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

Grow112

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By introducing the enthalpy

. . . . .\(\displaystyle h\, =\, e\, +\, \dfrac{p}{\rho}\)

into the energy equation

. . . . .\(\displaystyle \dfrac{De}{Dt}\, +\, \dfrac{pD(\rho^{-1})}{Dt}\, =\, 0\)

show that, for steady flow,

. . . . .\(\displaystyle h_x\, -\, \dfrac{1}{\rho}p_x\, =\, 0\)

Prove that

. . . . .\(\displaystyle h\, +\, \dfrac{1}{2}v^2\, =\, \mbox{constant}\)



Any help is appreciated
 

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One dimensional dynamic system

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By introducing the enthalpy

. . . . .\(\displaystyle h\, =\, e\, +\, \dfrac{p}{\rho}\)

into the energy equation

. . . . .\(\displaystyle \dfrac{De}{Dt}\, +\, \dfrac{pD(\rho^{-1})}{Dt}\, =\, 0\)

show that, for steady flow,

. . . . .\(\displaystyle h_x\, -\, \dfrac{1}{\rho}p_x\, =\, 0\)

Prove that

. . . . .\(\displaystyle h\, +\, \dfrac{1}{2}v^2\, =\, \mbox{constant}\)



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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