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| | == シャオヤンペースは、その体内で甘く魅力的です == |
| {{Continuum mechanics| cTopic=Fluid mechanics}}
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| [[File:Teardrop shape.svg|thumb|300px|Typical [[aerodynamic]] teardrop shape, assuming a [[viscous]] medium passing from left to right, the diagram shows the pressure distribution as the thickness of the black line and shows the velocity in the [[boundary layer]] as the violet triangles. The green [[vortex generator]]s 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 employs [[Dermal denticle|shark like skin]], as any turbulence here will reduce the energy of the airflow. The truncation on the right, known as a [[Kammback]], also prevents back flow from the high pressure region in the back across the [[Spoiler (aeronautics)|spoiler]]s to the convergent part.]]
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| In [[physics]], '''fluid dynamics''' is a subdiscipline of [[fluid mechanics]] that deals with '''fluid flow'''—the [[natural science]] of [[fluid]]s ([[liquid]]s and [[gas]]es) in motion. It has several subdisciplines itself, including '''[[aerodynamics]]''' (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 [[force]]s and [[moment (physics)|moment]]s on [[aircraft]], determining the [[mass flow rate]] of [[petroleum]] through pipelines, predicting [[weather]] patterns, understanding [[nebula]]e in [[interstellar space]] and reportedly modelling [[fission weapon]] detonation. Some of its principles are even used in [[traffic engineering (transportation)|traffic engineering]], where traffic is treated as a continuous fluid.
| | 泉は言った：「マルチ古い謝玄」。<br><br>「ああ、ほんの少しのことを、「玄香港の息子は微笑み、そして群衆に直面すると、手を振った。<br><br>見て、シャオは遠くない多くの人が滞在する行く、式典の後に行を曲げ、ゆっくりと会場を出さ<br><br>群衆を見て終了し、Xuankong息子はちょうど、微笑んささやいた： [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-2.html カシオ腕時計 g-shock] ''医学 [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-9.html 電波時計 casio] 'ほこり、私たちは、そのフィールドを賭けていた、彼らはダンがああチャンピオンになるこのセッションを取得することができシャオヤンと英二を見ている、私はあなたが私を獲得することができ、これを知らないのか？ [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-7.html カシオ 腕時計 gps] '<br><br>1132番目章魂のフィンガープリント<br><br>1132番目章魂のフィンガープリント<br>ホールの外<br>ライン、ストレートDantaをリード、あまりにも多くの話を持っていなかったシャオヤンと曹操Yingさんは、チャネルの底に行に直面している [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-13.html 時計 カシオ]。<br><br>'のように肖氏ヤン、と [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-8.html カシオ レディース 電波ソーラー腕時計]。'<br>ちょうど撮影し<br>シャオヤンペースは、その体内で甘く魅力的です |
| | 相关的主题文章： |
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| | <li>[http://www.zlslkj.com/plus/feedback.php?aid=65 http://www.zlslkj.com/plus/feedback.php?aid=65]</li> |
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| | <li>[http://www.regalglass.com.cn/plus/feedback.php?aid=82 http://www.regalglass.com.cn/plus/feedback.php?aid=82]</li> |
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| | <li>[http://hablaameno.com/index.php/ http://hablaameno.com/index.php/]</li> |
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| | </ul> |
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| Fluid dynamics offers a systematic structure—which underlies these practical disciplines—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.
