# Incompressible fluid

In fluid mechanics, an **incompressible fluid** is a fluid whose density (often represented by the Greek letter *ρ*) is constant: it is the same throughout the field and it does not change through time. It is an idealization used to simplify analysis. In reality, all fluids are compressible to some extent.

Partial differential equations for incompressible fluids are as follows:

- .

**v**of an incompressible fluid is zero.

### Proof

The continuity equation is- .

## Relation to Solenoidal Field

An incompressible fluid is described by a velocity field which is solenoidal. But a solenoidal field, besides having a zero divergence, also has the additional connotation of having non-zero curl (i.e. a rotational component).Otherwise, if an incompressible fluid also has a curl of zero, so that it is also irrotational, then the velocity field is actually Laplacian.