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Vector field- fluid mechanics

  1. Jan 31, 2010 #1
    I was a under a little confusion about vector field.
    Consider velocity field of fluid flow:

    V = u i + v j + w k

    here V is vector and consider a cap over i, j, k (since they represent x,y,z directions)

    now we know that u,v,w are functions of x,y,z,t. This is where i am confused.

    u is velocity component in x direction then it should be function of only x and t. Why y and z also???????

    In a velocity field we see arrows representing magnitude and direction of velocity at any position, are these arrows over fluid particles? I mean can i assume each arrow as a particle at that position having certain velocity represented by the arrow??????

    I think i lack understanding of fluid velocity field. Can anyone expalin a bit.
  2. jcsd
  3. Jan 31, 2010 #2


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    Hi R Power! :smile:

    (use i j and k :wink:)
    Imagine a river of width 60m flowing steadily in the x-direction.

    The water is fastest in the middle, say 3 m/s, and zero near the bank.

    So in the middle, the velocity vector is 3i, and at distance y from the middle, it is (|30 - y|/10)i

    u is a function of y, but is independent of x. :wink:
    Yes, that's exactly correct, the value of the velocity field at each point is the velocity of the actual particle that is (instantaneously) at that point. :smile:
  4. Jan 31, 2010 #3
    If this is so streamlines should be same as pathlines whether flow is steady or unsteady. Am I correct?
    Tiny Tim, please answer my another post relating to streamlines,streaklines,pathlines in mechanical engineering section.
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