In contrast to incompressible inviscid flows where one-dimensional analysis is unexciting and yields only a very limited amount of useful information, one-dimensional analysis of a compressible flow gives rise to many useful concepts which we will cover in this lesson. One-dimensional conservation laws are valid across shock discontinuities and expansion fans, and, together with thermodynamic relations, provide fundamental relations to describe shocks, fans and other phenomena in compressible flows. Although we will not be discussing the flow across shocks and other compressible waves yet, we will show how one-dimensional conservation of energy can be re-arranged into a set of isentropic relations connecting static and total quantities which play an extremely important role in the analysis of compressible waves. We will also introduce the stagnation (or total) and sonic conditions in this lesson and discuss their physical significance and mathematical relations. Let us now take a look at these 1D governing equations of a compressible gas flow.
Here are the accompanying handout slides for this lesson.