compresibles

Compressibles denote substances whose density changes significantly with pressure. The term is most often applied to gases, whose compressibility is high, but all real materials are compressible to some extent. The behavior of compressible materials is described by an equation of state that relates pressure, density, and temperature. For gases under many conditions, the ideal gas law p = ρ R T provides a simple model, while the bulk modulus K = ρ (∂p/∂ρ)_T quantifies stiffness. The speed of sound in a compressible medium is c = sqrt(K/ρ) (or equivalently c = sqrt(γ p / ρ) for an ideal gas with γ = C_p/C_v).

Compressible flow concerns the motion of fluids where density changes are nonnegligible, especially at high speeds. It is governed by the compressible form of the Navier-Stokes equations together with an equation of state. The Mach number, M = v/c, characterizes flow regimes; phenomena such as shock waves and expansion fans arise when M crosses unity. Real-fluid effects and phase changes require nonideal equations of state and, for liquids and solids, finite compressibility given by the bulk modulus.

Common measures include the isothermal compressibility β_T = −(1/V)(∂V/∂P)_T and the adiabatic compressibility β_S = −(1/V)(∂V/∂P)_S. In many engineering contexts, liquids are treated as approximately incompressible because their compressibility is small; gases are highly compressible, and solids have relatively small but finite compressibility. Applications span aerodynamics, acoustics, shock-wave physics, and material science.