| | == 薬「少し風が受信されない理由を分裂 == |
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| Before the twentieth century, ''hydrodynamics'' was synonymous with fluid dynamics. This is still reflected in names of some fluid dynamics topics, like [[magnetohydrodynamics]] and [[hydrodynamic stability]], both of which can also be applied to gases.<ref>{{Cite book | title=The Dawn of Fluid Dynamics: A Discipline Between Science and Technology | first=Michael | last=Eckert | publisher=Wiley | year=2006 | isbn=3-527-40513-5 | page=ix }}</ref>
| | 無謀に長い間、単にハード飲み込んだ、7つの製品精錬 [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-9.html 電波時計 casio] '医学'分割後、修理を横になっていた遠くの行為を見て？限り、彼はすぐに開封したように、用超強力な幸せがたくさんあるでしょう、それは何も難しい問題であり、家に帰る道を破壊するために、人々のこの存在、彼らは震え助けておらず、ここで考えたショット、7つの製品精錬アピールの「医学」部門、誰も質問する勇気ない<br><br>薬「少し風が受信されない理由を分裂？？ [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-13.html カシオ腕時計 メンズ] 'チェン耀輝揮発顔」の他の精製このレベルに会ったが、この柳の家族」、飛行、7つの製品精錬「医学」部門のアイデアの心を左折、このファミリは、彼らの大きな男を呼び出すことができない、彼は理解することはできませんどのように、なぜ劉ファミリー、招待することができますか？<br>そう遠くない反対八尾ら中<br>、劉清、劉飛、歩行者は、あまりにも、彼がサポートされていない小燕の偶数ラウンドの手に実際にあるために、わずかに開いた口が地面上の距離を見て修理しなければならなかった |
| | | 相关的主题文章： |
| ==Equations of fluid dynamics==
| | <ul> |
| The foundational axioms of fluid dynamics are the [[conservation law]]s, specifically, [[conservation of mass]], [[conservation of momentum|conservation of linear momentum]] (also known as [[Newton's laws of motion|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|Reynolds Transport Theorem]].
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| | | <li>[http://aiyingfang.cn/bbs/showtopic-883990.aspx http://aiyingfang.cn/bbs/showtopic-883990.aspx]</li> |
| 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 [[infinitesimal]]ly 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.
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| | | <li>[http://www.law110.net/plus/feedback.php?aid=14 http://www.law110.net/plus/feedback.php?aid=14]</li> |
| 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 fluid]]s 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 [[Solution in closed form|closed-form solution]], so they are primarily of use in [[Computational Fluid Dynamics]]. 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.
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| | | <li>[http://lotus.raindrop.jp/cgi/joyful_exif/joyful.cgi http://lotus.raindrop.jp/cgi/joyful_exif/joyful.cgi]</li> |
| In addition to the mass, momentum, and energy conservation equations, a [[thermodynamics|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 [[Ideal gas law|perfect gas equation of state]]:
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| :<math>p= \frac{\rho R_u T}{M}</math>
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| where ''p'' is [[pressure]], ρ is [[density]], ''R<sub>u</sub>'' is the [[gas constant]], ''M'' is the [[molar mass]] and ''T'' is [[temperature]].
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| ===Conservation laws===
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| Three conservation laws are used to solve fluid dynamics problems, and may be written in [[integral]] or [[Differential (infinitesimal)|differential]] form. Mathematical formulations of these conservation laws may be interpreted by considering the concept of a ''control volume''. A control volume is a specified volume in space through which air can flow in and out. Integral formulations of the conservation laws consider the change in mass, momentum, or energy within the control volume. Differential formulations of the conservation laws apply [[Stokes' theorem]] to yield an expression which may be interpreted as the integral form of the law applied to an infinitesimal volume at a point within the flow.
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| *[[Continuity equation#Fluid dynamics|Mass continuity]] (conservation of mass): The rate of change of fluid mass inside a control volume must be equal to the net rate of fluid flow into the volume. Physically, this statement requires that mass is neither created nor destroyed in the control volume,<ref>Anderson, J.D., ''Fundamentals of Aerodynamics'', 4th Ed., McGraw–Hill, 2007.</ref> and can be translated into the integral form of the continuity equation:
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| ::<math>{\partial \over \partial t} \iiint_V \rho \, dV = - \, {} </math> {{oiint|preintegral = |intsubscpt =<math>{\scriptstyle S}</math>|integrand = <math>{}\,\rho\mathbf{u}\cdot d\mathbf{S}</math>}}
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| :Above, <math>\rho</math> is the fluid density, '''u''' is a velocity vector, and ''t'' is time. The left-hand side of the above expression contains a triple integral over the control volume, whereas the right-hand side contains a surface integral over the surface of the control volume. The differential form of the continuity equation is, by the [[divergence theorem]]:
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| ::<math>\ {\partial \rho \over \partial t} + \nabla \cdot (\rho \mathbf{u}) = 0 </math>
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| *[[Momentum|Conservation of momentum]]: This equation applies [[Newton's second law of motion]] to the control volume, requiring that any change in momentum of the air within a control volume be due to the net flow of air into the volume and the action of external forces on the air within the volume. In the integral formulation of this equation, [[body force]]s here are represented by ''f''<sub>body</sub>, the body force per unit mass. [[Surface force]]s, such as viscous forces, are represented by '''<math>\mathbf{F}_\text{surf}</math>''', the net force due to [[Stress (mechanics)|stresses]] on the control volume surface.
