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Encyclopedia > Fluid dynamics

--68.36.58.220 (talk) 22:59, 9 May 2008 (UTC)neyla

Continuum Mechanics
Conservation of mass
Conservation of momentum
Navier-Stokes equations
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Typical aerodynamic teardrop shape, showing the pressure distribution as the thickness of the black line and showing the velocity in the boundary layer as the violet triangles. The green vortex generators prompt the transition to turbulent flow and prevent back-flow also called flow separation from the high pressure region in the back. The surface in front is as smooth as possible or even employ shark like skin, as any turbulence here will reduce the energy of the airflow. The Kammback also prevents back flow from the high pressure region in the back across the spoilers to the convergent part. Putting stuff inside out results in tubes, they also face the problem of flow separation in their divergent parts, so called diffusers. Cutting the shape into halfs results in an aerofoil with the low pressure region on top leading to lift (force).

Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluid flow: fluids (liquids and gases) in motion. It has several subdisciplines itself, including aerodynamics (the study of gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and reportedly modeling fission weapon detonation. Some of its principles are even used in traffic engineering, where traffic is treated as a continuous fluid. This box:      Fluid mechanics is the study of how fluids move and the forces on them. ... This box:      A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of how small the applied stress. ... Fluid statics (also called hydrostatics) is the science of fluids at rest, and is a sub-field within fluid mechanics. ... For other uses, see Viscosity (disambiguation). ... A Newtonian fluid (named for Isaac Newton) is a fluid that flows like waterâ€”its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ... A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ... This box:      Surface tension is a property of the surface of a liquid that causes it to behave as an elastic sheet. ... Sir Isaac Newton FRS (4 January 1643 â€“ 31 March 1727) [ OS: 25 December 1642 â€“ 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Sir George Gabriel Stokes, 1st Baronet FRS (13 August 1819â€“1 February 1903), was an Irish mathematician and physicist, who at Cambridge made important contributions to fluid dynamics (including the Navier-Stokes equations), optics, and mathematical physics (including Stokes theorem). ... Claude-Louis Navier (born Claude Louis Marie Henri Navier on February 10, 1785 in Dijon, died August 21, 1836 in Paris) was a French engineer and physicist. ... Augustin Louis Cauchy Augustin Louis Cauchy (August 21, 1789 – May 23, 1857) was a French mathematician. ... Robert Hooke, FRS (July 18, 1635 â€“ March 3, 1703) was an English polymath who played an important role in the scientific revolution, through both experimental and theoretical work. ... In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. ... 1967 Model Cessna 182K in flight showing after-market vortex generators on the wing leading edge After-market Micro Dynamics vortex generators mounted on the wing of a Cessna 182K The Symphony SA-160 has two unique vortex generators on its wing to ensure aileron effectiveness through the stall A... Turbulent flow around an obstacle; the flow further away is laminar Laminar and turbulent water flow over the hull of a submarine Turbulence creating a vortex on an airplane wing In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by low-momentum diffusion, high momentum convection, and... Airflow separating from a wing which is at a high angle of attack All solid objects travelling through a fluid (or alternatively a stationary object exposed to a moving fluid) acquire a boundary layer of fluid around them where friction between the fluid molecules and the objects rough surface... Denticles or placoid scales are small outgrowths which cover the skin of many cartilaginous fish including sharks. ... A Kamm tail on a Citroen CX sedan This 1974 AMC Gremlin sports a Kamm tail according to AMC Audi A2 2004 Toyota Prius, an example of a Kammback achieving a drag coefficient of 0. ... This KLM cityhopper Fokker 70 still has its spoilers deployed (the cream-coloured panels projecting above the top surface of the wing) after landing at Bristol International Airport, England. ... Piping is used to convey fluids (usually liquids and gases but sometimes loose solids) from one location to another. ... A diffuser is an aerodynamic device primarily used on automobiles. ... An airfoil (or aerofoil in British English) is a specially shaped cross-section of a wing or blade, used to provide lift or downforce, depending on its application. ... The lift force, or simply lift, is a mechanical force, generated by a solid object as it moves through a fluid, directed perpendicular to the flow direction. ... This box:      Fluid mechanics is the study of how fluids move and the forces on them. ... This box:      A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of how small the applied stress. ... For other uses, see Liquid (disambiguation). ... For other uses, see Gas (disambiguation). ... For the Daft Punk song, see Aerodynamic (song). ... For other uses, see Force (disambiguation). ... It has been suggested that this article or section be merged with torque. ... Flying machine redirects here. ... Mass flow rate is the movement of mass per time. ... Petro redirects here. ... For the geological process, see Weathering or Erosion. ... The Triangulum Emission Nebula NGC 604 The Pillars of Creation from the Eagle Nebula For other uses, see Nebula (disambiguation). ... The interstellar medium (or ISM) is a term used in astronomy to describe the rarefied gas and dust that exists between the stars (or their immediate circumstellar environment) within a galaxy. ... For another meaning of the term traffic engineering, please see telecommunications traffic engineering. ...

Fluid dynamics offers a systematic structure that underlies these practical disciplines and that embraces empirical and semi-empirical laws, derived from flow measurement, used to solve practical problems. The solution of a fluid dynamics problem typically involves calculation of various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time. Flow measurement is the quantification of bulk fluid or gas movement. ... This article is about velocity in physics. ... This article is about pressure in the physical sciences. ... For other uses, see Density (disambiguation). ... For other uses, see Temperature (disambiguation). ...

