fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

, a fluid parcel, also known as a fluid element or material element, is an

infinitesimal In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referred to the " ...

volume Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...

of fluid, identifiable throughout its dynamic history while moving with the fluid flow. As it moves, the

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

of a fluid parcel remains constant, while—in a

compressible flow Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressibility, compressible, flows are usually treated as being incompressible flow, incom ...

—its volume may change, and its shape changes due to distortion by the flow. In an

incompressible flow In fluid mechanics, or more generally continuum mechanics, incompressible flow is a flow in which the material density does not vary over time. Equivalently, the divergence of an incompressible flow velocity is zero. Under certain conditions, t ...

, the volume of the fluid parcel is also a constant ( isochoric flow). Material surfaces and material lines are the corresponding notions for

surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...

s and lines, respectively. The mathematical concept of a fluid parcel is closely related to the description of fluid motion—its

kinematics In physics, kinematics studies the geometrical aspects of motion of physical objects independent of forces that set them in motion. Constrained motion such as linked machine parts are also described as kinematics. Kinematics is concerned with s ...

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 In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field. The material de ...

streamlines, streaklines, and pathlines Streamlines, streaklines and pathlines are field lines in a fluid flow. They differ only when the flow changes with time, that is, when the flow is not steady flow, steady. Considering a velocity vector field in three-dimensional space in the f ...

; or for determining the

Stokes drift For a pure wave motion in fluid dynamics, the Stokes drift velocity is the average velocity when following a specific fluid parcel as it travels with the fluid flow. For instance, a particle floating at the free surface of water waves, experienc ...

. The fluid parcels, as used in

continuum mechanics Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a ''continuous medium'' (also called a ''continuum'') rather than as discrete particles. Continuum mec ...

, are to be distinguished from microscopic

particle In the physical sciences, a particle (or corpuscle in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from s ...

s (molecules and atoms) in

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

. Fluid parcels describe the

average In colloquial, ordinary language, an average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean the sum of the numbers divided by ...

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 af ...

which is large compared to the

mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...

, but small compared to the typical length scales of the specific flow under consideration. This requires the

Knudsen number The Knudsen number (Kn) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale. This length scale could be, for example, the radius of a body in a fluid. The number is nam ...

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 Molecular diffusion is the motion of atoms, molecules, or other particles of a gas or liquid at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid, size and density (or their product, ...

will slowly evolve the parcel properties.

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, bibcode=2018vffg.book.....B , s2cid=125902566 Fluid dynamics Continuum mechanics