The forum discussion centers on deriving fluid energy conservation equations, specifically the expressions ##\frac{Dp}{Dt} + \gamma p \nabla\cdot \vec{u} = 0## and ##\frac{D}{Dt} \frac{p}{\rho^{\gamma}} = 0## from the initial equation ##\frac{De}{Dt} + (\gamma - 1)e \nabla \cdot \vec{u} = - \frac{1}{\rho} (\vec{u} \cdot \nabla)p##. Participants emphasize the importance of the material derivative and the continuity equation in these derivations. The discussion also highlights the need to incorporate kinetic energy into the energy balance for accurate results, referencing the work of Bird et al. in "Transport Phenomena".
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I though I had to start with##Chestermiller said:This equation is the expression for adiabatic reversible expansion or compression of an ideal gas.
This can be derived from the previous equation using the continuity equation.
Basically, I have to do what @pasmith says in post #2?The starting point has to be the energy equation and the mass balance equation, also known as continuity equation.
I don’t think so. This equation can be derived.happyparticle said:I though I had to start with##
\frac{Dp}{Dt} + \gamma p \nabla\cdot \vec{u} = 0
##
I guess I misread post #3Chestermiller said:I don’t think so. This equation can be derived.