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| ::<math> \frac{\partial}{\partial t} \iiint_{\scriptstyle V} \rho\mathbf{u} \, dV = -\, {} </math> {{oiint|preintegral = |intsubscpt = <math>_{\scriptstyle S}</math> |integrand}} <math> (\rho\mathbf{u}\cdot d\mathbf{S}) \mathbf{u} -{}</math> {{oiint|intsubscpt = <math>{\scriptstyle S}</math>|integrand = <math> {}\, p \, d\mathbf{S}</math>}} <math>\displaystyle{}+ \iiint_{\scriptstyle V} \rho \mathbf{f}_\text{body} \, dV + \mathbf{F}_\text{surf}</math>
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| :The differential form of the momentum conservation equation is as follows. Here, both surface and body forces are accounted for in one total force, ''F''. For example, ''F'' may be expanded into an expression for the frictional and gravitational forces acting on an internal flow.
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| ::<math>\ {D \mathbf{u} \over D t} = \mathbf{F} - {\nabla p \over \rho} </math>
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| :In aerodynamics, air is assumed to be a [[Newtonian fluid]], which posits a linear relationship between the shear stress (due to internal friction forces) and the rate of strain of the fluid. The equation above is a vector equation: in a three dimensional flow, it can be expressed as three scalar equations. The conservation of momentum equations for the compressible, viscous flow case are called the Navier–Stokes equations.
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| *[[Conservation of energy]]: Although [[energy]] can be converted from one form to another, the total [[energy]] in a given closed system remains constant.
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| ::<math>\ \rho {Dh \over Dt} = {D p \over D t} + \nabla \cdot \left( k \nabla T\right) + \Phi </math>
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| :Above, ''h'' is [[enthalpy]], ''k'' is the [[thermal conductivity]] of the fluid, ''T'' is temperature, and <math>\Phi</math> is the viscous dissipation function. The viscous dissipation function governs the rate at which mechanical energy of the flow is converted to heat. The [[second law of thermodynamics]] requires that the dissipation term is always positive: viscosity cannot create energy within the control volume.<ref>White, F.M., ''Viscous Fluid Flow'', McGraw–Hill, 1974.</ref> The expression on the left side is a [[material derivative]]. | |
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| ===Compressible vs incompressible flow===
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| All fluids are [[compressibility|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 modelled as an [[incompressible flow]]. Otherwise the more general [[compressible flow]] equations must be used.
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| 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.,
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| : <math>\frac{\mathrm{D} \rho}{\mathrm{D}t} = 0 \, ,</math>
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| where ''D''/''Dt'' is the [[substantial derivative]], which is the sum of [[time derivative|local]] and [[convective derivative]]s. This additional constraint simplifies the governing equations, especially in the case when the fluid has a uniform density.
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| 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). [[acoustics|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.
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| ===Viscous vs inviscid flow===
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| [[File:Potential flow around a wing.gif|thumb|Potential flow around a wing]]
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| [[viscosity|Viscous]] problems are those in which fluid friction has significant effects on the fluid motion.
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| The [[Reynolds number]], which is a ratio between inertial and viscous forces, can be used to evaluate whether viscous or inviscid equations are appropriate to the problem.
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| [[Stokes flow]] is flow at very low Reynolds numbers, ''Re''<<1, such that inertial forces can be neglected compared to viscous forces.
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| 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]] completely, compared to inertial terms.
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| 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 (fluid dynamics)|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.
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| The Euler equations can be integrated along a streamline to get [[Bernoulli's equation]]. When the flow is everywhere [[Lamellar field|irrotational]] and inviscid, Bernoulli's equation can be used throughout the flow field. Such flows are called [[potential flow]]s.
