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Fluids Cons of Momentum

  • #1
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Homework Statement



Picture1-35.png


Homework 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?
 

Answers and Replies

  • #2
Doc Al
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Sounds lovely!
 
  • #3
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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.
 
  • #4
Doc Al
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I guess that what is confusing me now, is why they gave me
force/unit length into page
Consider it to be an arbitrarily wide sheet of water. Use momentum per unit length as well.
 
  • #5
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Consider it to be an arbitrarily wide sheet of water. Use momentum per unit length as well.
Okay, so the m-1 just drops out anyway, and this problem reduces to regular cons of mom
 
  • #6
Doc Al
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Yep.
 
  • #7
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Thanks! 83.4 degrees sounds reasonable I think :smile:
 
  • #8
Doc Al
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83.4 degrees sounds reasonable I think
Show how you got that answer.
 
  • #9
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Picture2-21.png
 
  • #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).
 
  • #11
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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?
 
  • #12
Doc Al
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Now you're cooking.
 
  • #13
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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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