@wikipedia
The fluid flow with zero material derivative of its density:
| LaTeX Math Block |
|---|
|
\frac{D \rho}{ Dt} = \frac{\partial \rho}{\partial t} + \rho \cdot \nabla {\bf u} = 0 |
With which is equivalent to (with account of Continuity equation):
| LaTeX Math Block |
|---|
| anchor | 3divergence |
|---|
| alignment | left |
|---|
|
\frac{\partial \rho}{\partial t} + \nabla (\rho \, {\bf u}) = 0 |
the and means that velocity of Incompressible flow criteria simplifies to:
| LaTeX Math Block |
|---|
|
\nabla {\bf u} = 0 |
is solenoidal.
The term Incompressible flow is a misnomer as it does not necessarily mean It does not necessarily means that the fluid itself is incompressible.
In many practical applications condition
| LaTeX Math Block Reference |
|---|
|
is met for compressible fluids (at least when fluid compressibility is relatively small) and the fluid flow satisfies | LaTeX Math Block Reference |
|---|
|
and is called incompressible flow.
See also
...
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Fluid flow
...
