Continuum mechanics

Conservation of mass Conservation of momentum Navier–Stokes equations

This box: view • talk • edit

Typical aerodynamic teardrop shape, showing the pressure distribution as the thickness of the black line and showing the velocity in the boundary layer as the violet triangles. Continuum mechanics is a branch of Mechanics that deals with the analysis of the Kinematics and mechanical behavior of materials modeled as a continuum e The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov - Lavoisier law says that the Mass of In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product The Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous Fluid substances such In Physics and Fluid mechanics, a boundary layer is that layer of Fluid in the immediate vicinity of a bounding surface The green vortex generators prompt the transition to turbulent flow and prevent back-flow also called flow separation from the high pressure region in the back. A vortex generator is an Aerodynamic surface consisting of a small Vane that creates a Vortex. In Fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic Stochastic property changes All solid objects travelling through a Fluid (or alternatively a stationary object exposed to a moving fluid acquire a Boundary layer of fluid around them where viscous The surface in front is as smooth as possible or even employ shark like skin, as any turbulence here will reduce the energy of the airflow. Denticles are body surface structures found on some fish and insects The Kammback also prevents back flow from the high pressure region in the back across the spoilers to the convergent part. A Kammback is a Car body style that derives from the research of the German aerodynamicist Wunibald Kamm in the 1930s this research itself deriving In Aeronautics a spoiler (sometimes called a lift dumper) is a device intended to reduce lift in an aircraft Putting stuff inside out results in tubes, they also face the problem of flow separation in their divergent parts, so called diffusers. For other uses see Pipe. Within Industry, piping is a system of pipes used to convey Fluids ( Liquids and A diffuser, in an automotive context is a shaped section of the Car underbody which improves the car's Aerodynamic properties by enhancing the transition between Cutting the shape into halfs results in an aerofoil with the low pressure region on top leading to lift (force). An airfoil (in American English) or aerofoil (in British English) is the shape of a Wing or blade (of a Propeller, rotor In the context of a Fluid flow relative to a body the lift force is the component of the Aerodynamic force that is Perpendicular to the flow

Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluid flow: fluids (liquids and gases) in motion. Fluid mechanics is the study of how Fluids move and the Forces on them FLUID ( F ast L ight '''U'''ser '''I'''nterface D esigner is a graphical editor that is used to produce FLTK Source code Liquid is one of the principal States of matter. A liquid is a Fluid that has the particles loose and can freely form a distinct surface at the boundaries of This page is about the physical properties of gas as a state of matter It has several subdisciplines itself, including aerodynamics (the study of gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and reportedly modeling fission weapon detonation. In Physics, a force is whatever can cause an object with Mass to Accelerate. In Physics, the moment of force (often just moment, though there are other quantities of that name such as Moment of inertia) is a Pseudovector Mass flow rate is the movement of Mass per Time. Its unit is mass divided by Time, so Kilogram per Second in SI Petroleum ( L petroleum, from Greek πετρέλαιον, lit The weather is a set of all the phenomena occurring in a given Atmosphere at a given Time. A nebula (from Latin: "mist" pl nebulae or nebulæ, with ligature or nebulas) is an Interstellar cloud of Some of its principles are even used in traffic engineering, where traffic is treated as a continuous fluid. Traffic engineering is a branch of Civil engineering that uses engineering techniques to achieve the safe and efficient movement of people and goods

Fluid dynamics offers a systematic structure that underlies these practical disciplines and that embraces empirical and semi-empirical laws, derived from flow measurement, used to solve practical problems. Flow measurement is the quantification of bulk Fluid movement The solution of a fluid dynamics problem typically involves calculation of various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time. In Physics, velocity is defined as the rate of change of Position. Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature

Equations of fluid dynamics

The foundational axioms of fluid dynamics are the conservation laws, specifically, conservation of mass, conservation of linear momentum (also known as Newton's Second Law of Motion), and conservation of energy (also known as First Law of Thermodynamics). In Physics, a conservation law states that a particular measurable property of an isolated Physical system does not change as the system evolves The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov - Lavoisier law says that the Mass of In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product Newton's laws of motion are three Physical laws which provide relationships between the Forces acting on a body and the motion of the In Physics, the law of conservation of energy states that the total amount of Energy in an isolated system remains constant and cannot be created although it may In Thermodynamics, the first law of thermodynamics is an expression of the more universal physical law of the Conservation of energy. These are based on classical mechanics and are modified in quantum mechanics and general relativity. Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 They are expressed using the Reynolds Transport Theorem. Reynolds transport theorem is a fundamental theorem used in formulating the basic conservation laws of Fluid dynamics.