## Equations of fluid dynamics GA_googleFillSlot("encyclopedia_square");

The foundational axioms of fluid dynamics are the conservation laws, specifically, conservation of mass, conservation of linear momentum (also known as Newton's Second Law of Motion), and conservation of energy (also known as First Law of Thermodynamics). These are based on classical mechanics and are modified in quantum mechanics and general relativity. They are expressed using the Reynolds Transport Theorem. In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov-Lavoisier law), states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... Newtons First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica. ... This article is about the law of conservation of energy in physics. ... In thermodynamics, the first law of thermodynamics is an expression of the more universal physical law of the conservation of energy. ... Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ... For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... For a generally accessible and less technical introduction to the topic, see Introduction to general relativity. ... Reynolds Transport Theorem Reynolds transport theorem is a fundamental theorem used in formulating the basic laws of fluid dynamics. ...

In addition to the above, fluids are assumed to obey the continuum assumption. Fluids are composed of molecules that collide with one another and solid objects. However, the continuum assumption considers fluids to be continuous, rather than discrete. Consequently, properties such as density, pressure, temperature, and velocity are taken to be well-defined at infinitesimally small points, and are assumed to vary continuously from one point to another. The fact that the fluid is made up of discrete molecules is ignored.

For fluids which are sufficiently dense to be a continuum, do not contain ionized species, and have velocities small in relation to the speed of light, the momentum equations for Newtonian fluids are the Navier-Stokes equations, which is a non-linear set of differential equations that describes the flow of a fluid whose stress depends linearly on velocity gradients and pressure. The unsimplified equations do not have a general closed-form solution, so they are only of use in Computational Fluid Dynamics or when they can be simplified. The equations can be simplified in a number of ways, all of which make them easier to solve. Some of them allow appropriate fluid dynamics problems to be solved in closed form. A Newtonian fluid (named for Isaac Newton) is a fluid that flows like waterâ€”its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ... In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... In mathematics, an equation or system of equations is said to have a closed-form solution just in case a solution can be expressed analytically in terms of a bounded number of well-known operations. ... A computer simulation of high velocity air flow around the Space Shuttle during re-entry. ...

In addition to the mass, momentum, and energy conservation equations, a thermodynamical equation of state giving the pressure as a function of other thermodynamic variables for the fluid is required to completely specify the problem. An example of this would be the perfect gas equation of state: Thermodynamics (from the Greek Î¸ÎµÏÎ¼Î·, therme, meaning heat and Î´Ï…Î½Î±Î¼Î¹Ï‚, dynamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Isotherms of an ideal gas The ideal gas law is the equation of state of a hypothetical ideal gas, first stated by BenoÃ®t Paul Ã‰mile Clapeyron in 1834. ...

$p= frac{rho R_u T}{M}$

where p is pressure, ρ is density, Ru is the gas constant, M is the molecular mass and T is temperature. This article is about pressure in the physical sciences. ... For other uses, see Density (disambiguation). ... The gas constant (also known as the molar, universal, or ideal gas constant, usually denoted by symbol R) is a physical constant which is featured in a large number of fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation. ... The molecular mass (abbreviated Mr) of a substance, formerly also called molecular weight and abbreviated as MW, is the mass of one molecule of that substance, relative to the unified atomic mass unit u (equal to 1/12 the mass of one atom of carbon-12). ... For other uses, see Temperature (disambiguation). ...

### Compressible vs incompressible flow

All fluids are compressible to some extent, that is changes in pressure or temperature will result in changes in density. However, in many situations the changes in pressure and temperature are sufficiently small that the changes in density are negligible. In this case the flow can be modeled as an incompressible flow. Otherwise the more general compressible flow equations must be used. Fluid Dynamics Compressibility (physics) is a measure of the relative volume change of fluid or solid as a response to a pressure (or mean stress) change: . For a gas the magnitude of the compressibility depends strongly on whether the process is adiabatic or isothermal, while this difference is small in... In fluid mechanics, an incompressible fluid is a fluid whose density (often represented by the Greek letter ρ) is constant: it is the same throughout the field and it does not change through time. ... A compressible flow is a situation in which the compressibility of a fluid must be taken into account. ...

Mathematically, incompressibility is expressed by saying that the density ρ of a fluid parcel does not change as it moves in the flow field, i.e.,

$frac{mathrm{D} rho}{mathrm{D}t} = 0 , ,$

where D / Dt is the substantial derivative, which is the sum of local and convective derivatives. This additional constraint simplifies the governing equations, especially in the case when the fluid has a uniform density. The convective derivative (also commonly known as the advective derivative, substantive derivative, or the material derivative) is a derivative taken with #REDIRECT respect to a coordinate system moving with velocity u, and is often used in fluid mechanics and classical mechanics. ...

For flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the Mach number of the flow is to be evaluated. As a rough guide, compressible effects can be ignored at Mach numbers below approximately 0.3. For liquids, whether the incompressible assumption is valid depends on the fluid properties (specifically the critical pressure and temperature of the fluid) and the flow conditions (how close to the critical pressure the actual flow pressure becomes). Acoustic problems always require allowing compressibility, since sound waves are compression waves involving changes in pressure and density of the medium through which they propagate. An F/A-18 Hornet breaking the sound barrier. ... Acoustics is the interdisciplinary sciences that always deals with the study of sound, ultrasound and infrasound (all mechanical waves in gases, liquids, and solids). ... This article is about compression waves. ...

### Viscous vs inviscid flow

Viscous problems are those in which fluid friction has significant effects on the fluid motion. For other uses, see Viscosity (disambiguation). ...

