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Pressure Field Equation / Differentials

  1. Sep 3, 2015 #1

    MacLaddy

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    Hello folks,

    I am having difficulty comprehending some material in my fluid dynamics course. This is not a homework question, just something missing in my understanding.

    When proving the "Pressure Field Equation," (something I am not yet able to do) there is a series of steps my instructor took.

    [itex]P=P_1+\Delta{P}[/itex]
    [itex]P=P_1+\Delta{y}\frac{dp}{dy}[/itex]

    Which somehow, magically, leads to...

    [itex]F_y = (P+\frac{\partial{p}}{\partial{y}}\frac{\delta{y}}{2})*\delta{x}\delta{z}[/itex]

    So my question is this.

    [itex]\frac{dp}{dy}[/itex] is simply the change of P wrt y

    [itex]\frac{\partial{p}}{\partial{y}}[/itex] is the change of p wrt y in a particular direction, or part of the gradiant.

    But what in the sam is [itex]\frac{\delta{y}}{2}[/itex]?

    Why the delta?

    Any help would be appreciated.

    Thanks,
    Mac
     
  2. jcsd
  3. Sep 3, 2015 #2

    fzero

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  4. Sep 4, 2015 #3

    MacLaddy

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    Great, thank you for the link. That is a better representation then my textbook provides. It treats the lengths as ##\delta y##, whereas this link just shows the lengths as dx, dy, and dz. It seems a new character was introduced without any real need.

    Mac
     
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