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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. ...

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. ...

Hydrodynamics simulation of the Rayleigh-Taylor instability [1]

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.

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

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]

Miscellaneous

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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