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Momentum Equation for compressible 1D flow

  1. Nov 7, 2017 #1
    1. The problem statement, all variables and given/known data
    Derive the differential momentum equation: [tex]dp=-\rho udu[/tex].

    2. Relevant equations
    [tex]\oint_{ CS}^{ } \rho \vec{U}(\vec{U}\cdot \vec{n})dA=-\oint_{ CS}^{ } p\vec{n}dA[/tex] for steady state flow...

    3. The attempt at a solution
    I tried to solve it like in the attached picture, but can someone explain where the [tex]p+\frac{1}{2}dp[/tex] (marked with red line in the picture) comes from? Is it a linear interpolation or something? Untitled1.png

    Thanks!
     
  2. jcsd
  3. Nov 7, 2017 #2
    That is a term for representing the force that the solid boundary exerts (in the x direction) on the fluid passing through the control volume.
     
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