Conservation Equations for Mass, Momentum and Energy

Abstract

In Chapters 2 and 3. we discussed the continuity and momentum equations for incompressible flows. Here, we extend the discussion to compressible flows. If the typical temperature difference in a gas flow is an appreciable fraction of the absolute temperature, the typical density difference will be an appreciable fraction of the absolute density, and the density appearing in the velocity field equations discussed in the previous chapters can no longer be taken as constant. Instead, the conservation equations for momentum and energy must be solved simultaneously since they are coupled, i.e., density appears in the momentum equations and is linked through an equation of state to the dependent variable of the energy equation.