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

For fluids which are sufficiently dense to be a continuum, do not contain ionized species, and have velocities small in relation to the speed of light, the momentum equations for Newtonian fluids are the Navier-Stokes equations, which is a non-linear set of differential equations that describes the flow of a fluid whose stress depends linearly on velocity gradients and pressure. A Newtonian fluid (named for Isaac Newton) is a Fluid whose stress versus rate of strain curve is linear and passes through the origin The Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous Fluid substances such This article describes the use of the term nonlinearity in mathematics A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the The unsimplified equations do not have a general closed-form solution, so they are only of use in Computational Fluid Dynamics or when they can be simplified. Computational fluid dynamics (CFD is one of the branches of Fluid mechanics that uses Numerical methods and algorithms to solve and analyze problems that involve 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.

In addition to the mass, momentum, and energy conservation equations, a thermodynamical equation of state giving the pressure as a function of other thermodynamic variables for the fluid is required to completely specify the problem. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " An example of this would be the perfect gas equation of state:

where p is pressure, ρ is density, R_u is the gas constant, M is the molecular mass and T is temperature. The ideal gas law is the Equation of state of a hypothetical Ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834 Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Relationship with the Boltzmann constant The Boltzmann constant kB (often abbreviated k) may be used in place of the gas constant by working The molecular mass (abbreviated m of a substance, more commonly referred to as molecular weight and abbreviated as MW, is the Mass of one Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature

Compressible vs incompressible flow

All fluids are compressible to some extent, that is changes in pressure or temperature will result in changes in density. In Thermodynamics and Fluid mechanics, compressibility is a measure of the relative volume change of a Fluid or Solid as a response However, in many situations the changes in pressure and temperature are sufficiently small that the changes in density are negligible. In this case the flow can be modeled as an incompressible flow. In Fluid mechanics or more generally Continuum mechanics, an incompressible flow is Solid or Fluid flow in which the Divergence of Otherwise the more general compressible flow equations must be used. A flow is considered to be a compressible flow if the change in Density of the flow with respect to Pressure is non-zero along a streamline.

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. ,

where D / Dt is the substantial derivative, which is the sum of local and convective derivatives. This additional constraint simplifies the governing equations, especially in the case when the fluid has a uniform density.

For flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the Mach number of the flow is to be evaluated. Mach number (\mathrm{Ma} or M (generally ˈmɑːk sometimes /ˈmɑːx/ or /ˈmæk/ is the speed of an object moving through air or any Fluid As a rough guide, compressible effects can be ignored at Mach numbers below approximately 0. 3. For liquids, whether the incompressible assumption is valid depends on the fluid properties (specifically the critical pressure and temperature of the fluid) and the flow conditions (how close to the critical pressure the actual flow pressure becomes). Acoustic problems always require allowing compressibility, since sound waves are compression waves involving changes in pressure and density of the medium through which they propagate. Acoustics is the interdisciplinary science that deals with the study of Sound, Ultrasound and Infrasound (all mechanical waves in gases liquids and solids Sound' is Vibration transmitted through a Solid, Liquid, or Gas; particularly sound means those vibrations composed of Frequencies

Viscous vs inviscid flow

Viscous problems are those in which fluid friction has significant effects on the fluid motion. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress.

The Reynolds number can be used to evaluate whether viscous or inviscid equations are appropriate to the problem. In Fluid mechanics and Heat transfer, the Reynolds number \mathrm{Re} is a Dimensionless number that gives a measure of the Ratio

Stokes flow is flow at very low Reynolds numbers, such that inertial forces can be neglected compared to viscous forces. Stokes flow (named after George Gabriel Stokes) is a type of Fluid flow where advective inertial forces are small compared with viscous

On the contrary, high Reynolds numbers indicate that the inertial forces are more significant than the viscous (friction) forces. Therefore, we may assume the flow to be an inviscid flow, an approximation in which we neglect viscosity at all, compared to inertial terms. In Fluid dynamics there are problems that are easily solved by using the simplifying assumption of an ideal Fluid that has no Viscosity. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress.

