IV - Equations

Abstract

In acoustics as well as shock-wave physics and detonics, a primary relation among the pressure (p), density (ρ), and internal energy (E) exists: p = f(ρ, E). The application of Newton's law (force = mass acceleration) to a fixed volume in a flow results in the Euler equation. Therefore, convective terms are present in greater than one-dimensional flow. These terms are ignored (by linearization) both in acoustics and in current shock relations, though they take into account that particles are moved into domains of a different flow velocity (u). This chapter provides comparison of the properties of the plane and spherical waves. The plane wave impedance is always constant and independent from any geometry and wave shape, as assumed in the plane-wave detonation theory. Spherical waves have a near-field term, while plane waves do not. Ignoring the near-field near a source is a most serious fault. Therefore, considerations near a hot spot in terms of plane waves are of no significance.