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Fluid dynamics

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31: 2350: 2290: 2076: 55: 1495: 1408: 1150: 1764:, 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, but it can be expressed as three scalar equations in three coordinate directions. The conservation of momentum equations for the compressible, viscous flow case is called the Navier–Stokes equations. 904:. At small scale, all fluids are composed of molecules that collide with one another and solid objects. However, the continuum assumption assumes that fluids are continuous, rather than discrete. Consequently, it is assumed that properties such as density, pressure, temperature, and flow velocity are well-defined at 2304:. Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time. Time dependent flow is known as unsteady (also called transient). Whether a particular flow is steady or unsteady, can depend on the chosen frame of reference. For instance, laminar flow over a 2388:(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. 1630:
In the above integral formulation of this equation, the term on the left is the net change of momentum within the volume. The first term on the right is the net rate at which momentum is convected into the volume. The second term on the right is the force due to pressure on the volume's surfaces. The
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is time. The left-hand side of the above expression is the rate of increase of mass within the volume and contains a triple integral over the control volume, whereas the right-hand side contains an integration over the surface of the control volume of mass convected into the system. Mass flow into
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In a compressible fluid, it is convenient to define the total conditions (also called stagnation conditions) for all thermodynamic state properties (such as total temperature, total enthalpy, total speed of sound). These total flow conditions are a function of the fluid velocity and have different
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To avoid potential ambiguity when referring to the properties of the fluid associated with the state of the fluid rather than its motion, the prefix "static" is commonly used (such as static temperature and static enthalpy). Where there is no prefix, the fluid property is the static condition (so
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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, and can be translated into the integral form of the continuity equation:
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of the flow is 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
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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
1067:. A control volume is a discrete volume in space through which fluid is assumed to flow. The integral formulations of the conservation laws are used to describe the change of mass, momentum, or energy within the control volume. Differential formulations of the conservation laws apply 2340:
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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to an extent; that is, changes in pressure or temperature cause 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
1625: 2599:). New phenomena occur at these regimes such as instabilities in transonic flow, shock waves for supersonic flow, or non-equilibrium chemical behaviour due to ionization in hypersonic flows. In practice, each of those flow regimes is treated separately. 1888: 1403: 1334:
applied to a control volume, is a statement that any change in momentum of the fluid within that control volume will be due to the net flow of momentum into the volume and the action of external forces acting on the fluid within the volume.
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A point in a fluid flow where the flow has come to rest (that is to say, 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
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This idea can work fairly well when the Reynolds number is high. However, problems such as those involving solid boundaries may require that the viscosity be included. Viscosity cannot be neglected near solid boundaries because the
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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
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The following is the differential form of the momentum conservation equation. Here, the volume is reduced to an infinitesimally small point, and both surface and body forces are accounted for in one total force,
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the system is accounted as positive, and since the normal vector to the surface is opposite to the sense of flow into the system the term is negated. The differential form of the continuity equation is, by the
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bringing the fluid to rest, there is no need to distinguish between total entropy and static entropy as they are always equal by definition. As such, entropy is most commonly referred to as simply "entropy".
2369:. 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 2013: 2391:
Most flows of interest have Reynolds numbers much too high for DNS to be a viable option, given the state of computational power for the next few decades. Any flight vehicle large enough to carry a human
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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
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For fluids that are sufficiently dense to be a continuum, do not contain ionized species, and have flow velocities that are small in relation to the speed of light, the momentum equations for
935:. The equations can be simplified in several ways, all of which make them easier to solve. Some of the simplifications allow some simple fluid dynamics problems to be solved in closed form. 5599: 1557: 159: 2984:
Nangia, Nishant; Johansen, Hans; Patankar, Neelesh A.; Bhalla, Amneet Pal S. (2017). "A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies".
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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.
1552: 2210:) indicate that the inertial effects have more effect on the velocity field than the viscous (friction) effects. In high Reynolds number flows, the flow is often modeled as an 1437: 1520: 1175: 2333:
is statistically stationary if all statistics are invariant under a shift in time. This roughly means that all statistical properties are constant in time. Often, the mean
2631:, fire and safety hazards, and astrophysics. In addition to conservation of mass, momentum and energy, conservation of individual species (for example, mass fraction of 942:
equation of state that gives the pressure as a function of other thermodynamic variables is required to completely describe the problem. An example of this would be the
2408:) have Reynolds numbers of 40 million (based on the wing chord dimension). Solving these real-life flow problems requires turbulence models for the foreseeable future. 1793: 1340: 50:
show the direction of the fluid flow, and the color gradient shows the pressure at each point, from blue to green, yellow, and red indicating increasing pressure
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first two terms on the right are negated since momentum entering the system is accounted as positive, and the normal is opposite the direction of the velocity
1247: 2824:) with a small-scale model it is necessary to keep the important characteristic numbers the same. Names and formulation of these numbers were standardized in 820:
and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as
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is the viscous dissipation function. The viscous dissipation function governs the rate at which the mechanical energy of the flow is converted to heat. The
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that describes the flow of a fluid whose stress depends linearly on flow velocity gradients and pressure. The unsimplified equations do not have a general
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to yield an expression that may be interpreted as the integral form of the law applied to an infinitesimally small volume (at a point) within the flow.
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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
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in methane combustion) need to be derived, where the production/depletion rate of any species are obtained by simultaneously solving the equations of
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requires that the dissipation term is always positive: viscosity cannot create energy within the control volume. The expression on the left side is a
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This branch of fluid dynamics augments the standard hydrodynamic equations with stochastic fluxes that model thermal fluctuations. As formulated by
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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
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small points in space and vary continuously from one point to another. The fact that the fluid is made up of discrete molecules is ignored.
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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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provides a model of the effects of the turbulent flow. Such a modelling mainly provides the additional momentum transfer by the
4173: 2051:. This additional constraint simplifies the governing equations, especially in the case when the fluid has a uniform density. 1180: 5394: 3481: 3388: 2968: 5722: 5554: 5516: 2189:
which characterises the magnitude of inertial effects compared to the magnitude of viscous effects. A low Reynolds number (
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Relativistic fluid dynamics studies the macroscopic and microscopic fluid motion at large velocities comparable to the
2396:> 3 m), moving faster than 20 m/s (72 km/h; 45 mph) is well beyond the limit of DNS simulation ( 1620:{\displaystyle \displaystyle {}+\iiint _{\scriptstyle V}\rho \mathbf {f} _{\text{body}}\,dV+\mathbf {F} _{\text{surf}}} 2883:"density" and "static density" mean the same thing). The static conditions are independent of the frame of reference. 5419: 5132: 4668: 4397: 3968: 3462: 3432: 3410: 3366: 3344: 3254: 3206: 3046: 2940: 701: 3176: 4488: 3618: 2219: 1331: 1637:
and pressure forces. The third term on the right is the net acceleration of the mass within the volume due to any
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Shengtai Li, Hui Li "Parallel AMR Code for Compressible MHD or HD Equations" (Los Alamos National Laboratory)
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Reactive flows are flows that are chemically reactive, which finds its applications in many areas, including
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are compression waves involving changes in pressure and density of the medium through which they propagate.
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may be expanded into an expression for the frictional and gravitational forces acting at a point in a flow.
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equations in a region close to the body. The two solutions can then be matched with each other, using the
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from the high-pressure region in the back. The surface in front is as smooth as possible or even employs
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everywhere, Bernoulli's equation can completely describe the flow everywhere. Such flows are called
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problems to estimate the force on, or flow field around, a long slender object in a viscous fluid.
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For flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the
1883:{\displaystyle \ \rho {\frac {Dh}{Dt}}={\frac {Dp}{Dt}}+\nabla \cdot \left(k\nabla T\right)+\Phi } 1398:{\displaystyle {\frac {\partial }{\partial t}}\iiint _{\scriptstyle V}\rho \mathbf {u} \,dV=-\,{}} 5871: 5679: 5604: 5526: 5455: 5399: 5331: 5227: 5142: 5052: 5017: 4493: 3828: 2846: 2497: 2223: 928: 644: 639: 308: 2214:, an approximation in which viscosity is completely neglected. Eliminating viscosity allows the 5669: 5631: 5511: 5222: 4653: 4279: 4141: 3728: 2673: 2370: 2186: 2175: 1768: 924: 874: 844: 196: 2531: 5881: 5689: 5367: 5326: 5042: 4713: 4533: 4305: 4284: 4253: 4116: 4037: 2778: 2733: 2729: 2657: 2429: 2358: 2109: 2048: 1044: 813: 806: 619: 237: 91: 3113:"Book Review: Cebeci, T. and Cousteix, J., Modeling and Computation of Boundary-Layer Flows" 2480:
of the domain to show that certain terms in the equations are small and so can be neglected.
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due to these viscous forces is linearly related to the strain rate. Such fluids are called
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Three conservation laws are used to solve fluid dynamics problems, and may be written in
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is the object of interest, and this is constant too in a statistically stationary flow.
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is identical to pressure and can be identified for every point in a fluid flow field.