The Reynolds number can be used to evaluate whether viscous or inviscid equations are appropriate to the problem. In fluid mechanics, the Reynolds number may be described as the ratio of inertial forces (vsÏ) to viscous forces (Î¼/L) and, consequently, it quantifies the relative importance of these two types of forces for given flow conditions. ...

Stokes flow is flow at very low Reynolds numbers, such that inertial forces can be neglected compared to viscous forces. Stokes flow is a type of flow where inertial forces are small as compared to viscous forces. ...

On the contrary, high Reynolds numbers indicate that the inertial forces are more significant than the viscous (friction) forces. Therefore, we may assume the flow to be an inviscid flow, an approximation in which we neglect viscosity at all, compared to inertial terms. A fluid flow where viscous (friction) forces are small in comparison to inertial forces is said to be inviscid. ... For other uses, see Viscosity (disambiguation). ...

This idea can work fairly well when the Reynolds number is high. However, certain problems such as those involving solid boundaries, may require that the viscosity be included. Viscosity often cannot be neglected near solid boundaries because the no-slip condition can generate a thin region of large strain rate (known as Boundary layer) which enhances the effect of even a small amount of viscosity, and thus generating vorticity. Therefore, to calculate net forces on bodies (such as wings) we should use viscous flow equations. As illustrated by d'Alembert's paradox, a body in an inviscid fluid will experience no drag force. The standard equations of inviscid flow are the Euler equations. Another often used model, especially in computational fluid dynamics, is to use the Euler equations away from the body and the boundary layer equations, which incorporates viscosity, in a region close to the body. In fluid dynamics, the no-slip condition states that fluids stick to surfaces past which they flow. ... In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. ... For other uses, see Viscosity (disambiguation). ... Vorticity is a mathematical concept used in fluid dynamics. ... // DAlemberts paradox is a contradiction reached by French mathematician Jean le Rond dAlembert in 1752 [1] using inviscid theory in the form of potential solutions of the incompressible Euler equations, to prove that the drag of a body of any shape moving through an inviscid fluid is... In fluid dynamics, the Euler equations govern the compressible, Inviscid flow. ... In fluid dynamics, the Euler equations govern the compressible, Inviscid flow. ... In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. ...

The Euler equations can be integrated along a streamline to get Bernoulli's equation. When the flow is everywhere irrotational and inviscid, Bernoulli's equation can be used throughout the flow field. Such flows are called potential flows. In fluid dynamics, the Euler equations govern the compressible, Inviscid flow. ... In fluid dynamics, Bernoullis equation, derived by Daniel Bernoulli, describes the behavior of a fluid moving along a streamline. ... In vector analysis and in fluid dynamics, a lamellar vector field is a vector field with no rotational component. ... A potential flow is characterized by an irrotational velocity field. ...

### Steady vs unsteady flow

Hydrodynamics simulation of the Rayleigh-Taylor instability [1]

When all the time derivatives of a flow field vanish, the flow is considered to be steady. Otherwise, it is called unsteady. Whether a particular flow is steady or unsteady, can depend on the chosen frame of reference. For instance, laminar flow over a sphere is steady in the frame of reference that is stationary with respect to the sphere. In a frame of reference that is stationary than the governing equations of the same problem without taking advantage of the steadiness of the flow field. Image File history File links Download high resolution version (857x694, 82 KB) Summary Hydrodynamic simulation of the Rayleigh-Taylor instability. ... Image File history File links Download high resolution version (857x694, 82 KB) Summary Hydrodynamic simulation of the Rayleigh-Taylor instability. ... RT fingers evident in the Crab Nebula Hydrodynamics simulation of the Rayleigh-Taylor instability [1] The Rayleigh-Taylor instability, or RT instability, occurs any time a dense, heavy fluid is being accelerated by light fluid. ... This article or section is in need of attention from an expert on the subject. ... For other uses, see Sphere (disambiguation). ...

Although strictly unsteady flows, time-periodic problems can often be solved by the same techniques as steady flows. For this reason, they can be considered to be somewhere between steady and unsteady.

### Laminar vs turbulent flow

Turbulence is flow dominated by recirculation, eddies, and apparent randomness. Flow in which turbulence is not exhibited is called laminar. It should be noted, however, that the presence of eddies or recirculation does not necessarily indicate turbulent flow--these phenomena may be present in laminar flow as well. Mathematically, turbulent flow is often represented via Reynolds decomposition, in which the flow is broken down into the sum of a steady component and a perturbation component. In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. ... In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid flows past an obstacle. ... Random redirects here. ... Laminar flow (bottom) and turbulent flow (top) over a submarine hull. ... In fluid dynamics and turbulence, Reynolds decomposition is a mathematical technique to separate the average and fluctuating parts of a quantity. ...

It is believed that turbulent flows obey the Navier-Stokes equations. Direct Numerical Simulation (DNS), based on the incompressible Navier-Stokes equations, makes it possible to simulate turbulent flows with moderate Reynolds numbers (restrictions depend on the power of computer and efficiency of solution algorithm). The results of DNS agree with the experimental data. The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. ... A direct numerical simulation (DNS) is a simulation in computational fluid dynamics in which the Navier-Stokes equations are numerically solved without any turbulence model. ...

