}\vec{v})_{inlet}=\sum F_{ext}[/tex]


    I only know that this is cons of momentum because my prof told us. I am having a hard time visualizing how to incorporate THETA into the above equation since it is not a nice right triangle.

    I am thinking that since the exit velocities are equal, than the inlet flow must be being split about the wedges horizontal axis of symmetry.

    Thus, I think I can divide the wedge into an "upper" and "lower" right triangle whose angle wrt to the horizontal is [itex]\frac{\theta}{2}[/itex].

    Then I can resolve the momentum eq into Cartesian coordinates.

    Sound good?
     
  2. jcsd
  3. May 23, 2009 #2

    Doc Al

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    Sounds lovely!
     
  4. May 23, 2009 #3
    Nice! I guess that what is confusing me now, is why they gave me
    force/unit length into page

    But I am just going to start plugging in and see what happens.
     
  5. May 23, 2009 #4

    Doc Al

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    Consider it to be an arbitrarily wide sheet of water. Use momentum per unit length as well.
     
  6. May 23, 2009 #5
    Okay, so the m-1 just drops out anyway, and this problem reduces to regular cons of mom
     
  7. May 23, 2009 #6

    Doc Al

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    Yep.
     
  8. May 23, 2009 #7
    Thanks! 83.4 degrees sounds reasonable I think :smile:
     
  9. May 23, 2009 #8

    Doc Al

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    Show how you got that answer.
     
  10. May 23, 2009 #9
  11. May 23, 2009 #10

    Doc Al

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    Rethink your result for m, the mass flow rate. You want it to be mass flow per unit width (or depth).
     
  12. May 23, 2009 #11
    I am not sure that I follow. Errr.... Okay. So that inlet with the 4 cm dimension is NOT a PIPE....right?

    It is a "sheet" with area 4cm*WIDTH. Thus my, mass flow rate should be, with h=4cm:

    [tex]\dot{m}=\rho V (h*W)\Rightarrow \frac{\dot{m}}{W}=\rho Vh[/tex]

    Am I with you now?
     
  13. May 23, 2009 #12

    Doc Al

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    Now you're cooking.
     
  14. May 23, 2009 #13
    Typical 'not-paying-attention' mistake. Perhaps I should turn off Band of Brothers while I do my studies? :smile:

    Thanks Doc!
     
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