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Computer generated animation of fluid in a tube flowing past a cylinder, showing the
3023: 2688:. This branch of fluid dynamics accounts for the relativistic effects both from the 1751:{\displaystyle \ {\frac {D\mathbf {u} }{Dt}}=\mathbf {F} -{\frac {\nabla p}{\rho }}} 5805: 5765: 5659: 5414: 5409: 4992: 4698: 4596: 4591: 4586: 4503: 4228: 4168: 4094: 3942: 3813: 3798: 3763: 3673: 3354: 3222: 3132: 3083: 3075: 3011: 2863: 2842: 2665: 2661: 2596: 2592: 2126:
have a more complicated, non-linear stress-strain behaviour. The sub-discipline of
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conditions (how close to the critical pressure the actual flow pressure becomes).
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It is believed that turbulent flows can be described well through the use of the
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Originally published in 1879, the 6th extended edition appeared first in 1932.
3015: 90:, also prevents backflow from the high-pressure region in the back across the 5865: 5810: 5486: 5337: 5232: 5197: 4967: 4962: 4917: 4912: 4758: 4733: 4728: 4703: 4673: 4543: 4442: 4422: 4402: 4313: 4188: 3927: 3922: 3912: 3902: 3867: 3862: 3803: 3743: 3733: 3713: 3708: 3678: 3643: 3567: 3383:. CRC Press, Taylor & Francis Group, Leiden, The Netherlands, 478 pages. 3144: 2757: 2518: 2425: 2421: 2211: 1667:
acting on the volume surface. The momentum balance can also be written for a
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form. The conservation laws may be applied to a region of the flow called a
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using an aneroid, Bourdon tube, mercury column, or various other methods.
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Mathematically, incompressibility is expressed by saying that the density
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In addition to the mass, momentum, and energy conservation equations, a
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The Dawn of Fluid Dynamics: A Discipline Between Science and Technology
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While many flows (such as flow of water through a pipe) occur at low
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describes the stress-strain behaviours of such fluids, which include
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Applied Hydrodynamics: An Introduction to Ideal and Real Fluid Flows
3177:"Transient state or unsteady state? -- CFD Online Discussion Forums" 2501:
can be used to describe a layer of relatively inviscid fluid with a
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flows are unsteady by definition. A turbulent flow can, however, be
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See, for example, Schlatter et al, Phys. Fluids 21, 051702 (2009);
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Fluid dynamics offers a systematic structure—which underlies these
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flows), many flows of practical interest in aerodynamics or in
2362: 2305: 2008:{\displaystyle {\frac {\mathrm {D} \rho }{\mathrm {D} t}}=0\,,} 1785: 1781: 798: 750: 432: 39: 4335: 816:—that embraces empirical and semi-empirical laws derived from 5574: 5007: 3507:, containing films on several subjects in fluid dynamics (in 2873: 2787: 2521:, and works with variables averaged over several pore-widths. 2506: 2169: 2159: 2155: 2143: 2105: 770: 746: 336: 2983: 2854:
to distinguish it from total pressure and dynamic pressure.
2436:(DES) — a combination of LES and RANS turbulence modelling. 5835: 5825: 5082: 5002: 2400:= 4 million). Transport aircraft wings (such as on an 2174:
The dynamic of fluid parcels is described with the help of
2672:. The fluid flow equations are solved simultaneously with 1932: 1074: 900:
In addition to the above, fluids are assumed to obey the
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problems always require allowing compressibility, since
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does not change as it moves in the flow field, that is,
1209:{\displaystyle {}\,\rho \mathbf {u} \cdot d\mathbf {S} } 3514: 3272:
Hydrodynamic Fluctuations in Fluids and Fluid Mixtures
3269: 2786:) have an important role in analyzing the behavior of 2373:, in which the flow is broken down into the sum of an 2365:. Flow in which turbulence is not exhibited is called 1572: 1506: 1422: 1364: 1161: 2879:
values in frames of reference with different motion.
2602: 2234:, because the velocity field may be expressed as the 1970: 1796: 1784:
can be converted from one form to another, the total
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National Committee for Fluid Mechanics Films (NCFMF)
2954: 2952: 2454:neglects variations in density except to calculate 2357:Turbulence is flow characterized by recirculation, 2226:. When, in addition to being inviscid, the flow is 3270:Ortiz de Zarate, Jose M.; Sengers, Jan V. (2006). 2555: 2246:generates a thin region of large strain rate, the 2007: 1882: 1750: 1619: 1546: 1514: 1484: 1431: 1397: 1305: 1208: 1169: 1139: 989: 861:The foundational axioms of fluid dynamics are the 153: 5730: 2949: 2886:Because the total flow conditions are defined by 763:(the study of air and other gases in motion) and 5863: 2344: 2300:A flow that is not a function of time is called 3442: 3312:International Organization for Standardization 3284: 3237: 2679: 2656:is the multidisciplinary study of the flow of 2284: 847:, both of which can also be applied to gases. 5716: 4321: 3983: 3969: 3544: 2353:The transition from laminar to turbulent flow 2104:showed that for many familiar fluids such as 1776:First law of thermodynamics (fluid mechanics) 1654:, such as viscous forces, are represented by 702: 3427:(6th ed.). Cambridge University Press. 2837:Terminology in incompressible fluid dynamics 2707: 2420:, although the turbulence also enhances the 1317: 757:. It has several subdisciplines, including 154:{\displaystyle J=-D{\frac {d\varphi }{dx}}} 5723: 5709: 5088:High efficiency glandless circulating pump 4337:Heating, ventilation, and air conditioning 4328: 4314: 3976: 3962: 3551: 3537: 3476:, CRC Press (Taylor & Francis group), 2874:Terminology in compressible fluid dynamics 2550: 2254:effects dominate and which thus generates 2170:Inviscid versus viscous versus Stokes flow 990:{\displaystyle p={\frac {\rho R_{u}T}{M}}} 709: 695: 3474:Fluid Dynamics via Examples and Solutions 3471: 3353: 3087: 2997: 2763: 2696:. The governing equations are derived in 2462:problems where density changes are small. 