Most flows of interest have Reynolds numbers too high for DNS to be a viable option (see: Pope), given the state of computational power for the next few decades. Any flight vehicle large enough to carry a human (L > 3 m), moving faster than 72 km/h (20 m/s) is well beyond the limit of DNS simulation (Re = 4 million). Transport aircraft wings (such as on an Airbus A300 or Boeing 747) have Reynolds numbers of 40 million (based on the wing chord). In order to solve these real life flow problems, turbulence models will be a necessity for the foreseeable future. Reynolds-Averaged Navier-Stokes equations (RANS) combined with turbulence modeling provides a model of the effects of the turbulent flow, mainly the additional momentum transfer provided by the Reynolds stresses, although the turbulence also enhances the heat and mass transfer. Large Eddy Simulation (LES) also holds promise as a simulation methodology, especially in the guise of Detached Eddy Simulation (DES), which is a combination of turbulence modeling and large eddy simulation. The Airbus A300 is a short to medium range widebody aircraft. ... The Boeing 747, sometimes nicknamed the Jumbo Jet,[4][5] is a long-haul, widebody commercial airliner manufactured by Boeing in the United States. ... The Reynolds-averaged Navier-Stokes equations are time-averaged equations of motion for fluid flow. ... Turbulence modeling is the area of physical modeling where a simpler mathematical model than the full time dependent Navier-Stokes Equations is used to predict of the effects of turbulence. ... In fluid dynamics, the Reynolds stresses (or, the Reynolds stress tensor) is the stress tensor in a fluid due to the random turbulent fluctuations in fluid momentum. ... In thermal physics, heat transfer is the passage of thermal energy from a hot to a colder body. ... Mass transfer is the phrase commonly used in engineering for physical processes that involve molecular and convective transport of atoms and molecules within physical systems. ... Large eddy simulation (LES) is a numerical technique used to solve the partial differential equations governing turbulent fluid flow. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... Turbulence modeling is the area of physical modeling where a simpler mathematical model than the full time dependent Navier-Stokes Equations is used to predict of the effects of turbulence. ...

### Newtonian vs non-Newtonian fluids

Sir Isaac Newton showed how stress and the rate of strain are very close to linearly related for many familiar fluids, such as water and air. These Newtonian fluids are modeled by a coefficient called viscosity, which depends on the specific fluid. Sir Isaac Newton FRS (4 January 1643 â€“ 31 March 1727) [ OS: 25 December 1642 â€“ 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Stress is a measure of force per unit area within a body. ... This article is about the deformation of materials. ... Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ... Air redirects here. ... A Newtonian fluid (named for Isaac Newton) is a fluid that flows like waterâ€”its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ... For other uses, see Viscosity (disambiguation). ...

However, some of the other materials, such as emulsions and slurries and some visco-elastic materials (eg. blood, some polymers), have more complicated non-Newtonian stress-strain behaviours. These materials include sticky liquids such as latex, honey, and lubricants which are studied in the sub-discipline of rheology. For other uses, see Blood (disambiguation). ... A polymer (from Greek: Ï€Î¿Î»Ï…, polu, many; and Î¼Î­ÏÎ¿Ï‚, meros, part) is a substance composed of molecules with large molecular mass composed of repeating structural units, or monomers, connected by covalent chemical bonds. ... A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ... This article is about the typesetting system. ... For other uses, see Honey (disambiguation). ... Rheology is the study of the deformation and flow of matter under the influence of an applied stress. ...

### Magnetohydrodynamics

Main article: Magnetohydrodynamics

Magnetohydrodynamics is the multi-disciplinary study of the flow of electrically conducting fluids in electromagnetic fields. Examples of such fluids include plasmas, liquid metals, and salt water. The fluid flow equations are solved simultaneously with Maxwell's equations of electromagnetism. Magnetohydrodynamics (MHD) (magnetofluiddynamics or hydromagnetics) is the academic discipline which studies the dynamics of electrically conducting fluids. ... Magnetohydrodynamics (MHD) (magnetofluiddynamics or hydromagnetics) is the academic discipline which studies the dynamics of electrically conducting fluids. ... Conduction is the movement of electrically charged particles through a transmission medium (electrical conductor). ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... Look up plasma in Wiktionary, the free dictionary. ... Salt water may refer to: Saline water, water containing dissolved salts Brine, water saturated or nearly saturated with salt Brackish water, water that is saltier than fresh water, but not as salty as sea water Seawater, water from a sea or ocean Saline (medicine), a solution of sodium chloride in... For thermodynamic relations, see Maxwell relations. ...

### Other approximations

There are a large number of other possible approximations to fluid dynamic problems. Some of the more commonly used are listed below.

• The Boussinesq approximation neglects variations in density except to calculate buoyancy forces. It is often used in free convection problems where density changes are small.
• Lubrication theory exploits the large aspect ratio of the domain to show that certain terms in the equations are small and so can be neglected.
• Slender-body theory is a methodology used in Stokes flow problems to estimate the force on, or flow field around, a long slender object in a viscous fluid.
• The shallow-water equations can be used to describe a layer of relatively inviscid fluid with a free surface, in which surface gradients are small.
• The Boussinesq equations are applicable to surface waves on thicker layers of fluid and with steeper surface slopes.
• Darcy's law is used for flow in porous media, and works with variables averaged over several pore-widths.
• In rotating systems, the quasi-geostrophic approximation assumes an almost perfect balance between pressure gradients and the Coriolis force. It is useful in the study of atmospheric dynamics.

