Fluid mechanics is the branch of
physics concerned with the
mechanics of
fluids (
liquids,
gas
Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma).
A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...
es, and
plasmas) and the
forces on them.
It has applications in a wide range of disciplines, including
mechanical,
aerospace
Aerospace is a term used to collectively refer to the atmosphere and outer space. Aerospace activity is very diverse, with a multitude of commercial, industrial and military applications. Aerospace engineering consists of aeronautics and astr ...
,
civil,
chemical and
biomedical engineering
Biomedical engineering (BME) or medical engineering is the application of engineering principles and design concepts to medicine and biology for healthcare purposes (e.g., diagnostic or therapeutic). BME is also traditionally logical sciences ...
,
geophysics,
oceanography,
meteorology
Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...
,
astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the he ...
, and
biology
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...
.
It can be divided into
fluid statics, the study of fluids at rest; and
fluid dynamics, the study of the effect of forces on fluid motion.
It is a branch 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 subject which models matter without using the information that it is made out of atoms; that is, it models matter from a ''macroscopic'' viewpoint rather than from ''microscopic''. Fluid mechanics, especially fluid dynamics, is an active field of research, typically mathematically complex. Many problems are partly or wholly unsolved and are best addressed by
numerical methods, typically using computers. A modern discipline, called
computational fluid dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the ...
(CFD), is devoted to this approach.
Particle image velocimetry, an experimental method for visualizing and analyzing fluid flow, also takes advantage of the highly visual nature of fluid flow.
Brief history
The study of fluid mechanics goes back at least to the days of
ancient Greece
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cult ...
, when
Archimedes
Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scientists i ...
investigated fluid statics and
buoyancy
Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pr ...
and formulated his famous law known now as the
Archimedes' principle
Archimedes' principle (also spelled Archimedes's principle) states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. Archimedes ...
, which was published in his work ''
On Floating Bodies''—generally considered to be the first major work on fluid mechanics. Rapid advancement in fluid mechanics began with
Leonardo da Vinci (observations and experiments),
Evangelista Torricelli (invented the
barometer
A barometer is a scientific instrument that is used to measure air pressure in a certain environment. Pressure tendency can forecast short term changes in the weather. Many measurements of air pressure are used within surface weather analysis ...
),
Isaac Newton (investigated
viscosity) and
Blaise Pascal
Blaise Pascal ( , , ; ; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic writer.
He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest m ...
(researched
hydrostatics, formulated
Pascal's law
Pascal's law (also Pascal's principle or the principle of transmission of fluid-pressure) is a principle in fluid mechanics given by Blaise Pascal that states that a pressure change at any point in a confined incompressible fluid is transmitted ...
), and was continued by
Daniel Bernoulli with the introduction of mathematical fluid dynamics in ''Hydrodynamica'' (1739).
Inviscid flow was further analyzed by various mathematicians (
Jean le Rond d'Alembert,
Joseph Louis Lagrange
Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangia[Pierre-Simon Laplace
Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized ...](_blank)
,
Siméon Denis Poisson) and viscous flow was explored by a multitude of
engineers including
Jean Léonard Marie Poiseuille and
Gotthilf Hagen. Further mathematical justification was provided by
Claude-Louis Navier
Claude-Louis Navier (born Claude Louis Marie Henri Navier; ; 10 February 1785 – 21 August 1836) was a French mechanical engineer, affiliated with the French government, and a physicist who specialized in continuum mechanics.
The Navier–Stok ...
and
George Gabriel Stokes
Sir George Gabriel Stokes, 1st Baronet, (; 13 August 1819 – 1 February 1903) was an Irish English physicist and mathematician. Born in County Sligo, Ireland, Stokes spent all of his career at the University of Cambridge, where he was the L ...
in the
Navier–Stokes equations
In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician Geo ...
, and
boundary layers
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condi ...
were investigated (
Ludwig Prandtl
Ludwig Prandtl (4 February 1875 – 15 August 1953) was a German fluid dynamicist, physicist and aerospace scientist. He was a pioneer in the development of rigorous systematic mathematical analyses which he used for underlying the science of ...
,
Theodore von Kármán), while various scientists such as
Osborne Reynolds
Osborne Reynolds (23 August 1842 – 21 February 1912) was an Irish-born innovator in the understanding of fluid dynamics. Separately, his studies of heat transfer between solids and fluids brought improvements in boiler and condenser design. ...
,
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...