2410:Reynolds-averaged Navier–Stokes equations 2001: 1766: 1594: 1535: 1531: 1392: 1379: 1186: 1134: 1121: 27:Aspects of fluid mechanics involving flow 5522:Mold growth, assessment, and remediation 3452: 2958: 2771:Dimensionless numbers in fluid mechanics 2664:fields. Examples of such fluids include 2377:component and a perturbation component. 2348: 2288: 2074: 1760:In aerodynamics, air is assumed to be a 53: 29: 3375: 3334: 3110: 2642: 2439: 2279:method of matched asymptotic expansions 1933:Compressible versus incompressible flow 14: 5864: 4174:Atomic, molecular, and optical physics 3397: 3192: 3190: 3061: 2930: 2907:List of publications in fluid dynamics 5704: 5395:Programmable communicating thermostat 4309: 3957: 3532: 3405:. London: Pitman Publishing Limited. 3036: 2963:(4th ed.). London: McGraw–Hill. 2820:To compare a real situation (e.g. an 2269:A commonly used model, especially in 2071:Newtonian versus non-Newtonian fluids 1788:in a closed system remains constant. 5517:Mechanical, electrical, and plumbing 3419: 3196: 2203:In contrast, high Reynolds numbers ( 1547:{\displaystyle {}\,p\,d\mathbf {S} } 1050: 3558: 3187: 2841:The concepts of total pressure and 2790:and their flow as well as in other 2428:. Another promising methodology is 807:modelling fission weapon detonation 70:as the violet triangles. The green 24: 5378:Minimum efficiency reporting value 3328: 2603:Reactive versus non-reactive flows 2238:of a potential energy expression. 1985: 1975: 1927: 1877: 1863: 1849: 1736: 1350: 1346: 1277: 1265: 1257: 1099: 1095: 931:, so they are primarily of use in 836:, as functions of space and time. 78:and prevent back-flow also called 25: 5898: 5420:Standard temperature and pressure 5133:Packaged terminal air conditioner 4669:Passive daytime radiative cooling 4398:Heat pump and refrigeration cycle 3498: 3359:An Introduction to Fluid Dynamics 2458:forces. It is often used in free 2432:(LES), especially in the form of 1432:{\displaystyle _{\scriptstyle S}} 4489:Absorption-compression heat pump 2986:Journal of Computational Physics 2769:This section is an excerpt from 2293:Hydrodynamics simulation of the 1726: 1707: 1606: 1584: 1540: 1515:{\displaystyle {\scriptstyle S}} 1493: 1473: 1465: 1454: 1406: 1375: 1290: 1202: 1191: 1170:{\displaystyle {\scriptstyle S}} 1148: 42:in the flow behind it, called a 5384:Normal temperature and pressure 4764:Vapor-compression refrigeration 4295:Timeline of physics discoveries 3278: 3263: 3231: 3215: 2726:fluctuation-dissipation theorem 2724:contribution obtained from the 2556:Flows according to Mach regimes 2542:. It is useful in the study of 893:. They are expressed using the 871:conservation of linear momentum 3443:Milne-Thompson, L. M. (1968). 3361:. Cambridge University Press. 3290:Lifshitz, Evgenii Mikhailovich 3243:Lifshitz, Evgenii Mikhailovich 3201:. Cambridge University Press. 3169: 3151: 3104: 3055: 3030: 2977: 2924: 2743: 1469: 1447: 1294: 1283: 13: 1: 5731:Seamanship (seafaring) topics 5532:Testing, adjusting, balancing 5476:Building information modeling 5471:Building services engineering 5048:Ground-coupled heat exchanger 4576:Demand controlled ventilation 4524:Building insulation materials 3449:Originally published in 1938. 2917: 2345:Laminar versus turbulent flow 1946:. Otherwise the more general 1332:Newton's second law of motion 944:perfect gas equation of state 5093:High-pressure cut-off switch 4644:Ice storage air conditioning 4565:Dedicated outdoor air system 3599:Computational fluid dynamics 3524:List of Fluid Dynamics books 3490:Encyclopedia: Fluid dynamics 3062:Wilson, DI (February 2018). 2961:Fundamentals of Aerodynamics 2694:general theory of relativity 2690:special theory of relativity 2318:. The random velocity field 2271:computational fluid dynamics 2262:, a limitation known as the 1918:second law of thermodynamics 933:computational fluid dynamics 850: 7: 5796:Ship-to-ship cargo transfer 5436:Thermostatic radiator valve 5238:Thermostatic radiator valve 4749:Underfloor air distribution 4684:Radiant heating and cooling 4602:Energy recovery ventilation 4514:Automobile air conditioning 4378:Domestic energy consumption 4259:Quantum information science 3455:Lectures on Fluid Mechanics 2894: 2680:Relativistic fluid dynamics 2578:occur at high fractions of 2527:quasi-geostrophic equations 2386:Direct numerical simulation 2295:Rayleigh–Taylor instability 2285:Steady versus unsteady flow 879:First Law of Thermodynamics 795:predicting weather patterns 62:teardrop shape, assuming a 10: 5903: 5585:Institute of Refrigeration 5466:Architectural technologist 4938:Electrostatic precipitator 4090:Classical electromagnetism 3472:Nazarenko, Sergey (2014), 3447:(5th ed.). Macmillan. 3111:Platzer, B. (2006-12-01). 2898: 2768: 2646: 2559: 2218:to be simplified into the 1773: 1324: 895:Reynolds transport theorem 854: 5831:Man overboard rescue turn 5736: 5647: 5638:Volatile organic compound 5613: 5540: 5497:Environmental engineering 5461:Architectural engineering 5444: 5292: 5263:Ultra-low particulate air 4848:Automatic balancing valve 4795: 4776:Variable refrigerant flow 4628:Heat recovery ventilation 4571:Deep water source cooling 4481: 4343: 4267: 4204: 4132: 4048: 4020: 3992: 3629: 3589: 3566: 3519:American Physical Society 3445:Theoretical Hydrodynamics 3337:Elementary Fluid Dynamics 3197:Pope, Stephen B. (2000). 3041:. New York: McGraw–Hill. 3016:10.1016/j.jcp.2017.06.047 2912:List of fluid dynamicists 2901:Outline of fluid dynamics 2708:Fluctuating hydrodynamics 2524:In rotating systems, the 2488:is a methodology used in 74:prompt the transition to 5685:Template:Home automation 5507:Kitchen exhaust cleaning 5203:Solar-assisted heat pump 4803:Air conditioner inverter 4582:Displacement ventilation 4473:Vapour pressure of water 4458:Thermal destratification 4196:Condensed matter physics 2959:Anderson, J. D. (2007). 2931:Eckert, Michael (2006). 2451:Boussinesq approximation 2434:detached eddy simulation 2316:statistically stationary 1950:equations must be used. 1327:Cauchy momentum equation 1320:Conservation of momentum 1043:for a particular gas. A 213:Clausius–Duhem (entropy) 163:Fick's laws of diffusion 44:von KĂĄrmĂĄn vortex street 5680:World Refrigeration Day 5527:Refrigerant reclamation 5456:Architectural acoustics 5400:Programmable thermostat 5332:Clean air delivery rate 5228:Thermal expansion valve 5143:Pressurisation ductwork 5053:Ground source heat pump 4494:Absorption refrigerator 3609:Navier–Stokes equations 3515:Gallery of fluid motion 3335:Acheson, D. J. (1990). 2658:electrically conducting 2551:Multidisciplinary types 2498:shallow-water equations 2382:Navier–Stokes equations 2216:Navier–Stokes equations 2198:Stokes or creeping flow 1663:, the net force due to 917:Navier–Stokes equations 371:Navier–Stokes equations 309:Material failure theory 94:to the convergent part. 5670:Glossary of HVAC terms 5632:Sick building syndrome 5512:Mechanical engineering 5223:Smoke exhaust ductwork 4654:Mixed-mode ventilation 4280:Nobel Prize in Physics 4142:Relativistic mechanics 3286:Landau, Lev Davidovich 3274:. Amsterdam: Elsevier. 