Incompressible flow

Incompressible flow is fluid motion in which each moving fluid element retains constant density. In continuum models, it is commonly represented by a velocity field with zero divergence.

Continuity equation: The equation expressing conservation of mass in a moving fluid. For constant density, mass conservation reduces to the zero-divergence constraint.
Density: Mass per unit volume of a material. Incompressibility concerns whether density changes as a fluid element moves.
Potential flow: An idealized flow with velocity expressible as the gradient of a scalar potential. Its incompressible form obeys Laplace’s equation, enabling tractable flow solutions.
Compressible flow: Fluid motion in which density changes significantly within the flow. It retains density variations that incompressible-flow models set aside.
Divergence: A measure of the net outward flow of a vector field per unit volume. Its value for the velocity field distinguishes local expansion from incompressible motion.
Material derivative: The rate of change of a quantity following a moving fluid element. It expresses the density-change condition along each fluid trajectory.
Boundary layer: A thin region near a surface where viscosity strongly affects fluid motion. Incompressible boundary-layer equations model many low-speed flows over bodies.
Sound wave: A propagating pressure and density disturbance transmitted through a medium. Acoustic waves rely on compressibility, unlike the usual incompressible-flow approximation.
Pressure Poisson equation: An elliptic equation that determines pressure from velocity and forcing in incompressible flow. Pressure adjusts throughout the fluid to keep the velocity divergence-free.
Continuum mechanics: The study of materials modeled as continuously distributed matter. Incompressible flow uses continuum fields to describe fluid motion and density.

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