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In
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) and ...
, 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) and ...
. As it moves, the
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementa ...
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 Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
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 of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a fie ...
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. Considering a velocity vector field in three-dimensional space in the framework of ...
; 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, experien ...
. The fluid parcels, as used in continuum mechanics, are to be distinguished from microscopic
particle In the physical sciences, a particle (or corpuscule 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 natural science that studies matter, its 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 which relat ...
. Fluid parcels describe the
average In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7 ...
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 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 named ...
to be small, as is also a pre-requisite for the
continuum hypothesis In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that or equivalently, that In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to ...
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, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) o ...
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