3239:Landau, Lev Davidovich 3137:10.1002/zamm.200690053 2784:characteristic numbers 2764:Characteristic numbers 2591:) or in excess of it ( 2371:Reynolds decomposition 2354: 2297: 2187:dimensionless quantity 2083: 2049:convective derivatives 2043:, which is the sum of 2009: 1884: 1769:Conservation of energy 1752: 1621: 1548: 1516: 1486: 1433: 1399: 1307: 1223:is the fluid density, 1210: 1171: 1141: 1079:(conservation of mass) 991: 925:differential equations 881:). These are based on 875:conservation of energy 845:hydrodynamic stability 737:is a subdiscipline of 155: 95: 51: 5690:Template:Solar energy 5368:Intelligent buildings 5327:Carbon dioxide sensor 4714:Room air distribution 4534:Central solar heating 4285:Philosophy of physics 3631:Dimensionless numbers 3581:Archimedes' principle 3457:. Gordon and Breach. 3453:Shinbrot, M. (1973). 3037:White, F. M. (1974). 2935:. Wiley. p. ix. 2779:Dimensionless numbers 2734:viscous stress tensor 2730:statistical mechanics 2676:of electromagnetism. 2668:, liquid metals, and 2430:large eddy simulation 2412:(RANS) combined with 2352: 2292: 2078: 2010: 1885: 1753: 1641:(here represented by 1622: 1549: 1517: 1487: 1434: 1400: 1308: 1211: 1172: 1142: 1045:constitutive relation 992: 814:practical disciplines 366:Bernoulli's principle 359:Archimedes' principle 156: 57: 33: 5492:Duct leakage testing 5482:Deep energy retrofit 5426:Thermographic camera 5363:Infrared thermometer 4838:Air source heat pump 4787:Water heat recycling 4353:Air changes per hour 4244:Mathematical physics 3249:. London: Pergamon. 3080:10.1038/eye.2017.267 2847:Bernoulli's equation 2654:Magnetohydrodynamics 2649:Magnetohydrodynamics 2643:Magnetohydrodynamics 2544:atmospheric dynamics 2517:is used for flow in 2440:Other approximations 2414:turbulence modelling 2264:d'Alembert's paradox 2224:Bernoulli's equation 2124:Non-Newtonian fluids 2094:; it has dimensions 1968: 1912:is temperature, and 1906:thermal conductivity 1794: 1694: 1558: 1526: 1502: 1444: 1415: 1341: 1248: 1181: 1157: 1090: 1047:may also be useful. 1022:absolute temperature 953: 929:closed-form solution 902:continuum assumption 885:and are modified in 867:conservation of mass 841:magnetohydrodynamics 458:Cohesion (chemistry) 280:Infinitesimal strain 116: 5887:Continuum mechanics 5358:HVAC control system 5348:Home energy monitor 5322:Building automation 5108:Inverter compressor 4770:Variable air volume 4679:Passive ventilation 4649:Kitchen ventilation 4549:Constant air volume 4519:Autonomous building 4219:Atmospheric physics 4058:Classical mechanics 3986:branches of physics 3339:. Clarendon Press. 3296:. London: Pergamon. 3129:2006ZaMM...86..981P 3064:"What is Rheology?" 3008:2017JCoPh.347..437N 2868:stagnation pressure 2794:. They include the 2792:transport phenomena 2702:Minkowski spacetime 2698:Riemannian geometry 2674:Maxwell's equations 2505:, in which surface 2485:Slender-body theory 2476:exploits the large 2176:Newton's second law 2086:All fluids, except 2041:material derivative 1944:incompressible flow 1922:material derivative 883:classical mechanics 877:(also known as the 857:Transport phenomena 741:that describes the 376:Poiseuille equation 107:Continuum mechanics 101:Part of a series on 5781:Naval architecture 5621:Indoor air quality 5565:ASTM International 5502:Hydronic balancing 5279:Wood-burning stove 5158:Radiator reflector 4943:Evaporative cooler 4754:Underfloor heating 4739:Thermal insulation 4275:History of physics 3774:Keulegan–Carpenter 3308:"ISO 80000-1:2009" 3181:www.cfd-online.com 3163:2016-03-03 at the 3039:Viscous Fluid Flow 2536:pressure gradients 2467:Lubrication theory 2355: 2298: 2142:materials such as 2084: 2005: 1880: 1748: 1617: 1616: 1576: 1544: 1512: 1510: 1482: 1429: 1426: 1395: 1368: 1303: 1240:divergence theorem 1206: 1167: 1165: 1137: 987: 891:general relativity 803:interstellar space 781:, determining the 727:physical chemistry 582:Magnetorheological 577:Electrorheological 314:Fracture mechanics 151: 96: 52: 5859: 5858: 5698: 5697: 5614:Health and safety 5193:Scroll compressor 5148:Process duct work 4903:Convection heater 4898:Condensing boiler 4828:Air-mixing plenum 4724:Solar combisystem 4560:Cross ventilation 4363:Building envelope 4303: 4302: 4290:Physics education 4239:Materials science 4206:Interdisciplinary 4164:Quantum mechanics 3951: 3950: 3483:978-1-43-988882-7 3390:978-0-415-49271-3 3227:10.1063/1.3139294 2970:978-0-07-125408-3 2686:velocity of light 2637:chemical kinetics 2530:assume an almost 2418:Reynolds stresses 2244:no-slip condition 1993: 1948:compressible flow 1844: 1821: 1799: 1746: 1720: 1699: 1613: 1591: 1357: 1272: 1253: 1106: 1051:Conservation laws 985: 887:quantum mechanics 863:conservation laws 719: 718: 594: 593: 528: 527: 297:Contact mechanics 220: 219: 149: 72:vortex generators 16:(Redirected from 5894: 5806:Passage planning 5766:Maritime studies 5725: 5718: 5711: 5702: 5701: 5660:Building science 5415:Smart thermostat 5410:Room temperature 4993:Fireplace insert 4699:Radon mitigation 4597:Electric heating 4592:District heating 4587:District cooling 4504:Air conditioning 4330: 4323: 4316: 4307: 4306: 4229:Chemical physics 4169:Particle physics 4095:Classical optics 3978: 3971: 3964: 3955: 3954: 3553: 3546: 3539: 3530: 3529: 3486: 3468: 3448: 3438: 3416: 3394: 3372: 3355:Batchelor, G. K. 3350: 3322: 3321: 3319: 3318: 3304: 3298: 3297: 3282: 3276: 3275: 3267: 3261: 3260: 3235: 3229: 3219: 3213: 3212: 3194: 3185: 3184: 3173: 3167: 3155: 3149: 3148: 3108: 3102: 3101: 3091: 3059: 3053: 3052: 3034: 3028: 3027: 3001: 2981: 2975: 2974: 2956: 2947: 2946: 2928: 2864:stagnation point 2843:dynamic pressure 2732:is added to the 2597:hypersonic flows 2586: 2399: 2395: 2332: 2209: 2195: 2118:Newtonian fluids 2099: 2038: 2037: 2035: 2034: 2028: 2025: 2014: 2012: 2011: 2006: 1994: 1992: 1988: 1982: 1978: 1972: 1956: 1915: 1911: 1903: 1896:is the specific 1895: 1889: 1887: 1886: 1881: 1873: 1869: 1845: 1843: 1835: 1827: 1822: 1820: 1812: 1804: 1797: 1757: 1755: 1754: 1749: 1747: 1742: 1734: 1729: 1721: 1719: 1711: 1710: 1701: 1697: 1686: 1681:. For example, 1680: 1671:control volume. 