, and
Geoffrey Ingram Taylor
Sir Geoffrey Ingram Taylor OM FRS FRSE (7 March 1886 – 27 June 1975) was a British physicist and mathematician, and a major figure in fluid dynamics and wave theory. His biographer and one-time student, George Batchelor, described him as " ...
advanced the understanding of fluid viscosity and
turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
.
Main branches
Fluid statics
Fluid statics or hydrostatics is the branch of fluid mechanics that studies
fluids at rest. It embraces the study of the conditions under which fluids are at rest in
stable equilibrium; and is contrasted with
fluid dynamics, the study of fluids in motion. Hydrostatics offers physical explanations for many phenomena of everyday life, such as why
atmospheric pressure
Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1013.25 millibars, ...
changes with
altitude
Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
, why wood and
oil
An oil is any nonpolar chemical substance that is composed primarily of hydrocarbons and is hydrophobic (does not mix with water) & lipophilic (mixes with other oils). Oils are usually flammable and surface active. Most oils are unsaturated ...
float on water, and why the surface of water is always level whatever the shape of its container. Hydrostatics is fundamental to
hydraulics
Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counter ...
, the
engineering of equipment for storing, transporting and using
fluids. It is also relevant to some aspects of
geophysics and
astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the he ...
(for example, in understanding
plate tectonics and anomalies in the
Earth's gravitational field), to
meteorology
Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...
, to
medicine (in the context of
blood pressure), and many other fields.
Fluid dynamics
''
Fluid dynamics'' is a subdiscipline of fluid mechanics that deals with ''fluid flow''—the science of liquids and gases in motion. Fluid dynamics offers a systematic structure—which underlies these
practical disciplines
Applied science is the use of the scientific method and knowledge obtained via conclusions from the method to attain practical goals. It includes a broad range of disciplines such as engineering and medicine. Applied science is often contrasted ...
—that embraces empirical and semi-empirical laws derived from
flow measurement and used to solve practical problems. The solution to a
fluid dynamics problem typically involves calculating various properties of the fluid, such as
velocity,
pressure,
density, and
temperature, as functions of space and time. It has several subdisciplines itself, including ''
aerodynamics
Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dyn ...
'' (the study of air and other gases in motion) and ''hydrodynamics'' (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating
forces and
movement
Movement may refer to:
Common uses
* Movement (clockwork), the internal mechanism of a timepiece
* Motion, commonly referred to as movement
Arts, entertainment, and media
Literature
* "Movement" (short story), a short story by Nancy Fu ...
s on
aircraft
An aircraft is a vehicle that is able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines. ...
, determining the
mass flow rate
In physics and engineering, mass flow rate is the mass of a substance which passes per unit of time. Its unit is kilogram per second in SI units, and slug per second or pound per second in US customary units. The common symbol is \dot (''� ...
of
petroleum through pipelines, predicting evolving
weather
Weather is the state of the atmosphere, describing for example the degree to which it is hot or cold, wet or dry, calm or stormy, clear or cloudy. On Earth, most weather phenomena occur in the lowest layer of the planet's atmosphere, the t ...
patterns, understanding
nebula
A nebula ('cloud' or 'fog' in Latin; pl. nebulae, nebulæ or nebulas) is a distinct luminescent part of interstellar medium, which can consist of ionized, neutral or molecular hydrogen and also cosmic dust. Nebulae are often star-forming region ...
e in
interstellar space
Outer space, commonly shortened to space, is the expanse that exists beyond Earth and its atmosphere and between celestial bodies. Outer space is not completely empty—it is a near-perfect vacuum containing a low density of particles, predo ...
and modeling
explosions
An explosion is a rapid expansion in volume associated with an extreme outward release of energy, usually with the generation of high temperatures and release of high-pressure gases. Supersonic explosions created by high explosives are known ...
. Some fluid-dynamical principles are used in
traffic engineering and crowd dynamics.
Relationship to continuum mechanics
Fluid mechanics is a subdiscipline 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 ...
, as illustrated in the following table.
In a mechanical view, a fluid is a substance that does not support
shear stress; that is why a fluid at rest has the shape of its containing vessel. A fluid at rest has no shear stress.
Assumptions
The assumptions inherent to a fluid mechanical treatment of a physical system can be expressed in terms of mathematical equations. Fundamentally, every fluid mechanical system is assumed to obey:
*
Conservation of mass
In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass ca ...
*
Conservation of energy
In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means that ...
