CHAPTER IV - One-Dimensional Unsteady Motion of a Gas

Abstract

This chapter focuses on the one-dimensional unsteady motion of a gas. The motion of a gas or liquid is said to be one dimensional when all its properties depend on only one geometric coordinate and on the time. It can be shown that the only possible one-dimensional motions are produced by spherical, cylindrical, and plane waves. The methods of dimensional analysis can be used to find exact solutions of certain problems of one-dimensional unsteady motion of a compressible fluid. To distinguish the problems which can be solved by the methods of dimensional analysis, the chapter analyzes the dependent variables and the fundamental parameters of one-dimensional motion. The problem of gas motion converging on a point and of dispersion from a point is reviewed in the chapter. The problems of focusing and of dispersion of a gas in a uniform initial state are particular cases of the more general first initial Cauchy problem.