Editing Euler equations (fluid dynamics) (section)

===Incompressible constraint (revisited)===
Coming back to the incompressible case, it now becomes apparent that the ''incompressible constraint'' typical of the former cases actually is a particular form valid for incompressible flows of the ''energy equation'', and not of the mass equation. In particular, the incompressible constraint corresponds to the following very simple energy equation:
<math display="block">\frac{D e}{D t} = 0.</math>

Thus '''for an incompressible inviscid fluid the specific internal energy is constant along the flow lines''', also in a time-dependent flow. The pressure in an incompressible flow acts like a [[Lagrange multiplier]], being the multiplier of the incompressible constraint in the energy equation, and consequently in incompressible flows it has no thermodynamic meaning. In fact, thermodynamics is typical of compressible flows and degenerates in incompressible flows.{{sfn|Quartapelle|Auteri|2013|p=13|loc=Ch. 9}}

Basing on the mass conservation equation, one can put this equation in the conservation form:
<math display="block">{\partial \rho e \over \partial t} + \nabla \cdot (\rho e \mathbf u) = 0, </math>
meaning that for an incompressible inviscid nonconductive flow a continuity equation holds for the internal energy.