Different forms of fluid energy conservation equations

[happyparticle]

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.

I though I had to start with$\frac{Dp}{Dt} + \gamma p \nabla\cdot \vec{u} = 0$

The starting point has to be the energy equation and the mass balance equation, also known as continuity equation.

Basically, I have to do what @pasmith says in post #2?

 

[Chestermiller]

I though I had to start with$\frac{Dp}{Dt} + \gamma p \nabla\cdot \vec{u} = 0$

I don’t think so. This equation can be derived.

 

[happyparticle]

I don’t think so. This equation can be derived.

I guess I misread post #3

I guess I finally found both expression. I think I was completely wrong since the beginning. More than I thought.