1662: 1649: 1636: 1626: 1624: 1623: 1618: 1615: 1614: 1611: 1609: 1593: 1592: 1589: 1587: 1578: 1577: 1563: 1554: 1553: 1551: 1550: 1545: 1543: 1530: 1522: 1521: 1519: 1518: 1513: 1511: 1497: 1496: 1491: 1489: 1488: 1483: 1481: 1476: 1468: 1457: 1440: 1439: 1438: 1436: 1435: 1430: 1428: 1427: 1410: 1409: 1404: 1402: 1401: 1396: 1394: 1378: 1370: 1369: 1358: 1356: 1345: 1312: 1310: 1309: 1304: 1293: 1273: 1271: 1263: 1255: 1251: 1236: 1228: 1222: 1216: 1215: 1213: 1212: 1207: 1205: 1194: 1185: 1177: 1176: 1174: 1173: 1168: 1166: 1152: 1151: 1146: 1144: 1143: 1138: 1136: 1117: 1116: 1107: 1105: 1094: 1038: 1030: 1019: 1011: 1003: 996: 994: 993: 988: 986: 981: 977: 976: 963: 913:Newtonian fluids 865:, specifically, 818:flow measurement 797:, understanding 711: 704: 697: 543: 542: 508:Gay-Lussac's law 498:Combined gas law 448:Capillary action 333: 332: 176: 175: 160: 158: 157: 152: 150: 148: 140: 132: 98: 97: 21: 5902: 5901: 5897: 5896: 5895: 5893: 5892: 5891: 5862: 5861: 5860: 5855: 5732: 5729: 5699: 5694: 5655:ASHRAE Handbook 5643: 5627:Passive smoking 5609: 5542: 5536: 5448: 5446: 5440: 5294: 5288: 5269:Whole-house fan 5183:Run-around coil 5178:Reversing valve 5123:Mechanical room 5113:Kerosene heater 5103:Infrared heater 5033:Gasoline heater 4973:Fan filter unit 4888:Condensate pump 4873:Centrifugal fan 4791: 4694:Radiant heating 4689:Radiant cooling 4664:Passive cooling 4659:Microgeneration 4529:Central heating 4477: 4453:Thermal comfort 4345: 4339: 4334: 4304: 4299: 4263: 4249:Medical physics 4200: 4159:Nuclear physics 4128: 4122:Non-equilibrium 4044: 4016: 3988: 3982: 3952: 3947: 3625: 3619:Entrance length 3585: 3562: 3560:Fluid mechanics 3557: 3501: 3484: 3465: 3435: 3413: 3391: 3369: 3347: 3331: 3329:Further reading 3326: 3325: 3316: 3314: 3306: 3305: 3301: 3294:Fluid Mechanics 3283: 3279: 3268: 3264: 3257: 3247:Fluid Mechanics 3236: 3232: 3220: 3216: 3209: 3199:Turbulent Flows 3195: 3188: 3175: 3174: 3170: 3165:Wayback Machine 3156: 3152: 3123:(12): 981–982. 3109: 3105: 3060: 3056: 3049: 3035: 3031: 2982: 2978: 2971: 2957: 2950: 2943: 2929: 2925: 2920: 2903: 2897: 2876: 2856:Static pressure 2852:static pressure 2839: 2834: 2833: 2774: 2766: 2746: 2710: 2682: 2662:electromagnetic 2651: 2645: 2605: 2589:transonic flows 2579: 2564: 2558: 2553: 2532:perfect balance 2442: 2397: 2393: 2361:, and apparent 2347: 2319: 2287: 2232:potential flows 2220:Euler equations 2204: 2190: 2183:Reynolds number 2172: 2095: 2079:Flow around an 2073: 2029: 2026: 2023: 2022: 2020: 2019: 1984: 1983: 1974: 1973: 1971: 1969: 1966: 1965: 1954: 1937:All fluids are 1935: 1930: 1928:Classifications 1913: 1909: 1901: 1893: 1859: 1855: 1836: 1828: 1826: 1813: 1805: 1803: 1795: 1792: 1791: 1778: 1771: 1762:Newtonian fluid 1735: 1733: 1725: 1712: 1706: 1702: 1700: 1695: 1692: 1691: 1682: 1676: 1661: 1655: 1648: 1642: 1632: 1610: 1605: 1604: 1588: 1583: 1582: 1571: 1567: 1562: 1559: 1556: 1555: 1539: 1529: 1527: 1524: 1523: 1505: 1503: 1500: 1499: 1498: 1494: 1492: 1480: 1472: 1464: 1453: 1445: 1442: 1441: 1421: 1418: 1416: 1413: 1412: 1411: 1407: 1405: 1393: 1374: 1363: 1359: 1349: 1344: 1342: 1339: 1338: 1329: 1322: 1289: 1264: 1256: 1254: 1249: 1246: 1245: 1234: 1224: 1220: 1201: 1190: 1184: 1182: 1179: 1178: 1160: 1158: 1155: 1154: 1153: 1149: 1147: 1135: 1112: 1108: 1098: 1093: 1091: 1088: 1087: 1080: 1077:Mass continuity 1069:Stokes' theorem 1053: 1036: 1029: 1025: 1017: 1009: 1001: 972: 968: 964: 962: 954: 951: 950: 906:infinitesimally 859: 853: 739:fluid mechanics 715: 686: 685: 684: 604: 596: 595: 549:Viscoelasticity 540: 530: 529: 517: 467: 463:Surface tension 427: 330: 328:Fluid mechanics 320: 319: 318: 232: 230:Solid mechanics 222: 221: 173: 165: 141: 133: 131: 117: 114: 113: 84:shark-like skin 80:flow separation 38:of a series of 28: 23: 22: 15: 12: 11: 5: 5900: 5890: 5889: 5884: 5879: 5874: 5872:Fluid dynamics 5857: 5856: 5854: 5853: 5848: 5843: 5838: 5833: 5828: 5823: 5818: 5813: 5808: 5803: 5801:Propeller walk 5798: 5793: 5788: 5786:Ship stability 5783: 5778: 5776:Nautical terms 5773: 5768: 5763: 5758: 5756:Ice navigation 5753: 5748: 5742: 5740: 5734: 5733: 5728: 5727: 5720: 5713: 5705: 5696: 5695: 5693: 5692: 5687: 5682: 5677: 5672: 5667: 5662: 5657: 5651: 5649: 5645: 5644: 5642: 5641: 5635: 5629: 5624: 5617: 5615: 5611: 5610: 5608: 5607: 5602: 5597: 5592: 5587: 5582: 5577: 5572: 5567: 5562: 5557: 5552: 5546: 5544: 5538: 5537: 5535: 5534: 5529: 5524: 5519: 5514: 5509: 5504: 5499: 5494: 5489: 5484: 5479: 5473: 5468: 5463: 5458: 5452: 5450: 5442: 5441: 5439: 5438: 5433: 5428: 5423: 5417: 5412: 5407: 5405:Psychrometrics 5402: 5397: 5392: 5387: 5381: 5375: 5370: 5365: 5360: 5355: 5350: 5345: 5340: 5335: 5329: 5324: 5319: 5314: 5309: 5304: 5302:Air flow meter 5298: 5296: 5290: 5289: 5287: 5286: 5281: 5276: 5271: 5266: 5260: 5255: 5250: 5245: 5240: 5235: 5230: 5225: 5220: 5215: 5210: 5205: 5200: 5195: 5190: 5185: 5180: 5175: 5170: 5165: 5160: 5155: 5150: 5145: 5140: 5135: 5130: 5125: 5120: 5115: 5110: 5105: 5100: 5095: 5090: 5085: 5080: 5078:Heating system 5075: 5070: 5065: 5060: 5058:Heat exchanger 5055: 5050: 5045: 5040: 5035: 5030: 5025: 5023:Gas compressor 5020: 5015: 5010: 5005: 5000: 4995: 4990: 4985: 4980: 4975: 4970: 4965: 4960: 4958:Expansion tank 4955: 4950: 4945: 4940: 4935: 4930: 4925: 4920: 4915: 4910: 4905: 4900: 4895: 4890: 4885: 4880: 4878:Ceramic heater 4875: 4870: 4865: 4860: 4855: 4850: 4845: 4840: 4835: 4830: 4825: 4820: 4815: 4810: 4805: 4799: 4797: 4793: 4792: 4790: 4789: 4784: 4779: 4773: 4767: 4761: 4756: 4751: 4746: 4741: 4736: 4731: 4726: 4721: 4719:Solar air heat 4716: 4711: 4709:Renewable heat 4706: 4701: 4696: 4691: 4686: 4681: 4676: 4671: 4666: 4661: 4656: 4651: 4646: 4641: 4636: 4631: 4625: 4620: 4618:Forced-air gas 4615: 4610: 4605: 4599: 4594: 4589: 4584: 4579: 4573: 4568: 4562: 4557: 4552: 4546: 4541: 4536: 4531: 4526: 4521: 4516: 4511: 4506: 4501: 4496: 4491: 4485: 4483: 4479: 4478: 4476: 4475: 4470: 4468:Thermodynamics 4465: 4460: 4455: 4450: 4445: 4440: 4438:Psychrometrics 4435: 4430: 4425: 4420: 4415: 4410: 4405: 4400: 4395: 4393:Gas compressor 4390: 4388:Fluid dynamics 4385: 4380: 4375: 4370: 4365: 4360: 4355: 4349: 4347: 4341: 4340: 4333: 4332: 4325: 4318: 4310: 4301: 4300: 4298: 4297: 4292: 4287: 4282: 4277: 4271: 4269: 4265: 4264: 4262: 4261: 4256: 4251: 4246: 4241: 4236: 4231: 4226: 4221: 4216: 4210: 4208: 4202: 4201: 4199: 4198: 4193: 4192: 4191: 4186: 4181: 4171: 4166: 4161: 4156: 4155: 4154: 4149: 4138: 4136: 4130: 4129: 4127: 4126: 4125: 4124: 4119: 4112:Thermodynamics 4109: 4108: 4107: 4102: 4092: 4087: 4082: 4081: 4080: 4075: 4070: 4065: 4054: 4052: 4046: 4045: 4043: 4042: 4041: 4040: 4030: 4024: 4022: 4018: 4017: 4015: 4014: 4013: 4012: 4002: 3996: 3994: 3990: 3989: 3981: 3980: 3973: 3966: 3958: 3949: 3948: 3946: 3945: 3940: 3935: 3930: 3925: 3920: 3915: 3910: 3905: 3900: 3895: 3890: 3885: 3880: 3875: 3870: 3865: 3860: 3855: 3854: 3853: 3843: 3838: 3837: 3836: 3831: 3821: 3816: 3811: 3806: 3801: 3796: 3791: 3786: 3781: 3776: 3771: 3766: 3761: 3756: 3751: 3746: 3741: 3736: 3731: 3726: 3721: 3716: 3711: 3706: 3701: 3696: 3691: 3686: 3681: 3676: 3671: 3666: 3661: 3656: 3651: 3646: 3641: 3635: 3633: 3627: 3626: 3624: 3623: 3622: 3621: 3614:Boundary layer 3611: 3606: 3601: 3595: 3593: 3591:Fluid dynamics 3587: 3586: 3584: 3583: 3578: 3572: 3570: 3564: 3563: 3556: 3555: 3548: 3541: 3533: 3527: 3526: 3521: 3512: 3500: 3499:External links 3497: 3496: 3495: 3487: 3482: 3469: 3463: 3450: 3440: 3433: 3417: 3411: 3395: 3389: 3373: 3367: 3351: 3345: 3330: 3327: 3324: 3323: 3299: 3277: 3262: 3255: 3230: 3214: 3207: 3186: 3168: 3150: 3103: 3074:(2): 179–183. 