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. In Fluid dynamics, the no-slip condition for viscous fluid states that at a solid boundary the fluid will have zero velocity relative to the boundary In Physics and Fluid mechanics, a boundary layer is that layer of Fluid in the immediate vicinity of a bounding surface Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress. Vorticity is a mathematical concept used in Fluid dynamics. It can be related to the amount of " circulation " or "rotation" (or more strictly the 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. In Fluid dynamics, d'Alembert's paradox is a contradiction reached by French mathematician Jean le Rond d'Alembert in 1752 who proves that for — Incompressible The standard equations of inviscid flow are the Euler equations. Another often used model, especially in computational fluid dynamics, is to use the Euler equations away from the body and the boundary layer equations, which incorporates viscosity, in a region close to the body. In Physics and Fluid mechanics, a boundary layer is that layer of Fluid in the immediate vicinity of a bounding surface

The Euler equations can be integrated along a streamline to get Bernoulli's equation. In Fluid dynamics, Bernoulli's principle states that for an Inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in When the flow is everywhere irrotational and inviscid, Bernoulli's equation can be used throughout the flow field. In Vector analysis and in fluid dynamics, a lamellar vector field is a Vector field with no rotational component Such flows are called potential flows. In Fluid dynamics, a potential flow is a Velocity field which is described as the Gradient of a scalar function the velocity potential

Steady vs unsteady flow

Hydrodynamics simulation of the Rayleigh–Taylor instability ^[1]

When all the time derivatives of a flow field vanish, the flow is considered to be a steady flow. The Rayleigh–Taylor instability, or RT instability (after Lord Rayleigh and G Otherwise, it is called unsteady. Whether a particular flow is steady or unsteady, can depend on the chosen frame of reference. See also Inertial frame A frame of reference in Physics, may refer to a Coordinate system or set of axes within which to For instance, laminar flow over a sphere is steady in the frame of reference that is stationary with respect to the sphere. "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe In a frame of reference that is stationary than the governing equations of the same problem without taking advantage of the steadiness of the flow field.

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

Laminar vs turbulent flow

Turbulence is flow dominated by recirculation, eddies, and apparent randomness. In Fluid dynamics, turbulence or turbulent flow is a fluid regime characterized by chaotic Stochastic property changes In Fluid dynamics, an eddy is the swirling of a Fluid and the reverse current created when the fluid flows past an obstacle Randomness is a lack of order Purpose, cause, or predictability Flow in which turbulence is not exhibited is called laminar. Laminar flow, sometimes known as streamline flow occurs when a fluid flows in parallel layers with no disruption between the layers It should be noted, however, that the presence of eddies or recirculation does not necessarily indicate turbulent flow--these phenomena may be present in laminar flow as well. Mathematically, turbulent flow is often represented via Reynolds decomposition, in which the flow is broken down into the sum of a steady component and a perturbation component. In Fluid dynamics and the theory of Turbulence, Reynolds decomposition is a mathematicaltechnique to separate the average and fluctuating parts of a quantity

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

Most flows of interest have Reynolds numbers too high for DNS to be a viable option (see: Pope), given the state of computational power for the next few decades. Any flight vehicle large enough to carry a human (L > 3 m), moving faster than 72 km/h (20 m/s) is well beyond the limit of DNS simulation (Re = 4 million). Transport aircraft wings (such as on an Airbus A300 or Boeing 747) have Reynolds numbers of 40 million (based on the wing chord). WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout WikipediaWikiProject Aircraft. Please see WikipediaWikiProject Aircraft/page content for recommended layout In order to solve these real life flow problems, turbulence models will be a necessity for the foreseeable future. Reynolds-Averaged Navier-Stokes equations (RANS) combined with turbulence modeling provides a model of the effects of the turbulent flow, mainly the additional momentum transfer provided by the Reynolds stresses, although the turbulence also enhances the heat and mass transfer. The Reynolds-averaged Navier–Stokes (RANS equations are time-averagedequations of motion for Fluid flow. Turbulence modeling is the area of physical modeling where a simpler Mathematical model than the full time dependent Navier-Stokes Equations is used to predict the In Fluid dynamics, the Reynolds stresses (or the Reynolds Stress tensor) is the stress tensor in a fluid due to the random turbulent fluctuations in fluid momentum In thermal physics, heat transfer is the passage of Thermal energy from a hot to a colder body Mass transfer is the phrase commonly used in engineering for physical processes that involve molecular and convective transport of Atoms and Molecules Large Eddy Simulation (LES) also holds promise as a simulation methodology, especially in the guise of Detached Eddy Simulation (DES), which is a combination of turbulence modeling and large eddy simulation. Large eddy simulation (LES is a numerical technique used to solve the Partial differential equations governing turbulent fluid flow. Detached eddy simulation ( DES) is a modification of a RANS model in which the model switches to a subgrid scale formulation in regions fine enough for LES Turbulence modeling is the area of physical modeling where a simpler Mathematical model than the full time dependent Navier-Stokes Equations is used to predict the

Newtonian vs non-Newtonian fluids

Sir Isaac Newton showed how stress and the rate of strain are very close to linearly related for many familiar fluids, such as water and air. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Stress is a measure of the average amount of Force exerted per unit Area. Water is a common Chemical substance that is essential for the survival of all known forms of Life. Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five These Newtonian fluids are modeled by a coefficient called viscosity, which depends on the specific fluid. A Newtonian fluid (named for Isaac Newton) is a Fluid whose stress versus rate of strain curve is linear and passes through the origin Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress.

