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

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

By introducing the enthalpy

. . . . .$h\, =\, e\, +\, \dfrac{p}{\rho}$

into the energy equation

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

. . . . .$h_x\, -\, \dfrac{1}{\rho}p_x\, =\, 0$

Prove that

. . . . .$h\, +\, \dfrac{1}{2}v^2\, =\, \mbox{constant}$

Any help is appreciated

2. ## One dimensional dynamic system

3. Originally Posted by Grow112
By introducing the enthalpy

. . . . .$h\, =\, e\, +\, \dfrac{p}{\rho}$

into the energy equation

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

. . . . .$h_x\, -\, \dfrac{1}{\rho}p_x\, =\, 0$

Prove that

. . . . .$h\, +\, \dfrac{1}{2}v^2\, =\, \mbox{constant}$

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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