3054: 3047: 3029: 2976: 2969: 2948: 2941: 2922: 2921: 2919: 2916: 2915: 2914: 2909: 2899:Main article: 2896: 2893: 2888:isentropically 2875: 2872: 2838: 2835: 2812:speed of sound 2775: 2767: 2765: 2762: 2745: 2742: 2709: 2706: 2681: 2678: 2647:Main article: 2644: 2641: 2627:, and so on), 2604: 2601: 2560:Main article: 2557: 2554: 2552: 2549: 2548: 2547: 2540:Coriolis force 2522: 2510: 2493: 2481: 2473:Hele–Shaw flow 2463: 2441: 2438: 2346: 2343: 2286: 2283: 2275:boundary layer 2248:boundary layer 2171: 2168: 2152:sticky liquids 2072: 2069: 2016: 2015: 2004: 2000: 1997: 1991: 1987: 1981: 1977: 1934: 1931: 1929: 1926: 1925: 1908:of the fluid, 1891: 1890: 1879: 1876: 1872: 1868: 1865: 1862: 1858: 1854: 1851: 1848: 1842: 1839: 1834: 1831: 1825: 1819: 1816: 1811: 1808: 1802: 1772: 1767: 1765: 1759: 1758: 1745: 1741: 1738: 1732: 1728: 1724: 1718: 1715: 1709: 1705: 1659: 1652:Surface forces 1646: 1628: 1627: 1608: 1603: 1600: 1597: 1586: 1581: 1575: 1570: 1566: 1542: 1538: 1534: 1509: 1479: 1475: 1471: 1467: 1463: 1460: 1456: 1452: 1449: 1425: 1420: 1391: 1388: 1385: 1382: 1377: 1373: 1367: 1362: 1355: 1352: 1348: 1323: 1318: 1316: 1315: 1314: 1313: 1302: 1299: 1296: 1292: 1288: 1285: 1282: 1279: 1276: 1270: 1267: 1262: 1259: 1218: 1217: 1204: 1200: 1197: 1193: 1189: 1164: 1133: 1130: 1127: 1124: 1120: 1115: 1111: 1104: 1101: 1097: 1081: 1075: 1065:control volume 1052: 1049: 1027: 998: 997: 984: 980: 975: 971: 967: 961: 958: 852: 849: 783:mass flow rate 735:fluid dynamics 717: 716: 714: 713: 706: 699: 691: 688: 687: 683: 682: 677: 672: 667: 662: 657: 652: 647: 642: 637: 632: 627: 622: 617: 612: 606: 605: 602: 601: 598: 597: 592: 591: 590: 589: 584: 579: 571: 570: 564: 563: 562: 561: 556: 551: 541: 536: 535: 532: 531: 526: 525: 519: 518: 516: 515: 510: 505: 500: 495: 490: 485: 479: 476: 475: 469: 468: 466: 465: 460: 455: 453:Chromatography 450: 445: 439: 436: 435: 429: 428: 426: 425: 406: 405: 404: 385: 373: 368: 356: 343: 340: 339: 331: 326: 325: 322: 321: 317: 316: 311: 306: 305: 304: 294: 289: 284: 283: 282: 277: 267: 262: 257: 252: 251: 250: 240: 234: 233: 228: 227: 224: 223: 218: 217: 216: 215: 207: 206: 202: 201: 200: 199: 194: 189: 181: 180: 174: 171: 170: 167: 166: 161: 147: 144: 139: 136: 130: 127: 124: 121: 110: 109: 103: 102: 76:turbulent flow 68:boundary layer 26: 9: 6: 4: 3: 2: 5899: 5888: 5885: 5883: 5880: 5878: 5875: 5873: 5870: 5869: 5867: 5852: 5849: 5847: 5844: 5842: 5839: 5837: 5834: 5832: 5829: 5827: 5824: 5822: 5819: 5817: 5814: 5812: 5809: 5807: 5804: 5802: 5799: 5797: 5794: 5792: 5791:Hydrodynamics 5789: 5787: 5784: 5782: 5779: 5777: 5774: 5772: 5769: 5767: 5764: 5762: 5759: 5757: 5754: 5752: 5749: 5747: 5744: 5743: 5741: 5739: 5735: 5726: 5721: 5719: 5714: 5712: 5707: 5706: 5703: 5691: 5688: 5686: 5683: 5681: 5678: 5676: 5673: 5671: 5668: 5666: 5663: 5661: 5658: 5656: 5653: 5652: 5650: 5646: 5639: 5636: 5633: 5630: 5628: 5625: 5622: 5619: 5618: 5616: 5612: 5606: 5603: 5601: 5598: 5596: 5593: 5591: 5588: 5586: 5583: 5581: 5578: 5576: 5573: 5571: 5568: 5566: 5563: 5561: 5558: 5556: 5553: 5551: 5548: 5547: 5545: 5543:organizations 5539: 5533: 5530: 5528: 5525: 5523: 5520: 5518: 5515: 5513: 5510: 5508: 5505: 5503: 5500: 5498: 5495: 5493: 5490: 5488: 5487:Duct cleaning 5485: 5483: 5480: 5477: 5474: 5472: 5469: 5467: 5464: 5462: 5459: 5457: 5454: 5453: 5451: 5443: 5437: 5434: 5432: 5429: 5427: 5424: 5421: 5418: 5416: 5413: 5411: 5408: 5406: 5403: 5401: 5398: 5396: 5393: 5391: 5388: 5385: 5382: 5379: 5376: 5374: 5371: 5369: 5366: 5364: 5361: 5359: 5356: 5354: 5351: 5349: 5346: 5344: 5341: 5339: 5338:Control valve 5336: 5333: 5330: 5328: 5325: 5323: 5320: 5318: 5315: 5313: 5310: 5308: 5305: 5303: 5300: 5299: 5297: 5291: 5285: 5282: 5280: 5277: 5275: 5272: 5270: 5267: 5264: 5261: 5259: 5258:Turning vanes 5256: 5254: 5251: 5249: 5246: 5244: 5241: 5239: 5236: 5234: 5233:Thermal wheel 5231: 5229: 5226: 5224: 5221: 5219: 5216: 5214: 5211: 5209: 5206: 5204: 5201: 5199: 5198:Solar chimney 5196: 5194: 5191: 5189: 5186: 5184: 5181: 5179: 5176: 5174: 5171: 5169: 5166: 5164: 5161: 5159: 5156: 5154: 5151: 5149: 5146: 5144: 5141: 5139: 5136: 5134: 5131: 5129: 5126: 5124: 5121: 5119: 5116: 5114: 5111: 5109: 5106: 5104: 5101: 5099: 5096: 5094: 5091: 5089: 5086: 5084: 5081: 5079: 5076: 5074: 5071: 5069: 5066: 5064: 5061: 5059: 5056: 5054: 5051: 5049: 5046: 5044: 5041: 5039: 5036: 5034: 5031: 5029: 5026: 5024: 5021: 5019: 5016: 5014: 5011: 5009: 5006: 5004: 5001: 4999: 4996: 4994: 4991: 4989: 4986: 4984: 4981: 4979: 4976: 4974: 4971: 4969: 4968:Fan coil unit 4966: 4964: 4961: 4959: 4956: 4954: 4951: 4949: 4946: 4944: 4941: 4939: 4936: 4934: 4931: 4929: 4926: 4924: 4921: 4919: 4916: 4914: 4913:Cooling tower 4911: 4909: 4906: 4904: 4901: 4899: 4896: 4894: 4891: 4889: 4886: 4884: 4881: 4879: 4876: 4874: 4871: 4869: 4866: 4864: 4861: 4859: 4856: 4854: 4851: 4849: 4846: 4844: 4841: 4839: 4836: 4834: 4831: 4829: 4826: 4824: 4821: 4819: 4816: 4814: 4811: 4809: 4806: 4804: 4801: 4800: 4798: 4794: 4788: 4785: 4783: 4780: 4777: 4774: 4771: 4768: 4765: 4762: 4760: 4759:Vapor barrier 4757: 4755: 4752: 4750: 4747: 4745: 4742: 4740: 4737: 4735: 4734:Solar heating 4732: 4730: 4729:Solar cooling 4727: 4725: 4722: 4720: 4717: 4715: 4712: 4710: 4707: 4705: 4704:Refrigeration 4702: 4700: 4697: 4695: 4692: 4690: 4687: 4685: 4682: 4680: 4677: 4675: 4674:Passive house 4672: 4670: 4667: 4665: 4662: 4660: 4657: 4655: 4652: 4650: 4647: 4645: 4642: 4640: 4637: 4635: 4632: 4629: 4626: 4624: 4621: 4619: 4616: 4614: 4611: 4609: 4606: 4603: 4600: 4598: 4595: 4593: 4590: 4588: 4585: 4583: 4580: 4577: 4574: 4572: 4569: 4566: 4563: 4561: 4558: 4556: 4553: 4550: 4547: 4545: 4544:Chilled water 4542: 4540: 4537: 4535: 4532: 4530: 4527: 4525: 4522: 4520: 4517: 4515: 4512: 4510: 4507: 4505: 4502: 4500: 4497: 4495: 4492: 4490: 4487: 4486: 4484: 4480: 4474: 4471: 4469: 4466: 4464: 4461: 4459: 4456: 4454: 4451: 4449: 4446: 4444: 4443:Sensible heat 4441: 4439: 4436: 4434: 4431: 4429: 4426: 4424: 4423:Noise control 4421: 4419: 4416: 4414: 4411: 4409: 4406: 4404: 4403:Heat transfer 4401: 4399: 4396: 4394: 4391: 4389: 4386: 4384: 4381: 4379: 4376: 4374: 4371: 4369: 4366: 4364: 4361: 4359: 4356: 4354: 4351: 4350: 4348: 4342: 4338: 4331: 4326: 4324: 4319: 4317: 4312: 4311: 4308: 4296: 4293: 4291: 4288: 4286: 4283: 4281: 4278: 4276: 4273: 4272: 4270: 4266: 