Incompressibilnost

Incompressibilnost (incompressibility) is a concept used in physics and engineering to describe a property of a material or fluid in which density remains effectively constant when subjected to pressure or mechanical load. For liquids, density changes with pressure are typically very small, so they are often treated as incompressible. For solids, the degree of compressibility varies; many metals and ceramics are relatively incompressible, while polymers may be notably more compressible. The relation between pressure change and volume change is ΔP = K ΔV/V, where K is the bulk modulus; large K corresponds to small volume changes.

In fluid dynamics, incompressible flow refers to constant density in time, so ρ is constant and the continuity equation reduces to ∇·v = 0, meaning the velocity field has zero divergence. Pressure acts as a Lagrange multiplier enforcing this constraint; density changes due to heating or compressibility are neglected in the simplified model. Compressibility effects appear when density varies or when acoustic waves are present.

In solids and continuum mechanics, the incompressible limit corresponds to a Poisson's ratio approaching 0.5, where volumetric strains vanish under external loading. In reality, no material is perfectly incompressible, but many are nearly so, and incompressibility is a common assumption in finite element modeling. Mixed formulations can be used to handle the pressure-density coupling.

Applications and limitations: The incompressible assumption simplifies analysis in hydraulics, biomechanics and many steady flows. It is inappropriate for high-speed gas dynamics, shock waves or scenarios with large pressure changes where density variations are significant. Measurements and constitutive models should account for compressibility when precision demands it.