In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric flow) refers to a flow in which the material density is constant within a fluid parcel – an infinitesimal volume that moves with the velocity of the fluid. An equivalent statement implying incompressibility is, that the divergence of the fluid velocity is zero (see the derivation below, which illustrates why these conditions are equivalent).
Incompressible flow does not imply that the fluid itself is incompressible. It is shown in the derivation below that (under the right conditions) even compressible fluids can – to good approximation – be modelled as an incompressible flow. Incompressible flow implies that the density remains constant within a parcel of fluid which moves with the fluid velocity.
Read more about Incompressible Flow: Derivation, Relation To Compressibility, Relation To Solenoidal Field, Difference Between Incompressible Flow and Material, Related Flow Constraints, Numerical Approximations of Incompressible Flow
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