ABSTRACT
One-dimensional motions of a liquid or gas are determined as motions whose characteristics depend only on a single geometrical coordinate and on time. It can be shown that one-dimensional motions are produced only by spherical, cylindrical, and plane waves. In order to characterize problems that can be solved by dimensional theory methods, this chapter considers the desired functions and characteristic parameters of one-dimensional motion. One can establish independently of particular boundary or initial conditions algebraic integrals for the system of ordinary differential equations by means of dimensional theory considerations for self-similar motions. In other words, in a general case one can always reduce the order of the system of ordinary equations. To determine the system of governing parameters and similarity conditions, one should note dimensional and dimensionless parameters — the body characteristics determining its sizes and shape, its mass and distribution over the body, the parameters characterizing the internal cohesion, and body inertia.
