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Thread: Material derivative

  1. #1
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    Material derivative

    How did this guy: https://www.youtube.com/watch?v=BLVY69SYVBQ at 6:27 get the right hand side expression?

    He said: When we apply chain-rule, but I still don't get.
    Thank you.
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  2. #2
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    Re: Material derivative

    So no one understands material derivative? Maybe I should ask on physics forum, because this is a physics topic.
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  3. #3
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    Re: Material derivative

    It's the chain rule for multiple variables - if f is a function of two variables x and y, each of which is a function of t, then:

    $\frac{df}{dt} = \frac{\partial f}{\partial x}\frac{dx}{dt}+\frac{\partial f}{\partial y}\frac{dy}{dt}$

    Changes in t cause changes in both x and y, which each cause changes in f, and the effects are additive.

    To understand what follows later, it might help to break r into x, y, and z. Then you'd have 4 terms, but the x, y, and z terms should combine to that $v \cdot \nabla C$.

    - Hollywood
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    Re: Material derivative

    Quote Originally Posted by Nforce View Post
    So no one understands material derivative? Maybe I should ask on physics forum, because this is a physics topic.
    A "material" derivative can have several meanings in Physics but it is still the same as a derivative in Mathematics.

    -Dan
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  5. #5
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    Re: Material derivative

    Quote Originally Posted by hollywood View Post
    It's the chain rule for multiple variables - if f is a function of two variables x and y, each of which is a function of t, then:

    $\frac{df}{dt} = \frac{\partial f}{\partial x}\frac{dx}{dt}+\frac{\partial f}{\partial y}\frac{dy}{dt}$

    Changes in t cause changes in both x and y, which each cause changes in f, and the effects are additive.

    To understand what follows later, it might help to break r into x, y, and z. Then you'd have 4 terms, but the x, y, and z terms should combine to that $v \cdot \nabla C$.

    - Hollywood
    Yes but by definition we get also ordinary derivative and he got 3 partial derivatives and no ordinary one. Can someone write down step by step, how do we get then the expression?
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  6. #6
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    Re: Material derivative

    Sorry, but is there no one who has time to write down step by step derivation?
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