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Thread: Enthalpy: Show that h_x - (1/rho)p_x = 0, h + v^2/2 = (constant)

  1. #1

    Enthalpy: Show that h_x - (1/rho)p_x = 0, h + v^2/2 = (constant)

    By introducing the enthalpy

    . . . . .[tex]h\, =\, e\, +\, \dfrac{p}{\rho}[/tex]

    into the energy equation

    . . . . .[tex]\dfrac{De}{Dt}\, +\, \dfrac{pD(\rho^{-1})}{Dt}\, =\, 0[/tex]

    show that, for steady flow,

    . . . . .[tex]h_x\, -\, \dfrac{1}{\rho}p_x\, =\, 0[/tex]

    Prove that

    . . . . .[tex]h\, +\, \dfrac{1}{2}v^2\, =\, \mbox{constant}[/tex]



    Any help is appreciated
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    Last edited by stapel; 11-10-2017 at 03:47 PM. Reason: Typing out the text in the graphic; creating useful subject line.

  2. #2

    One dimensional dynamic system

    Last edited by Grow112; 11-08-2017 at 11:15 PM.

  3. #3
    Elite Member stapel's Avatar
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    Cool

    Quote Originally Posted by Grow112 View Post
    By introducing the enthalpy

    . . . . .[tex]h\, =\, e\, +\, \dfrac{p}{\rho}[/tex]

    into the energy equation

    . . . . .[tex]\dfrac{De}{Dt}\, +\, \dfrac{pD(\rho^{-1})}{Dt}\, =\, 0[/tex]

    show that, for steady flow,

    . . . . .[tex]h_x\, -\, \dfrac{1}{\rho}p_x\, =\, 0[/tex]

    Prove that

    . . . . .[tex]h\, +\, \dfrac{1}{2}v^2\, =\, \mbox{constant}[/tex]



    Any help is appreciated
    Please reply showing your thoughts and efforts so far. When you reply, please include definitions for the various variables, and the relationships between them. (We can try to help you with the math, but you'll need to provide the thermodynamics, etc, info.) Thank you!

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