In physics, buoyancy is the upward force on an object produced by the surrounding fluid (i. ... Convection in the most general terms refers to the movement of currents within fluids (i. ... A thin layer of liquid mixed with particles flowing down an inclined plane. ... The aspect ratio of a two-dimensional shape is the ratio of its longer dimension to its shorter dimension. ... Stokes flow is a type of flow where inertial forces are small as compared to viscous forces. ... The free surface of the sea, viewed from below In physics a free surface is the surface of a body that is subject to neither perpendicular normal stress nor parallel shear stress,[1] such as the boundary between two homogenous fluids,[2] for example liquid water and the air in... This article is about the mathematical term. ... In physics, a surface wave is a wave that is guided along the interface between two different media for a mechanical wave, or by a refractive index gradient for an electromagnetic wave. ... This article is about the mathematical term. ... In fluid dynamics, Darcys law is a phenomologically derived constitutive equation that describes the flow of a fluid through a porous medium. ... A porous medium or a porous material is a solid (often called frame or matrix) permeated by an interconnected network of pores (voids) filled with a fluid (liquid or gas). ... In Atmospheric Science, Balanced Flow is an idealization of atmospheric motion in which flow is considered steady-state. ... Pressure Gradient is the change in pressure over a distance. ... In physics, the Coriolis effect is an inertial force first described by Gaspard-Gustave Coriolis, a French scientist, in 1835. ... Atmospheric dynamics is the study of the forces that result in the changing motions of air within the Earths atmosphere. ...

## Terminology in fluid dynamics

The concept of pressure is central to the study of both fluid statics and fluid dynamics. A pressure can be identified for every point in a body of fluid, regardless of whether the fluid is in motion or not. Pressure can be measured using an aneroid, Bourdon tube, mercury column, or various other methods. This article is about pressure in the physical sciences. ... The construction of a bourdon tube gauge, construction elements are made of brass Many techniques have been developed for the measurement of pressure and vacuum. ...

Some of the terminology that is necessary in the study of fluid dynamics is not found in other similar areas of study. In particular, some of the terminology used in fluid dynamics is not used in fluid statics. Fluid statics (also called hydrostatics) is the science of fluids at rest, and is a sub-field within fluid mechanics. ...

### Terminology in incompressible fluid dynamics

The concepts of total pressure (also known as stagnation pressure) and dynamic pressure arise from Bernoulli's equation and are significant in the study of all fluid flows. (These two pressures are not pressures in the usual sense - they cannot be measured using an aneroid, Bourdon tube or mercury column.) To avoid potential ambiguity when referring to pressure in fluid dynamics, many authors use the term static pressure to distinguish it from total pressure and dynamic pressure. Static pressure is identical to pressure and can be identified for every point in a fluid flow field. Stagnation pressure is the pressure at a stagnation point in a fluid flow, where the kinetic energy is converted into pressure energy. ... Velocity pressure is also called fluid dynamic pressure or Q given by the equation. ... In fluid dynamics, Bernoullis equation, derived by Daniel Bernoulli, describes the behavior of a fluid moving along a streamline. ... This article is about pressure in the physical sciences. ... Static pressure is a term used in ventilation engineering, airspeed indication, fluid statics, hydraulics and flow measurement. ... Static pressure is a term used in ventilation engineering, airspeed indication, fluid statics, hydraulics and flow measurement. ... This article is about pressure in the physical sciences. ...

In Aerodynamics, L.J. Clancy writes (page 21): "To distinguish it from the total and dynamic pressures, the actual pressure of the fluid, which is associated not with its motion but with its state, is often referred to as the static pressure, but where the term pressure alone is used it refers to this static pressure."

A point in a fluid flow where the flow has come to rest (i.e. speed is equal to zero adjacent to some solid body immersed in the fluid flow) is of special significance. It is of such importance that it is given a special name - a stagnation point. The pressure at the stagnation point is also of special significance and is given its own name - stagnation pressure. A point in a flow where the velocity is zero, where any streamline touches a solid surface at an angle. ... This article is about pressure in the physical sciences. ... Stagnation pressure is the pressure at a stagnation point in a fluid flow, where the kinetic energy is converted into pressure energy. ...

### Terminology in compressible fluid dynamics

In a compressible fluid, such as air, the temperature and density are essential when determining the state of the fluid. In addition to the concept of total pressure (also known as stagnation pressure), the concepts of total (or stagnation) temperature and total (or stagnation) density are also essential in any study of compressible fluid flows. To avoid potential ambiguity when referring to temperature and density, many authors use the terms static temperature and static density. Static temperature is identical to temperature; and static density is identical to density; and both can be identified for every point in a fluid flow field. Stagnation pressure is the pressure at a stagnation point in a fluid flow, where the kinetic energy is converted into pressure energy. ...

The temperature and density at a stagnation point are called stagnation temperature and stagnation density. A point in a flow where the velocity is zero, where any streamline touches a solid surface at an angle. ...

Readers might wonder if there are such concepts as dynamic temperature or dynamic density. There aren't.

A similar approach is also taken with the thermodynamic properties of compressible fluids. Many authors use the terms total (or stagnation) enthalpy and total (or stagnation) entropy. The terms static enthalpy and static entropy appear to be less common, but where they are used they mean nothing more than enthalpy and entropy respectively, and the prefix 'static' is being used to avoid ambiguity with their 'total' or 'stagnation' counterparts. t In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or Î”H, or rarely as Ï‡) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ... For other uses, see: information entropy (in information theory) and entropy (disambiguation). ...