*
Conservation of momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and ...
*
The continuum assumption
For example, the assumption that mass is conserved means that for any fixed
control volume
In continuum mechanics and thermodynamics, a control volume (CV) is a mathematical abstraction employed in the process of creating mathematical models of physical processes. In an inertial frame of reference, it is a fictitious region of a given v ...
(for example, a spherical volume)—enclosed by a
control surface—the
rate of change of the mass contained in that volume is equal to the rate at which mass is passing through the surface from ''outside'' to ''inside'', minus the rate at which mass is passing from ''inside'' to ''outside''. This can be expressed as an
equation in integral form over the control volume.
The is an idealization 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 ...
under which fluids can be treated as
continuous, even though, on a microscopic scale, they are composed of
molecules
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...
. Under the continuum assumption, macroscopic (observed/measurable) properties such as density, pressure, temperature, and bulk velocity are taken to be well-defined at "infinitesimal" volume elements—small in comparison to the characteristic length scale of the system, but large in comparison to molecular length scale. Fluid properties can vary continuously from one volume element to another and are average values of the molecular properties. The continuum hypothesis can lead to inaccurate results in applications like supersonic speed flows, or molecular flows on nano scale.
Those problems for which the continuum hypothesis fails can be solved using
statistical mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...
. To determine whether or not the continuum hypothesis applies, the
Knudsen number, defined as the ratio of the molecular
mean free path to the characteristic length
scale, is evaluated. Problems with Knudsen numbers below 0.1 can be evaluated using the continuum hypothesis, but molecular approach (statistical mechanics) can be applied to find the fluid motion for larger Knudsen numbers.
Navier–Stokes equations
The Navier–Stokes equations (named after
Claude-Louis Navier
Claude-Louis Navier (born Claude Louis Marie Henri Navier; ; 10 February 1785 – 21 August 1836) was a French mechanical engineer, affiliated with the French government, and a physicist who specialized in continuum mechanics.
The Navier–Stok ...
and
George Gabriel Stokes
Sir George Gabriel Stokes, 1st Baronet, (; 13 August 1819 – 1 February 1903) was an Irish English physicist and mathematician. Born in County Sligo, Ireland, Stokes spent all of his career at the University of Cambridge, where he was the L ...
) are
differential equations that describe the force balance at a given point within a fluid. For an
incompressible fluid
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 ...
with vector velocity field
, the Navier–Stokes equations are
:
.
These differential equations are the analogues for deformable materials to Newton's equations of motion for particles – the Navier–Stokes equations describe changes in
momentum (
force) in response to
pressure and viscosity, parameterized by the
kinematic viscosity here. Occasionally,
body forces, such as the gravitational force or Lorentz force are added to the equations.
Solutions of the Navier–Stokes equations for a given physical problem must be sought with the help of
calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
. In practical terms, only the simplest cases can be solved exactly in this way. These cases generally involve non-turbulent, steady flow in which the
Reynolds number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domin ...
is small. For more complex cases, especially those involving
turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
, such as global weather systems, aerodynamics, hydrodynamics and many more, solutions of the Navier–Stokes equations can currently only be found with the help of computers. This branch of science is called
computational fluid dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the ...
.
Inviscid and viscous fluids
An inviscid fluid has no
viscosity,
. In practice, an inviscid flow is an
idealization, one that facilitates mathematical treatment. In fact, purely inviscid flows are only known to be realized in the case of
superfluidity
Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two i ...
. Otherwise, fluids are generally viscous, a property that is often most important within a
boundary layer
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condi ...
near a solid surface,
where the flow must match onto the
no-slip condition at the solid. In some cases, the mathematics of a fluid mechanical system can be treated by assuming that the fluid outside of boundary layers is inviscid, and then
matching its solution onto that for a thin
laminar
Laminar means "flat". Laminar may refer to:
Terms in science and engineering:
* Laminar electronics or organic electronics, a branch of material sciences dealing with electrically conductive polymers and small molecules
* Laminar armour or "band ...
boundary layer.
For fluid flow over a porous boundary, the fluid velocity can be discontinuous between the free fluid and the fluid in the porous media (this is related to the Beavers and Joseph condition). Further, it is useful at low
subsonic speeds to assume that gas is
incompressible
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 ...
—that is, the density of the gas does not change even though the speed and
static pressure
In fluid mechanics the term static pressure has several uses:
* In the design and operation of aircraft, ''static pressure'' is the air pressure in the aircraft's static pressure system.