4260: 4257: 4255: 4254:Ocean physics 4252: 4250: 4247: 4245: 4242: 4240: 4237: 4235: 4232: 4230: 4227: 4225: 4222: 4220: 4217: 4215: 4212: 4211: 4209: 4207: 4203: 4197: 4194: 4190: 4189:Modern optics 4187: 4185: 4182: 4180: 4177: 4176: 4175: 4172: 4170: 4167: 4165: 4162: 4160: 4157: 4153: 4150: 4148: 4145: 4144: 4143: 4140: 4139: 4137: 4135: 4131: 4123: 4120: 4118: 4115: 4114: 4113: 4110: 4106: 4103: 4101: 4098: 4097: 4096: 4093: 4091: 4088: 4086: 4083: 4079: 4076: 4074: 4071: 4069: 4066: 4064: 4061: 4060: 4059: 4056: 4055: 4053: 4051: 4047: 4039: 4038:Computational 4036: 4035: 4034: 4031: 4029: 4026: 4025: 4023: 4019: 4011: 4008: 4007: 4006: 4003: 4001: 3998: 3997: 3995: 3991: 3987: 3979: 3974: 3972: 3967: 3965: 3960: 3959: 3956: 3944: 3941: 3939: 3936: 3934: 3931: 3929: 3926: 3924: 3921: 3919: 3916: 3914: 3911: 3909: 3906: 3904: 3901: 3899: 3896: 3894: 3891: 3889: 3886: 3884: 3881: 3879: 3876: 3874: 3871: 3869: 3866: 3864: 3861: 3859: 3856: 3852: 3849: 3848: 3847: 3844: 3842: 3839: 3835: 3832: 3830: 3827: 3826: 3825: 3822: 3820: 3817: 3815: 3812: 3810: 3807: 3805: 3802: 3800: 3797: 3795: 3792: 3790: 3787: 3785: 3782: 3780: 3777: 3775: 3772: 3770: 3767: 3765: 3762: 3760: 3757: 3755: 3752: 3750: 3747: 3745: 3742: 3740: 3737: 3735: 3732: 3730: 3727: 3725: 3722: 3720: 3717: 3715: 3712: 3710: 3707: 3705: 3702: 3700: 3697: 3695: 3692: 3690: 3687: 3685: 3684:Chandrasekhar 3682: 3680: 3677: 3675: 3672: 3670: 3667: 3665: 3662: 3660: 3657: 3655: 3652: 3650: 3647: 3645: 3642: 3640: 3637: 3636: 3634: 3632: 3628: 3620: 3617: 3616: 3615: 3612: 3610: 3607: 3605: 3602: 3600: 3597: 3596: 3594: 3592: 3588: 3582: 3579: 3577: 3574: 3573: 3571: 3569: 3568:Fluid statics 3565: 3561: 3554: 3549: 3547: 3542: 3540: 3535: 3534: 3531: 3525: 3522: 3520: 3516: 3513: 3510: 3506: 3503: 3502: 3494: 3491: 3488: 3485: 3479: 3475: 3470: 3466: 3464:0-677-01710-3 3460: 3456: 3451: 3446: 3441: 3436: 3434:0-521-45868-4 3430: 3426: 3425:Hydrodynamics 3422: 3418: 3414: 3412:0-273-01120-0 3408: 3404: 3400: 3399:Clancy, L. J. 3396: 3392: 3386: 3382: 3378: 3374: 3370: 3368:0-521-66396-2 3364: 3360: 3356: 3352: 3348: 3346:0-19-859679-0 3342: 3338: 3333: 3332: 3313: 3309: 3303: 3295: 3291: 3287: 3281: 3273: 3266: 3258: 3256:0-08-033933-6 3252: 3248: 3244: 3240: 3234: 3228: 3224: 3218: 3210: 3208:0-521-59886-9 3204: 3200: 3193: 3191: 3182: 3178: 3172: 3166: 3162: 3159: 3154: 3146: 3142: 3138: 3134: 3130: 3126: 3122: 3118: 3114: 3107: 3099: 3095: 3090: 3085: 3081: 3077: 3073: 3069: 3065: 3058: 3050: 3048:0-07-069710-8 3044: 3040: 3033: 3025: 3021: 3017: 3013: 3009: 3005: 3000: 2995: 2991: 2987: 2980: 2972: 2966: 2962: 2955: 2953: 2944: 2942:3-527-40513-5 2938: 2934: 2927: 2923: 2913: 2910: 2908: 2905: 2904: 2902: 2892: 2889: 2884: 2880: 2871: 2869: 2865: 2859: 2857: 2853: 2848: 2844: 2831: 2827: 2823: 2819: 2817: 2813: 2809: 2805: 2801: 2797: 2793: 2789: 2785: 2781: 2780: 2772: 2761: 2759: 2758:fluid statics 2754: 2752: 2741: 2739: 2735: 2731: 2727: 2723: 2719: 2715: 2705: 2703: 2699: 2695: 2691: 2687: 2677: 2675: 2671: 2667: 2663: 2659: 2655: 2650: 2640: 2638: 2634: 2630: 2626: 2622: 2618: 2614: 2610: 2600: 2598: 2594: 2590: 2585: 2583: 2577: 2576:turbomachines 2573: 2569: 2563: 2545: 2541: 2537: 2533: 2529: 2528: 2523: 2520: 2516: 2515: 2511: 2508: 2504: 2500: 2499: 2494: 2491: 2487: 2486: 2482: 2479: 2475: 2474: 2469: 2468: 2464: 2461: 2457: 2453: 2452: 2447: 2446: 2445: 2437: 2435: 2431: 2427: 2426:mass transfer 2423: 2419: 2415: 2411: 2407: 2403: 2389: 2387: 2383: 2378: 2376: 2372: 2368: 2364: 2360: 2351: 2342: 2338: 2336: 2330: 2326: 2322: 2317: 2313: 2309: 2307: 2303: 2296: 2291: 2282: 2280: 2276: 2272: 2267: 2265: 2261: 2257: 2253: 2249: 2245: 2239: 2237: 2233: 2229: 2225: 2221: 2217: 2213: 2212:inviscid flow 2207: 2201: 2199: 2193: 2188: 2184: 2179: 2177: 2167: 2165: 2161: 2157: 2153: 2149: 2145: 2141: 2137: 2133: 2129: 2125: 2121: 2119: 2115: 2111: 2107: 2103: 2098: 2093: 2089: 2082: 2077: 2068: 2066: 2062: 2057: 2052: 2050: 2046: 2042: 2033: 2002: 1998: 1995: 1989: 1979: 1964: 1963: 1962: 1960: 1951: 1949: 1945: 1940: 1923: 1919: 1907: 1899: 1874: 1870: 1866: 1860: 1856: 1852: 1846: 1840: 1837: 1832: 1829: 1823: 1817: 1814: 1809: 1806: 1800: 1790: 1789: 1787: 1783: 1779: 1777: 1770: 1763: 1743: 1739: 1730: 1722: 1716: 1713: 1703: 1690: 1689: 1688: 1685: 1679: 1672: 1670: 1666: 1658: 1653: 1645: 1640: 1635: 1601: 1598: 1595: 1579: 1573: 1568: 1564: 1536: 1532: 1507: 1477: 1461: 1458: 1450: 1423: 1419: 1389: 1386: 1383: 1380: 1371: 1365: 1360: 1353: 1337: 1336: 1333: 1330: 1328: 1321: 1300: 1297: 1286: 1280: 1274: 1268: 1260: 1244: 1243: 1241: 1232: 1231:flow velocity 1227: 1198: 1195: 1187: 1162: 1131: 1128: 1125: 1122: 1118: 1113: 1109: 1102: 1086: 1085: 1082: 1078: 1073: 1072: 1070: 1066: 1062: 1058: 1048: 1046: 1042: 1034: 1023: 1015: 1007: 982: 978: 973: 969: 965: 959: 956: 949: 948: 947: 945: 941: 940:thermodynamic 936: 934: 930: 926: 922: 918: 914: 909: 907: 903: 898: 896: 892: 888: 884: 880: 876: 872: 868: 864: 858: 848: 846: 842: 837: 835: 831: 827: 823: 822:flow velocity 819: 815: 810: 808: 804: 800: 796: 792: 788: 784: 780: 776: 772: 768: 767: 766:hydrodynamics 762: 761: 756: 752: 748: 744: 740: 736: 732: 728: 724: 712: 707: 705: 700: 698: 693: 692: 690: 689: 681: 678: 676: 673: 671: 668: 666: 663: 661: 658: 656: 653: 651: 648: 646: 643: 641: 638: 636: 633: 631: 628: 626: 623: 621: 618: 616: 613: 611: 608: 607: 600: 599: 588: 585: 583: 580: 578: 575: 574: 573: 572: 569: 566: 565: 560: 557: 555: 552: 550: 547: 546: 545: 544: 539: 534: 533: 524: 521: 520: 514: 511: 509: 506: 504: 501: 499: 496: 494: 493:Charles's law 491: 489: 486: 484: 481: 480: 478: 477: 474: 471: 470: 464: 461: 459: 456: 454: 451: 449: 446: 444: 441: 440: 438: 437: 434: 431: 430: 424: 421: 417: 414: 410: 407: 402: 401:non-Newtonian 399: 395: 391: 390: 389: 386: 384: 381: 377: 374: 372: 369: 367: 364: 360: 357: 355: 352: 348: 345: 344: 342: 341: 338: 335: 334: 329: 324: 323: 315: 312: 310: 307: 303: 300: 299: 298: 295: 293: 290: 288: 287:Compatibility 285: 281: 278: 276: 275:Finite strain 273: 272: 271: 268: 266: 263: 261: 258: 256: 253: 249: 246: 245: 244: 241: 239: 236: 235: 231: 226: 225: 214: 211: 210: 209: 208: 204: 203: 198: 195: 193: 190: 188: 185: 184: 183: 182: 179:Conservations 178: 177: 169: 168: 164: 145: 142: 137: 134: 128: 125: 122: 119: 112: 111: 108: 105: 104: 100: 99: 93: 89: 85: 81: 77: 73: 69: 65: 61: 56: 49: 45: 41: 37: 32: 19: 18:Hydrodynamics 5882:Aerodynamics 5811:Maritime law 5790: 5751:Watchkeeping 5665:Fireproofing 5449:and services 5445:Professions, 5343:Gas detector 5243:Trickle vent 5218:Smoke damper 5213:Smoke canopy 5208:Space heater 5138:Plenum space 5073:Heating film 4953:Exhaust hood 4923:Dehumidifier 4863:Blast damper 4858:Barrier pipe 4833:Air purifier 