## References

• Acheson, D.J. (1990) "Elementary Fluid Dynamics" (Clarendon Press).
• Batchelor, G.K. (1967) "An Introduction to Fluid Dynamics" (Cambridge University Press).
• Clancy, L.J. (1975) "Aerodynamics" (Pitman Publishing Limited).
• Lamb, H. (1994) "Hydrodynamics" (Cambridge University Press, 6th ed.). Originally published in 1879, the 6th extended edition appeared first in 1932.
• Landau, L.D. and Lifshitz, E.M. (1987) "Fluid Mechanics" (Pergamon Press).
• Milne-Thompson, L.M. (1968) "Theoretical Hydrodynamics" (Macmillan, 5th ed.). Originally published in 1938.
• Pope, S.B. (2000) "Turbulent Flows" (Cambridge University Press).
• Shinbrot, Marvin (1973) "Lectures on Fluid Mechanics" (Gordon and Breach)

George Keith Batchelor (March 8, 1920 - March 30, 2000) was an Australian applied mathematician and fluid dynamicist. ... Sir Horace Lamb FRS (November 29, 1849 - December 4, 1934) was a British applied mathematician and author of several influential texts on classical physics, among them Hydrodynamics (1895) and Dynamical Theory of Sound (1910). ... Lev Davidovich Landau Lev Davidovich Landau (Russian language: Ð›ÐµÌÐ² Ð”Ð°Ð²Ð¸ÌÐ´Ð¾Ð²Ð¸Ñ‡ Ð›Ð°Ð½Ð´Ð°ÌÑƒ) (January 22, 1908 â€“ April 1, 1968) was a prominent Soviet physicist, who made fundamental contributions to many areas of theoretical physics. ... Evgeny Mikhailovich Lifshitz (Russian: ; February 21, 1915 â€“ October 29, 1985) was a notable Soviet physicist. ...

## Notes

1. ^ Shengtai Li, Hui Li "Parallel AMR Code for Compressible MHD or HD Equations" (Los Alamos National Laboratory) [1]