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| ===Steady vs unsteady flow===<!-- [[Steady flow]] redirects here -->
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| [[File:HD-Rayleigh-Taylor.gif|thumb|320px|Hydrodynamics simulation of the [[Rayleigh–Taylor instability]] <ref>Shengtai Li, Hui Li "Parallel AMR Code for Compressible MHD or HD Equations" (Los Alamos National Laboratory) [http://math.lanl.gov/Research/Highlights/amrmhd.shtml]</ref> ]]
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| When all the time derivatives of a flow field vanish, the flow is considered to be a '''steady flow'''. Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time. Otherwise, flow is called unsteady (also called transient<ref>[http://www.cfd-online.com/Forums/main/118306-transient-state-unsteady-state.html Transient state or unsteady state?]</ref>). 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 with respect to a background flow, the flow is unsteady.
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| [[Turbulence|Turbulent]] flows are unsteady by definition. A turbulent flow can, however, be [[stationary process|statistically stationary]]. According to Pope:<ref>See Pope (2000), page 75.</ref>
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| {{quote|
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| The random field ''U''(''x'',''t'') is statistically stationary if all statistics are invariant under a shift in time.
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| }}
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| This roughly means that all statistical properties are constant in time. Often, the mean field is the object of interest, and this is constant too in a statistically stationary flow.
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| Steady flows are often more tractable than otherwise similar unsteady flows. The governing equations of a steady problem have one dimension fewer (time) than the governing equations of the same problem without taking advantage of the steadiness of the flow field.
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| ===Laminar vs turbulent flow===
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| [[Turbulence]] is flow characterized by recirculation, [[Eddy (fluid dynamics)|eddies]], and apparent [[random]]ness. Flow in which turbulence is not exhibited is called [[laminar flow|laminar]]. It should be noted, however, that the presence of eddies or recirculation alone does not necessarily indicate turbulent flow—these phenomena may be present in laminar flow as well. Mathematically, turbulent flow is often represented via a [[Reynolds decomposition]], in which the flow is broken down into the sum of an [[average]] component and a perturbation component.
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| It is believed that turbulent flows can be described well through the use of the [[Navier–Stokes equations]]. [[Direct numerical simulation]] (DNS), based on the Navier–Stokes equations, makes it possible to simulate turbulent flows at moderate Reynolds numbers. Restrictions depend on the power of the computer used and the efficiency of the solution algorithm. The results of DNS have been found to agree well with experimental data for some flows.<ref>See, for example, Schlatter et al, Phys. Fluids 21, 051702 (2009); {{doi|10.1063/1.3139294}}</ref>
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| Most flows of interest have Reynolds numbers much too high for DNS to be a viable option,<ref>See Pope (2000), page 344.</ref> 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 modelling]] provides a model of the effects of the turbulent flow. Such a modelling mainly provides the additional momentum transfer by the [[Reynolds stresses]], although the turbulence also enhances the [[heat transfer|heat]] and [[mass transfer]]. Another promising methodology is [[large eddy simulation]] (LES), especially in the guise of [[detached eddy simulation]] (DES)—which is a combination of RANS turbulence modelling and large eddy simulation.
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| ===Newtonian vs non-Newtonian fluids===
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| Sir [[Isaac Newton]] showed how [[stress (physics)|stress]] and the rate of [[Strain (materials science)|strain]] are very close to linearly related for many familiar fluids, such as [[water]] and [[Earth's atmosphere|air]]. These [[Newtonian fluid]]s are modelled by a coefficient called [[viscosity]], which depends on the specific fluid.
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| However, some of the other materials, such as emulsions and slurries and some visco-elastic materials (e.g. [[blood]], some [[polymer]]s), have more complicated ''[[Non-Newtonian fluid|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]].
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| ===Subsonic vs transonic, supersonic and hypersonic flows===
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| While many terrestrial flows (e.g. flow of water through a pipe) occur at low mach numbers, many flows of practical interest (e.g. in aerodynamics) occur at high fractions of the Mach Number M=1 or in excess of it (supersonic flows). New phenomena occur at these Mach number regimes (e.g. shock waves for supersonic flow, transonic instability in a regime of flows with M nearly equal to 1, non-equilibrium chemical behaviour due to ionization in hypersonic flows) and it is necessary to treat each of these flow regimes separately.