4744:Thermosiphon 4623:Free cooling 4539:Chilled beam 4463:Thermal mass 4448:Stack effect 4433:Particulates 4413:Infiltration 4387: 4344:Fundamental 4214:Astrophysics 4028:Experimental 3604:Aerodynamics 3590: 3493:Scholarpedia 3473: 3454: 3444: 3424: 3421:Lamb, Horace 3403:Aerodynamics 3402: 3380: 3358: 3336: 3315:. Retrieved 3302: 3293: 3280: 3271: 3265: 3246: 3233: 3217: 3198: 3180: 3171: 3153: 3120: 3116: 3106: 3071: 3067: 3057: 3038: 3032: 2989: 2985: 2979: 2960: 2932: 2926: 2885: 2881: 2877: 2860: 2840: 2830:ISO 80000-11 2800:Mach numbers 2783: 2777: 2776: 2755: 2747: 2711: 2683: 2652: 2606: 2581: 2568:Mach numbers 2565: 2525: 2519:porous media 2512: 2503:free surface 2496: 2483: 2478:aspect ratio 2471: 2465: 2449: 2443: 2390: 2379: 2356: 2339: 2328: 2324: 2320: 2310: 2301: 2299: 2268: 2240: 2228:irrotational 2205: 2202: 2191: 2180: 2173: 2151: 2140:viscoelastic 2122: 2102:Isaac Newton 2096: 2085: 2053: 2031: 2017: 1959:fluid parcel 1952: 1939:compressible 1936: 1683: 1677: 1673: 1668: 1665:shear forces 1656: 1643: 1633: 1629: 1233:vector, and 1225: 1064: 1061:differential 1054: 1033:gas constant 999: 937: 919:—which is a 910: 899: 860: 838: 811: 765: 764: 760:aerodynamics 758: 742: 734: 720: 568:Smart fluids 513:Graham's law 419: 412: 397: 383:Pascal's law 379: 362: 353: 350: 205:Inequalities 5816:Dry-docking 5675:Warm Spaces 5317:Blower door 5295:and control 5293:Measurement 5274:Windcatcher 5248:Trombe wall 5188:Sail switch 5168:Refrigerant 5163:Recuperator 5038:Grease duct 4998:Freeze stat 4983:Fire damper 4853:Back boiler 4823:Air ionizer 4818:Air handler 4782:Ventilation 4634:Hybrid heat 4499:Air barrier 4418:Latent heat 4117:Statistical 4033:Theoretical 4010:Engineering 3938:Weissenberg 3377:Chanson, H. 2992:: 437–462. 2845:arise from 2744:Terminology 2722:white noise 2629:detonations 2625:jet engines 2562:Mach number 2514:Darcy's law 2490:Stokes flow 2402:Airbus A300 2302:steady flow 2260:drag forces 2250:, in which 2092:strain rate 2088:superfluids 2065:sound waves 2056:Mach number 1639:body forces 834:temperature 731:engineering 587:Ferrofluids 488:Boyle's law 260:Hooke's law 238:Deformation 60:aerodynamic 48:streamlines 5866:Categories 5851:Sea anchor 5746:Navigation 5738:Seamanship 5431:Thermostat 5353:Humidistat 5284:Zone valve 5253:TurboSwing 5128:Oil heater 5098:Humidifier 5028:Gas heater 4978:Fan heater 4948:Evaporator 4933:Economizer 4908:Compressor 4813:Air filter 4796:Components 4613:Forced-air 4509:Antifreeze 4482:Technology 4428:Outgassing 4368:Convection 4234:Geophysics 4224:Biophysics 4068:Analytical 4021:Approaches 3858:Richardson 3639:Archimedes 3576:Hydraulics 3317:2019-09-15 2999:1704.00239 2918:References 2816:flow speed 2670:salt water 2660:fluids in 2617:propulsion 2609:combustion 2593:supersonic 2509:are small. 2460:convection 2406:Boeing 747 2363:randomness 2164:lubricants 1774:See also: 1325:See also: 1041:molar mass 921:non-linear 855:See also: 640:Gay-Lussac 603:Scientists 503:Fick's law 483:Atmosphere 302:frictional 255:Plasticity 243:Elasticity 5846:Anchoring 5541:Industry 5390:OpenTherm 5068:Heat pump 5063:Heat pipe 5013:Fume hood 4988:Fireplace 4893:Condenser 4843:Attic fan 4639:Hydronics 4184:Molecular 4085:Acoustics 4078:Continuum 4073:Celestial 4063:Newtonian 4050:Classical 3993:Divisions 3943:Womersley 3834:turbulent 3814:Ohnesorge 3799:Marangoni 3764:Iribarren 3689:Damköhler 3674:Capillary 3509:RealMedia 3145:0044-2267 2826:ISO 31-12 2808:viscosity 2738:heat flux 2619:devices ( 2613:IC engine 2507:gradients 2312:Turbulent 2256:vorticity 2252:viscosity 2146:and some 2132:emulsions 1980:ρ 1878:Φ 1864:∇ 1853:⋅ 1850:∇ 1801:ρ 1780:Although 1744:ρ 1737:∇ 1731:− 1580:ρ 1569:∭ 1478:− 1459:⋅ 1451:ρ 1390:− 1372:ρ 1361:∭ 1351:∂ 1347:∂ 1287:ρ 1281:⋅ 1278:∇ 1266:∂ 1261:ρ 1258:∂ 1196:⋅ 1188:ρ 1132:− 1119:ρ 1110:∭ 1100:∂ 1096:∂ 966:ρ 851:Equations 791:pipelines 787:petroleum 680:Truesdell 610:Bernoulli 559:Rheometer 554:Rheometry 394:Newtonian 388:Viscosity 138:φ 126:− 5821:Ropework 5761:Pilotage 5648:See also 5373:LonWorks 5307:Aquastat 5173:Register 5153:Radiator 4808:Air door 4608:Firestop 4408:Humidity 4383:Enthalpy 4373:Dilution 4358:Bake-out 4346:concepts 3918:Suratman 3908:Strouhal 3888:Sherwood 3851:magnetic 3846:Reynolds 3841:Rayleigh 3829:magnetic 3669:Brinkman 3423:(1994). 3401:(1975). 3379:(2009). 3357:(1967). 3292:(1959). 3245:(1987). 3161:Archived 3098:29271417 3024:37560541 2895:See also 2822:aircraft 2798:and the 2796:Reynolds 2751:measured 2718:Lifshitz 2692:and the 2595:or even 2572:subsonic 2538:and the 2534:between 2456:buoyancy 2236:gradient 2154:such as 2148:polymers 2136:slurries 2128:rheology 2061:Acoustic 1898:enthalpy 1057:integral 1024:, while 1006:pressure 915:are the 826:pressure 789:through 779:aircraft 538:Rheology 443:Adhesion 423:Pressure 409:Buoyancy 354:Dynamics 192:Momentum 92:spoilers 88:Kammback 58:Typical 40:vortices 36:shedding 5841:Mooring 5836:Buoyage 5771:Sailing 5447:trades, 5018:Furnace 4883:Chiller 4555:Coolant 4268:Related 4152:General 4147:Special 4005:Applied 3898:Stanton 3893:Shields 3883:Scruton 3878:Schmidt 3824:Prandtl 3809:Nusselt 3784:Laplace 3779:Knudsen 3769:Kapitza 3754:Görtler 3749:Grashof 3739:Galilei 3704:Deborah 3649:Bagnold 3511:format) 3125:Bibcode 3089:5811736 3004:Bibcode 2828:and in 2804:density 2666:plasmas 2633:methane 2621:rockets 2375:average 2367:laminar 2138:, some 2081:airfoil 2039:is the 2036:⁠ 2021:⁠ 1904:is the 1892:Above, 1229:is the 1219:Above, 1031:is the 1020:is the 1014:density 923:set of 830:density 799:nebulae 775:moments 751:liquids 723:physics 625:Charles 433:Liquids 347:Statics 292:Bending 64:viscous 5877:Piping 5600:SMACNA 5560:ASHRAE 5380:(MERV) 5334:(CADR) 5312:BACnet 5265:(ULPA) 5118:Louver 5043:Grille 4918:Damper 4868:Boiler 4766:(VCRS) 4567:(DOAS) 4179:Atomic 4134:Modern 3984:Major 3928:Ursell 3923:Taylor 3913:Stuart 3903:Stokes 3868:Rossby 3863:Roshko 3819:PĂ©clet 3804:Morton 3744:Graetz 3734:Froude 3724:Eötvös 3714:Eckert 3709:Dukhin 3679:Cauchy 3644:Atwood 3480:  3461:  3431:  3409:  3387:  3365:  3343:  3253:  3205:  3143:  3096:  3086:  3045:  3022:  2967:  2939:  2814:, and 2788:fluids 2714:Landau 2359:eddies 2306:sphere 2150:, and 2114:stress 2112:, the 2018:where 1798:  1786:energy 1782:energy 1698:  1669:moving 1252:  1016:, and 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Index

Hydrodynamics

shedding
vortices
von KĂĄrmĂĄn vortex street
streamlines

aerodynamic
viscous
boundary layer
vortex generators
turbulent flow
flow separation
shark-like skin
Kammback
spoilers
Continuum mechanics
Fick's laws of diffusion
Mass
Momentum
Energy
Clausius–Duhem (entropy)
Solid mechanics
Deformation
Elasticity
linear
Plasticity
Hooke's law
Stress
Strain

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