It is shown in the derivation below that ( under the right conditions ) even compressible fluids can to a good approximation be modelled as an incompressible flow.
32.
Convective acceleration is present in most flows ( exceptions include one-dimensional incompressible flow ), but its dynamic effect is disregarded in creeping flow ( also called Stokes flow ).
33.
Cnoidal waves can be derived directly from the incompressible flow equations, and expressed in terms of three invariants of the flow, as shown by in their research on undular bores.
34.
The incompressible flow assumption typically holds well with all fluids at low Mach numbers ( say up to about Mach 0.3 ), such as for modelling air winds at normal temperatures.
35.
The pressure in an incompressible flow acts like a Lagrange multiplier, being the multiplier of the incompressible constraint in the energy equation, and consequently in incompressible flows it has no thermodynamic meaning.
36.
The pressure in an incompressible flow acts like a Lagrange multiplier, being the multiplier of the incompressible constraint in the energy equation, and consequently in incompressible flows it has no thermodynamic meaning.
37.
Even in compressible flows, the term involving " ? " is often negligible; however it can occasionally be important even in nearly incompressible flows and is a matter of controversy.
38.
S . K . Sen and P . L . Bhatnagar, A numerical procedure for steady viscous incompressible flow in a channel bounded by two parallel infinite planes with a rectangular cavity, Unpublished.
39.
For the special case of an incompressible flow, the pressure constrains the flow so that the volume of fluid elements is constant : isochoric flow resulting in a solenoidal velocity field with 0 . }}
40.
In this cylindrical coordinate system, the incompressible flow can be described with a Stokes stream function " ? ", depending on " r " and " z ":
