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5.3.2.1: Non Deformable Control Volume

  • Page ID
    702
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    For this case the volume is constant therefore the mass is constant, and hence the mass change of the control volume is zero. Hence, the net flow (in and out) is zero. This condition can be written mathematically as

    \[ \label{mass:eq:cvCmCV}
    \overbrace{\dfrac{d\,\int}{dt}}^{ = 0} \longrightarrow
    \int_{S_{c.v.}} V_{rn} dA = 0
    \]

    or in a more explicit form as

    Steady State Continuity

    \[ \label{mass:eq:cvCmCV1}
    \int_{S_{in}} V_{rn}\, dA = \int_{S_{out}} V_{rn}\,dA = 0
    \]

    Notice that the density does not play a role in this equation since it is canceled out. Physically, the meaning is that volume flow rate in and the volume flow rate out have to equal.

    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 5.3.2.1: Non Deformable Control Volume 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 5.3.2.1: Non Deformable Control Volume 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.

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