Incompressible flow

A fluid which does not change its density along a trajectory at a constant temperature and change in pressure is incompressible called - in contrast to the compressible fluids. This means, conversely, that fluids whose density changes, for example due to thermal influences, can be incompressible. Since these effects in practice are usually considerably smaller than changes in density due to pressure changes, a fluid is considered to be incompressible, the density along each trajectory is constant. However, constant overall density is not a criterion for incompressibility.

Incompressibility is therefore equivalent to the disappearance of compressibility, which is defined as the relative change in volume of a pressure change and a constant temperature. It is calculated according to the formula:

Incompressible fluids do not exist, but for most calculations, such as water in water pipes under normal conditions, one can assume an incompressible fluid. This simplifies the calculation often enormous and the error it is negligibly small.

The mathematical formulation of the incompressibility derived, neglecting a possible temperature dependence, from the continuity equation as a vanishing divergence of the flow from:

The underlying mathematical model, the equations of the Navier-Stokes.

In the hydraulic or fluid power, however, is the low compressibility of the hydraulic fluid to be not quite ignore. In many applications, it has to be carefully taken into account.