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| ===Magnetohydrodynamics===
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| {{main|Magnetohydrodynamics}}
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| [[Magnetohydrodynamics]] is the multi-disciplinary study of the flow of [[electrical conduction|electrically conducting]] fluids in [[Electromagnetism|electromagnetic]] fields. Examples of such fluids include [[Plasma (physics)|plasma]]s, liquid metals, and [[Saline water|salt water]]. The fluid flow equations are solved simultaneously with [[Maxwell's equations]] of electromagnetism.
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| ===Other approximations===
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| There are a large number of other possible approximations to fluid dynamic problems. Some of the more commonly used are listed below.
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| * The '''[[Boussinesq approximation (buoyancy)|Boussinesq approximation]]''' neglects variations in density except to calculate [[buoyancy]] forces. It is often used in free [[convection]] problems where density changes are small.
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| * '''[[Lubrication theory]]''' and '''[[Hele–Shaw flow]]''' exploits the large [[aspect ratio]] of the domain to show that certain terms in the equations are small and so can be neglected.
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| * '''[[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.
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| * The '''[[shallow-water equations]]''' can be used to describe a layer of relatively inviscid fluid with a [[free surface]], in which surface [[slope|gradients]] are small.
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| * The '''[[Boussinesq equations (water waves)|Boussinesq equations]]''' are applicable to [[surface waves]] on thicker layers of fluid and with steeper surface [[slope]]s.
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| * '''[[Darcy's law]]''' is used for flow in [[porous medium|porous media]], and works with variables averaged over several pore-widths.
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| * In rotating systems, the '''[[Balanced flow#Geostrophic flow|quasi-geostrophic approximation]]''' assumes an almost perfect balance between [[pressure gradient]]s and the [[Coriolis force]]. It is useful in the study of [[atmospheric dynamics]].
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| == Terminology in fluid dynamics ==
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| 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 [[Pressure measurement|measured]] using an aneroid, Bourdon tube, mercury column, or various other methods.
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| 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]].
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| === Terminology in incompressible fluid dynamics ===
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| The concepts of total 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.
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| In ''Aerodynamics'', L.J. Clancy writes:<ref>Clancy, L.J. ''Aerodynamics'', page 21</ref> ''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.''
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| 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 static pressure at the stagnation point is of special significance and is given its own name—[[stagnation pressure]]. In incompressible flows, the stagnation pressure at a stagnation point is equal to the total pressure throughout the flow field.
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| === Terminology in compressible fluid dynamics ===
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| 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.
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| The temperature and density at a [[stagnation point]] are called stagnation temperature and stagnation density.
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| 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. Because the 'total' flow conditions are defined by [[isentropic]]ally bringing the fluid to rest, the total (or stagnation) entropy is by definition always equal to the "static" entropy.
