noncompressible

Noncompressible is a term used in physics and engineering to describe a material or flow in which density remains essentially constant under changes in pressure. In practice, it is most often applied as an approximation for liquids with a high bulk modulus, where density changes are small over the range of pressures considered. The closely related term incompressible is more common in literature.

In thermodynamics and continuum mechanics, compressibility is quantified by the compressibility coefficient β = -(1/V)(∂V/∂P)_T, or by the bulk modulus K = -V(∂P/∂V) = ρ(∂P/∂ρ). The incompressible limit corresponds to β → 0 (or K → ∞). For incompressible fluids, the continuity equation simplifies to ∇·u = 0, meaning the fluid’s volume element preserves its volume during flow.

Commonly, liquids such as water are treated as incompressible in many engineering problems because their density changes with pressure are small. For example, water at room temperature has a bulk modulus around 2.2 GPa, giving a compressibility of roughly 4.5×10^-10 Pa^-1. Some oils and other liquids are also treated as incompressible in practical calculations. Solids can be nearly incompressible as well; metals like steel have even larger bulk moduli, making volume changes under ordinary loads minimal.

Limitations include the fact that no material is perfectly incompressible. At high pressures, high-frequency phenomena, or large deformations, density can change noticeably, and compressibility must be included in models. Gas behavior is inherently compressible, and the incompressible assumption is rarely valid there.