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Homework Help: Eulerian Field vs LagrangianConceptual

  1. Oct 24, 2009 #1
    Okay. This is a very straight forward question. I believe that my text has an error or I am misunderstanding something.

    It describes the Eulerian Field as:

    Then we go on to derive the acceleration field in this eulerian field by taking the Total Derivative of the Velocity Field vector, which yields:

    [tex]\mathbf{a} = \frac{d\,\mathbf{V}}{d\,t} = \frac{\partial{V}}{\partial{t}} + (\mathbf{V}\cdot\nabla)\mathbf{V}[/tex]

    Okay great..I get all of that. Here is where I croak. It then summarizes what we just did by saying:

    This last quote keeps referring to "following a fixed particle" or "following a particle of fixed identity."

    Isn't that by definition the Lagrangian frame? Or am I misinterpreting how they are using the word "following"?

    Can someone clear up my confusion here?

    Thank you,
  2. jcsd
  3. Oct 25, 2009 #2
    I think what the text means is "specific" particle, i.e. one particular particle in the fluid. I agree, though, that fixed was a bad choice of word.
  4. Oct 25, 2009 #3
    Yes. I was assuming that by "fixed particle" they mean a "specific particle."

    My problem is that they are referring to a "fixed particle" but they are also saying that this is the eulerian approach. But I thought that the fixed particle approach was lagrangian?
  5. Oct 25, 2009 #4
    Any ideas on this one? I feel like I could move on, but I really want to understand what I am doing from here forward.
  6. Oct 25, 2009 #5
    In the lagrangian frame of reference, the origin is always at the specific particle, while in the eulerian frame of reference, it is not.
  7. Oct 25, 2009 #6
    Yes. I am quite aware of that. But that is not my question. Please look at what I am asking.

    The whole point of my question is that I KNOW that the eulerian frame stays fixed and watches different fluid particle entering and leaving. So why do they say

    The words in bold seem to contradict each other.
    Last edited: Oct 25, 2009
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