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| ==See also==
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| === Fields of study ===
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| {{columns-list|3|
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| *[[Acoustic theory]]
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| *[[Aerodynamics]]
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| *[[Aeroelasticity]]
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| *[[Aeronautics]]
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| *[[Computational fluid dynamics]]
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| *[[Flow measurement]]
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| *[[Geophysical fluid dynamics]]
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| *[[haemodynamics|Hemodynamics]]
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| *[[Hydraulics]]
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| *[[Hydrology]]
| |
| *[[Hydrostatics]]
| |
| *[[Electrohydrodynamics]]
| |
| *[[Magnetohydrodynamics]]
| |
| *[[Metafluid dynamics]]
| |
| *[[Rheology]]
| |
| *[[Quantum hydrodynamics]]
| |
| }}
| |
| | |
| ===Mathematical equations and concepts===
| |
| {{columns-list|3|
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| *[[Airy wave theory]]
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| *[[Bernoulli's equation]]
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| *[[Reynolds transport theorem]]
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| *[[Benjamin–Bona–Mahony equation]]
| |
| *[[Boussinesq approximation (buoyancy)]]
| |
| *[[Boussinesq approximation (water waves)]]
| |
| *[[Conservation laws]]
| |
| *[[Euler equations (fluid dynamics)]]
| |
| *[[Different Types of Boundary Conditions in Fluid Dynamics]]
| |
| *[[Darcy's law]]
| |
| *[[Dynamic pressure]]
| |
| *[[Fluid statics]]
| |
| *[[Hagen–Poiseuille equation]]
| |
| *[[Helmholtz's theorems]]
| |
| *[[Kirchhoff equations]]
| |
| *[[Knudsen equation]]
| |
| *[[Manning equation]]
| |
| *[[Mild-slope equation]]
| |
| *[[Morison equation]]
| |
| *[[Navier–Stokes equations]]
| |
| *[[Oseen flow]]
| |
| *[[Pascal's law]]
| |
| *[[Poiseuille's law]]
| |
| *[[Potential flow]]
| |
| *[[Pressure]]
| |
| *[[Static pressure]]
| |
| *[[Pressure head]]
| |
| *[[Relativistic Euler equations]]
| |
| *[[Reynolds decomposition]]
| |
| *[[Stokes flow]]
| |
| *[[Stokes stream function]]
| |
| *[[Stream function]]
| |
| *[[Streamlines, streaklines and pathlines]]
| |
| }}
| |
| | |
| === Types of fluid flow ===
| |
| {{columns-list|3|
| |
| *[[Cavitation]]
| |
| *[[Compressible flow]]
| |
| *[[Couette flow]]
| |
| *[[Free molecular flow]]
| |
| *[[Incompressible flow]]
| |
| *[[Inviscid flow]]
| |
| *[[Isothermal flow]]
| |
| *[[Laminar flow]]
| |
| *[[Open channel flow]]
| |
| *[[Secondary flow]]
| |
| *[[Stream thrust averaging]]
| |
| *[[Superfluidity]]
| |
| *[[Supersonic]]
| |
| *[[Transient flow]]
| |
| *[[Transonic]]
| |
| *[[Turbulence|Turbulent flow]]
| |
| *[[Two-phase flow]]
| |
| }}
| |
| | |
| === Fluid properties ===
| |
| {{columns-list|3|
| |
| *[[Density]]
| |
| *[[List of hydrodynamic instabilities]]
| |
| *[[Newtonian fluid]]
| |
| *[[Non-Newtonian fluid]]
| |
| *[[Surface tension]]
| |
| *[[Viscosity]]
| |
| *[[Vapour pressure]]
| |
| *[[Compressibility]]
| |
| }}
| |
| | |
| ===Fluid phenomena===
| |
| {{columns-list|3|
| |
| *[[Boundary layer]]
| |
| *[[Coanda effect]]
| |
| *[[Convection cell]]
| |
| *[[squeeze mapping#Corner flow|Convergence/Bifurcation]]
| |
| *[[Darwin drift]]
| |
| *[[Drag (force)]]
| |
| *[[Hydrodynamic stability]]
| |
| *[[Kaye effect]]
| |
| *[[Lift (force)]]
| |
| *[[Magnus effect]]
| |
| *[[Ocean surface waves]]
| |
| *[[Rossby wave]]
| |
| *[[Shock wave]]
| |
| *[[Soliton]]
| |
| *[[Stokes drift]]
| |
| *[[Turbulence]]
| |
| *[[Fluid thread breakup|Thread breakup]]
| |
| *[[Venturi effect]]
| |
| *[[Vortex]]
| |
| *[[Vorticity]]
| |
| *[[Water hammer]]
| |
| *[[Wave drag]]
| |
| }}
| |
| | |
| ===Applications===
| |
| {{columns-list|3|
| |
| *[[Acoustics]]
| |
| *[[Aerodynamics]]
| |