However, some of the other materials, such as emulsions and slurries and some visco-elastic materials (eg. blood, some polymers), have more complicated non-Newtonian stress-strain behaviours. Blood is a specialized Bodily fluid that delivers necessary substances to the body's cells ��such as nutrients and oxygen—and transports Waste products A polymer is a large Molecule ( Macromolecule) composed of repeating Structural units typically connected by Covalent Chemical bonds A non-Newtonian fluid is a Fluid whose flow properties are not described by a single constant value of Viscosity. These materials include sticky liquids such as latex, honey, and lubricants which are studied in the sub-discipline of rheology. LaTeX (ˈleɪtɛ Honey is a sweet and Viscous fluid produced by Honey bees (and some other species and derived from the nectar of Flowers According to the Rheology is the study of the flow of matter mainly liquids but also soft solids or solids under conditions in which they flow rather than deform elastically

Magnetohydrodynamics

Main article: Magnetohydrodynamics

Magnetohydrodynamics is the multi-disciplinary study of the flow of electrically conducting fluids in electromagnetic fields. Magnetohydrodynamics (MHD ( magnetofluiddynamics or hydromagnetics) is the Academic discipline which studies the dynamics of electrically Magnetohydrodynamics (MHD ( magnetofluiddynamics or hydromagnetics) is the Academic discipline which studies the dynamics of electrically Electrical conduction is the movement of electrically charged particles through a Transmission medium ( Electrical conductor) Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of Examples of such fluids include plasmas, liquid metals, and salt water. The fluid flow equations are solved simultaneously with Maxwell's equations of electromagnetism. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric

Other approximations

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

• The Boussinesq approximation neglects variations in density except to calculate buoyancy forces. In Fluid dynamics, the Boussinesq approximation (named for Joseph Valentin Boussinesq) is used in the field of buoyancy-driven flow (also known as Natural In Physics, buoyancy ( BrE IPA: /ˈbɔɪənsi/ is the upward Force on an object produced by the surrounding liquid or gas in which it is It is often used in free convection problems where density changes are small. Convection in the most general terms refers to the movement of molecules within Fluids (i
• Lubrication theory exploits the large aspect ratio of the domain to show that certain terms in the equations are small and so can be neglected. A branch of Fluid dynamics, lubrication theory is used to describe the flow of fluids (liquids or gases in a geometry in which one dimension is significantly smaller than the others The aspect ratio of a Shape is the ratio of its longer Dimension to its shorter dimension
• 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. Slender-body theory is a methodology that can be used to take advantage of the slenderness of a body to obtain an approximation to a field surrounding it and/or the net effect of the field Stokes flow (named after George Gabriel Stokes) is a type of Fluid flow where advective inertial forces are small compared with viscous
• The shallow-water equations can be used to describe a layer of relatively inviscid fluid with a free surface, in which surface gradients are small. The shallow water equations (also called Saint Venant equations after Adhémar Jean Claude Barré de Saint-Venant) are a set of Hyperbolic partial differential In Physics a free surface is the surface of a body that is subject to neither perpendicular normal stress nor parallel Shear stress,such as the boundary Slope is used to describe the steepness incline gradient or grade of a straight line.
• The Boussinesq equations are applicable to surface waves on thicker layers of fluid and with steeper surface slopes. In Fluid dynamics, the Boussinesq approximation for Water waves is an Approximation valid for weakly Non-linear and fairly long waves In Physics, surface wave can refer to a Mechanical wave that propagates along the interface between differing media usually two fluids with different densities Slope is used to describe the steepness incline gradient or grade of a straight line.
• Darcy's law is used for flow in porous media, and works with variables averaged over several pore-widths. In Fluid dynamics, Darcy's law is a phenomologically derived Constitutive equation that describes the flow of a Fluid through a Porous medium A porous medium or a porous Material is a Solid (often called frame or matrix permeated by an interconnected network of pores (voids filled with a
• In rotating systems, the quasi-geostrophic approximation assumes an almost perfect balance between pressure gradients and the Coriolis force. In Atmospheric science, balanced flow is an idealisation of atmospheric motion In atmospheric sciences ( Meteorology, Climatology and related fields the pressure gradient (typically of air, more generally of any Fluid) In physics the Coriolis effect is an apparent deflection of moving objects when they are viewed from a Rotating frame of reference. It is useful in the study of atmospheric dynamics. Atmospheric physics is the application of Physics to the study of the atmosphere.