* In fluid dynamics, many authors use the term ''static pres ...
change.
Newtonian versus non-Newtonian fluids
A Newtonian fluid (named after
Isaac Newton) is defined to be a
fluid whose
shear stress is linearly proportional to the
velocity gradient in the direction
perpendicular
In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can ...
to the plane of shear. This definition means regardless of the forces acting on a fluid, it ''continues to flow''. For example, water is a Newtonian fluid, because it continues to display fluid properties no matter how much it is stirred or mixed. A slightly less rigorous definition is that the
drag of a small object being moved slowly through the fluid is proportional to the force applied to the object. (Compare
friction). Important fluids, like water as well as most gasses, behave—to good approximation—as a Newtonian fluid under normal conditions on Earth.
By contrast, stirring a
non-Newtonian fluid
A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, i.e., constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup, for ex ...
can leave a "hole" behind. This will gradually fill up over time—this behavior is seen in materials such as pudding,
oobleck, or
sand (although sand isn't strictly a fluid). Alternatively, stirring a non-Newtonian fluid can cause the viscosity to decrease, so the fluid appears "thinner" (this is seen in non-drip
paints). There are many types of non-Newtonian fluids, as they are defined to be something that fails to obey a particular property—for example, most fluids with long molecular chains can react in a non-Newtonian manner.
Equations for a Newtonian fluid
The constant of proportionality between the viscous stress tensor and the velocity gradient is known as the
viscosity. A simple equation to describe incompressible Newtonian fluid behavior is
:
where
:
is the shear stress exerted by the fluid ("
drag")
:
is the fluid viscosity—a constant of proportionality
:
is the velocity gradient perpendicular to the direction of shear.
For a Newtonian fluid, the viscosity, by definition, depends only on
temperature, not on the forces acting upon it. If the fluid is
incompressible
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 equation governing the viscous stress (in
Cartesian coordinates
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in ...
) is
:
where
:
is the shear stress on the
face of a fluid element in the
direction
:
is the velocity in the
direction
:
is the
direction coordinate.
If the fluid is not incompressible the general form for the viscous stress in a Newtonian fluid is
:
where
is the second viscosity coefficient (or bulk viscosity). If a fluid does not obey this relation, it is termed a
non-Newtonian fluid
A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, i.e., constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force to either more liquid or more solid. Ketchup, for ex ...
, of which there are several types. Non-Newtonian fluids can be either plastic, Bingham plastic, pseudoplastic, dilatant, thixotropic, rheopectic, viscoelastic.
In some applications, another rough broad division among fluids is made: ideal and non-ideal fluids. An ideal fluid is non-viscous and offers no resistance whatsoever to a shearing force. An ideal fluid really does not exist, but in some calculations, the assumption is justifiable. One example of this is the flow far from solid surfaces. In many cases, the viscous effects are concentrated near the solid boundaries (such as in boundary layers) while in regions of the flow field far away from the boundaries the viscous effects can be neglected and the fluid there is treated as it were inviscid (ideal flow). When the viscosity is neglected, the term containing the viscous stress tensor
in the Navier–Stokes equation vanishes. The equation reduced in this form is called the
Euler equation.
See also
*
Transport phenomena
*
Aerodynamics
Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dyn ...
*
Applied mechanics
Applied mechanics is the branch of science concerned with the motion of any substance that can be experienced or perceived by humans without the help of instruments. In short, when mechanics concepts surpass being theoretical and are applied and e ...
*
Bernoulli's principle
In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after the Swiss mathematic ...
*
Communicating vessels
*
Computational fluid dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the ...
*
Compressor map
*
Secondary flow
In fluid dynamics, flow can be decomposed into primary plus secondary flow, a relatively weaker flow pattern superimposed on the stronger primary flow pattern. The primary flow is often chosen to be an exact solution to simplified or approximated ...
*
Different types of boundary conditions in fluid dynamics
Boundary conditions in fluid dynamics are the set of constraints to boundary value problems in computational fluid dynamics. These boundary conditions include inlet boundary conditions, outlet boundary conditions, wall boundary conditions, constant ...
References
Further reading
*
*
*
*
*
External links
Free Fluid Mechanics booksAnnual Review of Fluid MechanicsCFDWiki– the Computational Fluid Dynamics reference wiki.
Educational Particle Image Velocimetry – resources and demonstrations
{{DEFAULTSORT:Fluid Mechanics
Civil engineering