Incompressible Flow

Incompressible flow is a flow in which the material density does not vary over time. It is a theoretical model of fluid flow which can be used to describe real fluids under certain conditions.

Mathematically, it can be defined as a flow when the divergence of fluid velocity \(\vec u\) is zero:

\[\nabla \cdot \vec u = 0\]

In fact, this holds for any homogeneous and incompressible material with constant density throughout its volume.

An ideal fluid is a model of fluids often used in fluid mechanics to approximate the behavior of real fluids. Ideal fluids are:

  1. non-viscous, i.e. there is no internal resistance to flow,

  2. in steady, or laminar, flow,

  3. incompressible (see above),

  4. irrotational, i.e. its particles undergo no rotation around their center of mass.

Links:

  1. Wikipedia — Incompressible flow

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