Terminology in fluid dynamics

The concept of pressure is central to the study of both fluid statics and fluid dynamics. Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface A pressure can be identified for every point in a body of fluid, regardless of whether the fluid is in motion or not. Pressure can be measured using an aneroid, Bourdon tube, mercury column, or various other methods. Many techniques have been developed for the measurement of Pressure and Vacuum.

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

Terminology in incompressible fluid dynamics

The concepts of total pressure (also known as stagnation pressure) and dynamic pressure arise from Bernoulli's equation and are significant in the study of all fluid flows. In Fluid dynamics, stagnation pressure is the Pressure at a Stagnation point in a fluid flow where the kinetic energy is converted into pressure energy In Fluid dynamics dynamic pressure (indicated with q, or Q, and sometimes called velocity pressure) is the quantity defined by In Fluid dynamics, Bernoulli's principle states that for an Inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in (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. Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface In the design and operation of Aircraft, static pressure is the air pressure in the aircraft’s static pressure system. Static pressure is identical to pressure and can be identified for every point in a fluid flow field. In the design and operation of Aircraft, static pressure is the air pressure in the aircraft’s static pressure system. Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface

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

A point in a fluid flow where the flow has come to rest (i. e. speed is equal to zero adjacent to some solid body immersed in the fluid flow) is of special significance. It is of such importance that it is given a special name - a stagnation point. The stagnation point is a point on the surface of a body submerged in a fluid flow where the fluid Velocity is zero The pressure at the stagnation point is of special significance and is given its own name - stagnation pressure, which is equal to the total pressure. Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface In Fluid dynamics, stagnation pressure is the Pressure at a Stagnation point in a fluid flow where the kinetic energy is converted into pressure energy

Terminology in compressible fluid dynamics

In a compressible fluid, such as air, the temperature and density are essential when determining the state of the fluid. In addition to the concept of total pressure (also known as stagnation pressure), the concepts of total (or stagnation) temperature and total (or stagnation) density are also essential in any study of compressible fluid flows. In Fluid dynamics, stagnation pressure is the Pressure at a Stagnation point in a fluid flow where the kinetic energy is converted into pressure energy 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.

The temperature and density at a stagnation point are called stagnation temperature and stagnation density. The stagnation point is a point on the surface of a body submerged in a fluid flow where the fluid Velocity is zero

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

A similar approach is also taken with the thermodynamic properties of compressible fluids. Many authors use the terms total (or stagnation) enthalpy and total (or stagnation) entropy. In Thermodynamics and molecular chemistry, the enthalpy (denoted as H, h, or rarely as χ) is a quotient or description of In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy 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.

References

• Acheson, D. J. (1990) "Elementary Fluid Dynamics" (Clarendon Press).
• Batchelor, G.K. (1967) "An Introduction to Fluid Dynamics" (Cambridge University Press). George Keith Batchelor ( March 8 1920 - March 30 2000) was an Australian Applied mathematician and Fluid dynamicist
• Clancy, L. J. (1975) "Aerodynamics" (Pitman Publishing Limited).
• Lamb, H. (1994) "Hydrodynamics" (Cambridge University Press, 6^th ed. Sir Horace Lamb FRS ( 29 November 1849 – 4 December 1934) was a British Applied mathematician and author of several influential ). Originally published in 1879, the 6^th extended edition appeared first in 1932.
• Landau, L.D. and Lifshitz, E.M. (1987) "Fluid Mechanics" (Pergamon Press, 2^nd ed. Lev Davidovich Landau ( Russian language: Ле́в Дави́дович Ланда́у ( January 22, 1908 &ndash April 1, 1968 Evgeny Mikhailovich Lifshitz (Евгений Михайлович Лифшиц February 21 1915 &ndash October 29 1985) was a leading Soviet ).
• Milne-Thompson, L. M. (1968) "Theoretical Hydrodynamics" (Macmillan, 5^th ed. ). Originally published in 1938.
• Pope, S. B. (2000) "Turbulent Flows" (Cambridge University Press).
• Shinbrot, Marvin (1973) "Lectures on Fluid Mechanics" (Gordon and Breach)

Notes

See also

External links

• Fluid Mechanics @ Chemical Engineering Information Exchange
• Geophysical and Astrophysical Fluid Dynamics
• List of Fluid Dynamics books