Editing Fluid dynamics (section)

===Compressible versus incompressible flow===
All fluids are [[compressibility|compressible]] to an extent; that is, changes in pressure or temperature cause changes in density. However, in many situations the changes in pressure and temperature are sufficiently small that the changes in density are negligible. In this case the flow can be modelled as an [[incompressible flow]]. Otherwise the more general [[compressible flow]] equations must be used.

Mathematically, incompressibility is expressed by saying that the density {{mvar|ρ}} of a [[fluid parcel]] does not change as it moves in the flow field, that is,
<math display="block">\frac{\mathrm{D} \rho}{\mathrm{D}t} = 0 \, ,</math>
where {{math|{{sfrac|D|D''t''}}}} is the [[material derivative]], which is the sum of [[time derivative|local]] and [[convective derivative]]s. This additional constraint simplifies the governing equations, especially in the case when the fluid has a uniform density.

For flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the [[Mach number]] of the flow is evaluated. As a rough guide, compressible effects can be ignored at Mach numbers below approximately 0.3. For liquids, whether the incompressible assumption is valid depends on the fluid properties (specifically the critical pressure and temperature of the fluid) and the flow conditions (how close to the critical pressure the actual flow pressure becomes). [[acoustics|Acoustic]] problems always require allowing compressibility, since [[sound waves]] are compression waves involving changes in pressure and density of the medium through which they propagate.