The discussion revolves around deriving fluid energy conservation equations, specifically focusing on the relationships between pressure, density, and energy in the context of fluid dynamics. The subject area includes thermodynamics and fluid mechanics, particularly concerning adiabatic processes and the behavior of ideal gases.
The discussion is active, with participants sharing their approaches and reasoning. Some have provided insights into the relationships between different equations, while others express uncertainty about how to proceed with their derivations. There is no explicit consensus on the methods to derive the desired equations, but several productive lines of inquiry are being explored.
Participants note the complexity of the equations involved and the potential independence of certain expressions. There are references to specific conditions under which the equations apply, such as adiabatic processes, and discussions about the implications of the continuity equation and material derivatives.
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
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I guess I misread post #3Chestermiller said:I don’t think so. This equation can be derived.