## See also

### Miscellaneous

Acoustic theory is the field relating to mathematical description of sound waves. ... For the Daft Punk song, see Aerodynamic (song). ... Aeroelasticity is the science which studies the interaction among inertial, elastic, and aerodynamic forces. ... Six F-16 Fighting Falcons with the U.S. Air Force Thunderbirds aerial demonstration team fly in delta formation in front of the Empire State Building. ... A computer simulation of high velocity air flow around the Space Shuttle during re-entry. ... Flow measurement is the quantification of bulk fluid or gas movement. ... Categories: Pages needing attention | Stub ... Table of Hydraulics and Hydrostatics, from the 1728 Cyclopaedia. ... Water covers 70% of the Earths surface. ... Hydrostatics, also known as fluid statics, is the study of fluids at rest. ... Hydrodynamics is fluid dynamics applied to liquids, such as water, alcohol, oil, and blood. ... Electrohydrodynamics (EHD) is the study of the dynamics of electrically conducting fluids. ... Magnetohydrodynamics (MHD) (magnetofluiddynamics or hydromagnetics) is the academic discipline which studies the dynamics of electrically conducting fluids. ... Rheology is the study of the deformation and flow of matter under the influence of an applied stress. ... Quantum hydrodynamics is more than the study of superfluidity. ... In fluid dynamics, Bernoullis equation, derived by Daniel Bernoulli, describes the behavior of a fluid moving along a streamline. ... Reynolds Transport Theorem Reynolds transport theorem is a fundamental theorem used in formulating the basic laws of fluid dynamics. ... In fluid dynamics, the Boussinesq approximation is used in the field of buoyancy-driven flow. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... In fluid dynamics, the Euler equations govern the compressible, Inviscid flow. ... In fluid dynamics, Darcys law is a phenomologically derived constitutive equation that describes the flow of a fluid through a porous medium. ... Velocity pressure is also called fluid dynamic pressure or Q given by the equation. ... Fluid statics (also called hydrostatics) is the science of fluids at rest, and is a sub-field within fluid mechanics. ... In fluid mechanics, Helmholtzs theorems describe the behaviour of vortex lines in a fluid. ... Motion of a rigid body in an ideal fluid in projections onto the axes of the body fixed frame can be described by the equations where and are vectors of bodys angular velocity and the velocity of the point respectively; and are a central tensor of inertia of the... The Manning formula is an empirical formula for open channel flow, or flow driven by gravity. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. ... In the physical sciences, Pascals law or Pascals principle states that for all points at the same absolute height in a connected body of an incompressible fluid at rest, the fluid pressure is the same, even if additional pressure is applied on the fluid at some place. ... The Poiseuilles law (or the Hagen-Poiseuille law also named after Gotthilf Heinrich Ludwig Hagen (1797-1884) for his experiments in 1839) is the physical law concerning the voluminal laminar stationary flow Î¦V of incompressible uniform viscous liquid (so called Newtonian fluid) through a cylindrical tube with the constant... This article is about pressure in the physical sciences. ... Static pressure is a term used in ventilation engineering, airspeed indication, fluid statics, hydraulics and flow measurement. ... Fluid pressure is the pressure at some point within a fluid, such as water or air. ... In fluid mechanics and astrophysics, the relativistic Euler equations are a generalization of the Euler equations that account for the effects of special relativity. ... In fluid dynamics and turbulence, Reynolds decomposition is a mathematical technique to separate the average and fluctuating parts of a quantity. ... The stream function is defined for two-dimensional flows of various kinds. ... Solid blue lines and broken grey lines represent the streamlines. ... A compressible flow is a situation in which the compressibility of a fluid must be taken into account. ... The term Couette flow refers to the laminar flow of a viscous liquid in the space between two surfaces, one of which is moving relative to the other. ... Free molecular flow describes the fluid dynamics of gas where the mean free path of the molecules is larger than the size of the chamber or of the object under test. ... In fluid mechanics, an incompressible fluid is a fluid whose density (often represented by the Greek letter ρ) is constant: it is the same throughout the field and it does not change through time. ... A fluid flow where viscous (friction) forces are small in comparison to inertial forces is said to be inviscid. ... Laminar flow (bottom) and turbulent flow (top) over a submarine hull. ... The Manning formula is an empirical formula for open channel flow, or flow driven by gravity. ... A potential flow is characterized by an irrotational velocity field. ... Stokes flow is a type of flow where inertial forces are small as compared to viscous forces. ... Superfluidity is a phase of matter characterised by the complete absence of viscosity. ... A United States Navy F/A-18E/F Super Hornet in transonic flight. ... Transient flow is such a flow where the velocity and pressure changes over time. ... Transonic is an aeronautics term referring to a range of velocities just below and above the speed of sound. ... In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. ... In fluid mechanics, two-phase flow occurs in a system containing gas and liquid with a meniscus separating the two phases. ... For other uses, see Density (disambiguation). ... A Newtonian fluid (named for Isaac Newton) is a fluid that flows like waterâ€”its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ... A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ... This box:      Surface tension is a property of the surface of a liquid that causes it to behave as an elastic sheet. ... For other uses, see Viscosity (disambiguation). ... Vapor pressure is the pressure of a vapor in equilibrium with its non-vapor phases. ... Fluid Dynamics Compressibility (physics) is a measure of the relative volume change of fluid or solid as a response to a pressure (or mean stress) change: . For a gas the magnitude of the compressibility depends strongly on whether the process is adiabatic or isothermal, while this difference is small in... In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. ... The Coanda effect is the tendency of a stream of fluid to stay attached to a convex surface, rather than follow a straight line in its original direction. ... A convection cell is a phenomenon of fluid dynamics which occurs in situations where there are temperature differences within a body of liquid or gas. ... In mathematics, a squeeze mapping in linear algebra is a type of linear transformation that preserves Euclidean area of regions in the cartesian plane, but is not a Euclidean motion. ... In physics, the drag equation gives the drag experienced by an object moving through a fluid. ... The lift force, or simply lift, is a mechanical force, generated by a solid object as it moves through a fluid, directed perpendicular to the flow direction. ... Ocean waves Ocean surface waves are surface waves that occur at the surface of an ocean. ... Rossby (or planetary) waves are large-scale motions in the ocean or atmosphere whose restoring force is the variation in Coriolis effect with latitude. ... Introduction The shock wave is one of several different ways in which a gas in a supersonic flow can be compressed. ... In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed; solitons are caused by a delicate balance between nonlinear and dispersive effects in the medium. ... In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. ... A Venturi meter is shown in a diagram, the pressure in 1 conditions is higher than 2, and the relationship between the fluid speed in 2 and 1 respectively, is the same as for pressure. ... Vortex created by the passage of an aircraft wing, revealed by coloured smoke A vortex (pl. ... Vorticity is a mathematical concept used in fluid dynamics. ... Wave drag is an aerodynamics term that refers to a sudden and very powerful form of drag that appears on aircraft flying at high-subsonic speeds. ... Acoustics is the interdisciplinary sciences that always deals with the study of sound, ultrasound and infrasound (all mechanical waves in gases, liquids, and solids). ... For the Daft Punk song, see Aerodynamic (song). ... Fluid power is the technology that deals with the generation, control, and transmission of pressurized fluids. ... Gaming is an umbrella term that includes a number of special hobby game types: Board games