| *[[Cryosphere science]]
| |
| *[[Fluid power]]
| |
| *[[Hydraulic machinery]]
| |
| *[[Meteorology]]
| |
| *[[Naval architecture]]
| |
| *[[Oceanography]]
| |
| *[[Plasma physics]]
| |
| *[[Pneumatics]]
| |
| *[[3D computer graphics]]
| |
| }}
| |
| | |
| === Fluid dynamics journals ===
| |
| {{columns-list|3|
| |
| * ''Annual Reviews in Fluid Mechanics''
| |
| * ''[[Journal of Fluid Mechanics]]''
| |
| * ''[[Physics of Fluids]]''
| |
| * ''[[Experiments in Fluids]]''
| |
| * ''European Journal of Mechanics B: Fluids''
| |
| * ''Theoretical and Computational Fluid Dynamics''
| |
| * ''Computers and Fluids''
| |
| * ''[[International Journal for Numerical Methods in Fluids]]''
| |
| * ''[[Flow, Turbulence and Combustion]]''
| |
| }}
| |
| | |
| === Miscellaneous ===
| |
| {{columns-list|3|
| |
| *[[List of publications in physics#Fluid dynamics|Important publications in fluid dynamics]]
| |
| *[[Isosurface]]
| |
| *[[Keulegan–Carpenter number]]
| |
| *[[Rotating tank]]
| |
| *[[Sound barrier]]
| |
| *[[Beta plane]]
| |
| *[[Immersed boundary method]]
| |
| *[[Bridge scour]]
| |
| * [[Finite volume method for unsteady flow]]
| |
| }}
| |
| | |
| == Notes ==
| |
| {{reflist}}
| |
| | |
| == References ==
| |
| * {{cite book|last=Acheson|first=D. J.|title=Elementary Fluid Dynamics|publisher=Clarendon Press|year=1990|isbn=0-19-859679-0}}
| |
| * {{cite book|last=Batchelor|first=G. K.|authorlink=George Batchelor|title=An Introduction to Fluid Dynamics|publisher=Cambridge University Press|year=1967|isbn=0-521-66396-2}}
| |
| * {{cite book|last=Chanson|first=H.|authorlink=Hubert Chanson|title=Applied Hydrodynamics: An Introduction to Ideal and Real Fluid Flows|publisher=CRC Press, Taylor & Francis Group, Leiden, The Netherlands, 478 pages|year=2009|isbn=978-0-415-49271-3}}
| |
| * {{cite book|last=Clancy|first=L. J.|title=Aerodynamics|publisher=Pitman Publishing Limited|location=London|year=1975|isbn=0-273-01120-0}}
| |
| * {{cite book|last=Lamb|first=Horace|authorlink=Horace Lamb|title=Hydrodynamics|edition=6th|publisher=Cambridge University Press|year=1994|isbn=0-521-45868-4}} Originally published in 1879, the 6th extended edition appeared first in 1932.
| |
| * {{cite book|last1=Landau|first1=L. D.|author1-link=Lev Landau|last2=Lifshitz|first2=E. M.|author2-link=Evgeny Lifshitz|title=Fluid Mechanics|edition=2nd|series=[[Course of Theoretical Physics]] |publisher=Pergamon Press|year=1987|isbn=0-7506-2767-0}}
| |
| * {{cite book|last=Milne-Thompson|first=L. M.|title=Theoretical Hydrodynamics|edition=5th|publisher=Macmillan|year=1968}} Originally published in 1938.
| |
| * {{cite book|last=Pope|first=Stephen B.|title=Turbulent Flows|publisher=Cambridge University Press|year=2000|isbn=0-521-59886-9}}
| |
| * {{cite book|last=Shinbrot|first=M.|title=Lectures on Fluid Mechanics|publisher=Gordon and Breach|year=1973|isbn=0-677-01710-3}}
| |
| | |
| == External links ==
| |
| {{Commons category|Fluid dynamics}}
| |
| {{Commons category|Fluid mechanics}}
| |
| * [http://www.efluids.com/ eFluids], containing several galleries of fluid motion
| |
| * [http://web.mit.edu/hml/ncfmf.html National Committee for Fluid Mechanics Films (NCFMF)], containing films on several subjects in fluid dynamics (in [[RealMedia]] format)
| |
| * [http://www.salihnet.freeservers.com/engineering/fm/fm_books.html List of Fluid Dynamics books]
| |
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| {{NonDimFluMech}}
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| {{physics-footer|continuum='''[[Continuum mechanics]]'''}}
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| {{DEFAULTSORT:Fluid Dynamics}}
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| [[Category:Aerodynamics]]
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| [[Category:Chemical engineering]]
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| [[Category:Continuum mechanics]]
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| [[Category:Fluid dynamics| ]]
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| [[Category:Fluid mechanics| ]]
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| [[Category:Piping]]
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| [[ja:流体力学]]
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