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7.4.4.1: Energy Equation in Accelerated Coordinate with Uniform Flow

  • Page ID
    734
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    One of the way to simplify the general equation (105) is to assume uniform flow. In that case the time derivative term vanishes and equation (105) can be written as

    Energy Equation in steady state

    \[ \label{ene:eq:AccCVgeneralss1}
    \dot{Q} - \dot{W} =
    \int_{cv} \left( h + \dfrac{U^2}{2\dfrac{}{}} + a_x\,x + a_y\, y + (a_z + g) - z\, \dfrac{\omega^2 \,r^2}{2} \right)
    U_{rn}\, \rho\,dA\\
    \nonumber
    + \int_{cv} P\,U_{bn} \,dA
    \]

    Further simplification of equation (106) by assuming uniform flow for which

    \[ \label{ene:eq:ene:AccCVgeneralss}
    \dot{Q} - \dot{W} =
    \left( h + \dfrac

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    _{rn}\, \rho\,dA\\
    + \int_{cv} P\,{\overline{U}}_{bn} \,dA
    \]

    Note that the acceleration also have to be averaged. The correction factors have to introduced into the equation to account for the energy averaged verse to averaged velocity (mass averaged). These factor make this equation with larger error and thus less effective tool in the engineering calculation.

    Contributors and Attributions

    • Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.


    This page titled 7.4.4.1: Energy Equation in Accelerated Coordinate with Uniform Flow is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.


    This page titled 7.4.4.1: Energy Equation in Accelerated Coordinate with Uniform Flow is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Genick Bar-Meir via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.