incompresibles

Incompresibles, or incompressibles, refer to substances whose density remains effectively constant under applied pressure. The term is used in physics, engineering, and fluid dynamics to describe materials with very low compressibility on the scales of interest. In practice, many liquids are treated as incompressible because their bulk modulus is large (for example, water), while gases and some solids can be approximated as incompressible only under specific conditions.

In fluid dynamics, the incompressible flow assumption implies that density is constant in time and space, which leads to the condition that the divergence of the velocity field is zero (∇·v = 0). This simplifies the Navier–Stokes equations and allows pressure to be determined without tracking density changes. The approximation is valid when density variations due to pressure are small, typically at low Mach numbers (well below about 0.3) and modest temperature variations. It also underpins many hydraulic and low-speed aerodynamic analyses.

Common incompressibles include water and many oils; air is often treated as incompressible in low-speed flows but becomes significantly compressible at higher speeds. The degree of incompressibility is quantified by the bulk modulus K, with small pressure changes ΔP producing relative volume changes ΔV/V ≈ -ΔP/K. Water has a bulk modulus around 2.2 GPa; gases have much smaller values and are thus more compressible. Incompressibility is an approximation and may break down under high pressures, large temperature changes, or high-speed flows where compressibility effects such as sound waves and shocks become important.