fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

, within the framework of

continuum mechanics Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such m ...

, a fluid parcel is a very small amount of fluid, identifiable throughout its dynamic history while moving with the

fluid flow In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

. As it moves, the mass of a fluid parcel remains constant, while—in a compressible flow—its volume may change. And its shape changes due to the distortion by the flow. In an

incompressible flow In fluid mechanics or more generally continuum mechanics, incompressible flow ( isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An e ...

the volume of the fluid parcel is also a constant ( isochoric flow). This mathematical concept is closely related to the description of fluid motion—its

kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, Physical object, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause ...

and dynamics—in a Lagrangian frame of reference. In this reference frame, fluid parcels are labelled and followed through space and time. But also in the Eulerian frame of reference the notion of fluid parcels can be advantageous, for instance in defining the material derivative, streamlines, streaklines, and pathlines; or for determining the Stokes drift. The fluid parcels, as used in continuum mechanics, are to be distinguished from microscopic particles (molecules and atoms) in physics. Fluid parcels describe the average velocity and other properties of fluid particles, averaged over a

length scale In physics, length scale is a particular length or distance determined with the precision of at most a few orders of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot aff ...

which is large compared to the mean free path, but small compared to the typical length scales of the specific flow under consideration. This requires the Knudsen number to be small, as is also a pre-requisite for the continuum hypothesis to be a valid one. Further note, that unlike the mathematical concept of a fluid parcel which can be uniquely identified—as well as exclusively distinguished from its direct neighbouring parcels—in a real fluid such a parcel would not always consist of the same particles. Molecular diffusion will slowly evolve the parcel properties. For air flow, the corresponding term is air parcel. Another name for fluid parcel is material element of fluid. Correspondingly, also the notions of material line and material surface can be introduced, always consisting of the same material elements and moving with the fluid flow. Yet another name used for fluid parcel is fluid element.

References

Bibliography

* * * * * {{cite book, isbn=978-3-319-59694-5 , last1=Badin, first1=G., last2=Crisciani, first2=F., title=Variational Formulation of Fluid and Geophysical Fluid Dynamics - Mechanics, Symmetries and Conservation Laws - , publisher=Springer, year=2018 , pages=218 , doi= 10.1007/978-3-319-59695-2, s2cid=125902566 Fluid dynamics Continuum mechanics