Collectible card games Computer and video games Tabletop wargaming (i. ... // Meteorology (from Greek: Î¼ÎµÏ„Î­Ï‰ÏÎ¿Î½, meteoron, high in the sky; and Î»ÏŒÎ³Î¿Ï‚, logos, knowledge) is the interdisciplinary scientific study of the atmosphere that focuses on weather processes and forecasting. ... Steamer New York in c. ... Thermohaline circulation Oceanographic frontal systems on the southern hemisphere Oceanography (from the greek words Î©ÎºÎµÎ±Î½ÏŒÏ‚ meaning Ocean and Î³ÏÎ¬Ï†Ï‰ meaning to write), also called oceanology or marine science, is the branch of Earth Sciences that studies the Earths oceans and seas. ... A Plasma lamp In physics and chemistry, a plasma is an ionized gas, and is usually considered to be a distinct phase of matter. ... Pneumatics, a subsection of an area called fluid power, is the use of pressurized air to effect mechanical motion. ... This article is about a mechanical device. ... This is a list of important publications in physics, organized by field. ... Zirconocene with an isosurface showing areas of the molecule susceptible to electrophilic attack. ... A rotating tank is a device used for fluid dynamics experiments. ... U.S. Navy F/A-18 breaking the sound barrier. ... In geophysical fluid dynamics, an approximation whereby the Coriolis parameter, f, is set to vary linearly in space is called a beta plane approximation. ... In the physical sciences, a dimensionless number (or more precisely, a number with the dimensions of 1) is a quantity which describes a certain physical system and which is a pure number without any physical units; it does not change if one alters ones system of units of measurement... An Archimedes number, named after the ancient Greek scientist Archimedes, to determine the motion of fluids due to density differences, is a dimensionless number in the form where: g = gravitational acceleration (9. ... The Bagnold number, named after Ralph Alger Bagnold, used in granular flow calculations, is defined by where is the mass, is the grain diameter, is the surface tension and is the interstitial fluid viscosity. ... The Biot number (Bi) is a dimensionless number used in unsteady-state (or transient) heat transfer calculations. ... In fluid mechanics, the Bond number, notated Bo, is a dimensionless number expressing the ratio of body forces (often gravitational) to surface tension forces: where is the density, the acceleration associated with the body force, e. ... The Brinkman Number is a dimensionless group related to heat conduction from a wall to a flowing viscous fluid, commonly used in polymer processing. ... The capillary number represents the relative effect of viscous forces and surface tension acting across an interface between a liquid and a gas, or between two immiscible liquids. ... The DamkÃ¶hler numbers (Da) are dimensionless numbers used in chemical engineering to relate chemical reaction timescale to other phenomena occurring in a system. ... The Dean number is a dimensionless group in fluid mechanics, which occurs in the study of flow in curved pipes and channels. ... The Deborah number is a dimensionless number, used in rheology to characterize how fluid a material is. ... The Eckert number is a dimensionless number used in flow calculations. ... The Ekman number, named for V. Walfrid Ekman, is a dimensionless number used in describing geophysical phenomena in the oceans and atmosphere. ... In fluid dynamics the EÃ¶tvÃ¶s number (Eo) is a dimensionless number named after Hungarian physicist LorÃ¡nd EÃ¶tvÃ¶s (1848-1919). ... The Euler number or cavitation number is a dimensionless number used in flow calculations. ... The Froude number is a dimensionless number used to quantify the resistance of an object moving through water, and compare objects of different sizes. ... In fluid dynamics, the Galilei number (Ga), sometimes also referred to as Galileo number (see discussion), is a dimensionless number named after Italian scientist Galileo Galilei (1564-1642). ... The Grashof number is a dimensionless number in fluid dynamics which approximates the ratio of the buoyancy force to the viscous force acting on a fluid. ... The Hagen number is a dimensionless number used in forced flow calculations. ... The Knudsen number (Kn) is the ratio of the molecular mean free path length to a representative physical length scale. ... The Laplace number (La) is a dimensionless number used in the characterisation of free surface fluid dynamics. ... The Lewis number is a dimensionless number approximating the ratio of mass diffusivity and thermal diffusivity, and is used to characterize fluid flows in where there are simultaneous heat and mass transfer by convection. ... An F/A-18 Hornet breaking the sound barrier. ... The Reynolds number is the ratio of inertial forces (vsÏ) to viscous forces (Î¼/L) and is used for determining whether a flow will be laminar or turbulent. ... The Marangoni number (Mg) is a dimensionless number named after Italian scientist Carlo Marangoni. ... In fluid dynamics, the Morton number () is a dimensionless number used together with the EÃ¶tvÃ¶s number to characterize the shape of bubbles or drops. ... The Nusselt number is a dimensionless number that measures the enhancement of heat transfer from a surface compared to the heat transferred if just conduction occurred. ... The Ohnesorge number, Z , is a dimensionless number that relates the viscous and surface tension force. ... In physics, the PÃ©clet number is a dimensionless number relating the forced convection of a system to its heat conduction. ... The Prandtl Number is a dimensionless number approximating the ratio of momentum diffusivity and thermal diffusivity. ... In fluid mechanics, the Rayleigh number for a fluid is a dimensionless number associated with the heat transfer within the fluid. ... In fluid mechanics, the Reynolds number may be described as the ratio of inertial forces (vsÏ) to viscous forces (Î¼/L) and, consequently, it quantifies the relative importance of these two types of forces for given flow conditions. ... The Richardson number is named after Lewis Fry Richardson (1881 - 1953). ... In fluid mechanics, the Roshko number is a dimensionless number describing oscillating flow mechanisms. ... The Rossby number, named for Carl-Gustav Arvid Rossby, is a dimensionless number used in describing fluid flow, usually in geophysical phenomena in the oceans and atmosphere. ... The Ruark number (RU) is a dimensionless number see in fluid mechanics. ... The Schmidt number is a dimensionless number approximating the ratio of momentum diffusivity (viscosity) and mass diffusivity, and is used to characterize fluid flows in where there are simultaneous momentum and mass diffusion convection processes. ... The Sherwood number (Sh) is a dimensionless number used in mass-transfer operation. ... The Stanton number is a dimensionless number which measures the ratio of heat transferred into a fluid to the thermal capacity of fluid. ... The Stokes number is a dimensionless number corresponding to the behavior of particles suspended in a fluid flow. ... In dimensional analysis, the Strouhal number is a dimensionless number describing oscillating flow mechanisms. ... The Laplace number (La), also known as the Suratman number (Su), is a dimensionless number used in the characterization of free surface fluid dynamics. ... In physics, the Taylor number is a dimensionless quantity that characterizes the importance of rotation of a fluid about a vertical axis. ... The Weber number is a dimensionless quantity in fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. ... The Weissenberg number is a dimensionless number used in the study of viscoelastic flows. ... A Womersley number is a dimensionless number in biofluid mechanics. ...

Results from FactBites:

 Online Encyclopedia and Dictionary - Fluid dynamics (961 words) Fluid dynamics is the study of fluids (liquids and gases) in motion, and the effect of the fluid motion on fluid boundaries, such as solid containers or other fluids. Fluid dynamics is a branch of fluid mechanics, and has a number of subdisciplines, including aerodynamics (the study of gases in motion) and hydrodynamics (liquids in motion). The central equations for fluid dynamics are the Navier-Stokes equations, which are non-linear differential equations that describe the flow of a fluid whose stress depends linearly on velocity and on pressure.
 Fluid dynamics - Free Encyclopedia (867 words) Fluid dynamics (also called fluid mechanics) is the study of fluids, that is liquids and gases. Fluid Dynamics and its subdisciplines aerodynamics, hydrodynamics, and hydraulics have a wide range of applications. The central equations for fluid dynamics are the Navier-Stokes equations, which are non-linear differential equations that describe fluid flow.
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