1.
Eta
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Eta is the seventh letter of the Greek alphabet. Originally denoting a consonant /h/, its value in the classical Attic dialect of Ancient Greek was a long vowel, raised to in hellenistic Greek. In the system of Greek numerals it has a value of 8 and it was derived from the Phoenician letter heth. Letters that arose from eta include the Latin H and the Cyrillic letter И, the letter shape H was originally used in most Greek dialects to represent the sound /h/, a voiceless glottal fricative. In this function, it was borrowed in the 8th century BC by the Etruscan and other Old Italic alphabets and this also gave rise to the Latin alphabet with its letter H. Other regional variants of the Greek alphabet, in dialects that still preserved the sound /h/, in the southern Italian colonies of Heracleia and Tarentum, the letter shape was reduced to a half-heta lacking the right vertical stem. From this sign later developed the sign for rough breathing or spiritus asper, in 403 BC, Athens took over the Ionian spelling system and with it the vocalic use of H. This later became the standard orthography in all of Greece, itacism is continued into Modern Greek, where the letter name is pronounced and represents the sound /i/. It shares this function with other letters and digraphs, which are all pronounced alike. This phenomenon at large is called iotacism, Eta was also borrowed with the sound value of into the Cyrillic script, where it gave rise to the Cyrillic letter И. In Modern Greek the letter, pronounced, represents a close front unrounded vowel, in Classical Greek, it represented a long open-mid front unrounded vowel, /ɛː/. The upper-case letter Η is used as a symbol in textual criticism for the Alexandrian text-type, the lower-case letter η is used as a symbol in, Thermodynamics, the efficiency of a Carnot heat engine, or packing fraction. Chemistry, the hapticity, or the number of atoms of an attached to one coordination site of the metal in a coordination compound. For example, a group can coordinate to palladium in the η¹ mode or the η³ mode. Optics, the impedance of a medium, or the quantum efficiency of detectors. Particle physics, to represent the η mesons, experimental particle physics, η stands for pseudorapidity. Cosmology, η represents conformal time, dt = adη, relativity and Quantum field theory, η represents the metric tensor of Minkowski space. Statistics, η2 is the regression coefficient
2.
Mu (letter)
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Mu is the 12th letter of the Greek alphabet. In the system of Greek numerals it has a value of 40, Mu was derived from the Egyptian hieroglyphic symbol for water, which had been simplified by the Phoenicians and named after their word for water, to become
3.
Shear modulus
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Its dimensional form is M1L−1T−2, replacing force by mass times acceleration. The shear modulus is always positive, the shear modulus is one of several quantities for measuring the stiffness of materials. These moduli are not independent, and for materials they are connected via the equations 2 G = E =3 K. The shear modulus is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force, in the case of an object thats shaped like a rectangular prism, it will deform into a parallelepiped. Anisotropic materials such as wood, paper and also essentially all single crystals exhibit differing material response to stress or strain when tested in different directions, in this case one may need to use the full tensor-expression of the elastic constants, rather than a single scalar value. One possible definition of a fluid would be a material with zero shear modulus, in homogeneous and isotropic solids, there are two kinds of waves, pressure waves and shear waves. The velocity of a wave, is controlled by the shear modulus. The shear modulus of metals is usually observed to decrease with increasing temperature, at high pressures, the shear modulus also appears to increase with the applied pressure. Correlations between the temperature, vacancy formation energy, and the shear modulus have been observed in many metals. Several models exist that attempt to predict the shear modulus of metals, the Steinberg-Cochran-Guinan shear modulus model developed by and used in conjunction with the Steinberg-Cochran-Guinan-Lund flow stress model. The Nadal and LePoac shear modulus model that uses Lindemann theory to determine the temperature dependence and the SCG model for pressure dependence of the shear modulus. The MTS shear modulus model has the form, μ = μ0 − D exp −1 where μ0 is the shear modulus at T =0 K, the Nadal-Le Poac shear modulus model is a modified version of the SCG model. The empirical temperature dependence of the modulus in the SCG model is replaced with an equation based on Lindemann melting theory. Dynamic modulus Impulse excitation technique Shear strength Seismic moment
4.
Time
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Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future. Time is often referred to as the dimension, along with the three spatial dimensions. Time has long been an important subject of study in religion, philosophy, and science, nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems. Two contrasting viewpoints on time divide prominent philosophers, one view is that time is part of the fundamental structure of the universe—a dimension independent of events, in which events occur in sequence. Isaac Newton subscribed to this realist view, and hence it is referred to as Newtonian time. This second view, in the tradition of Gottfried Leibniz and Immanuel Kant, holds that time is neither an event nor a thing, Time in physics is unambiguously operationally defined as what a clock reads. Time is one of the seven fundamental physical quantities in both the International System of Units and International System of Quantities, Time is used to define other quantities—such as velocity—so defining time in terms of such quantities would result in circularity of definition. The operational definition leaves aside the question there is something called time, apart from the counting activity just mentioned, that flows. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy. Furthermore, it may be there is a subjective component to time. Temporal measurement has occupied scientists and technologists, and was a motivation in navigation. Periodic events and periodic motion have long served as standards for units of time, examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, and the beat of a heart. Currently, the unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms. Time is also of significant social importance, having economic value as well as value, due to an awareness of the limited time in each day. In day-to-day life, the clock is consulted for periods less than a day whereas the calendar is consulted for periods longer than a day, increasingly, personal electronic devices display both calendars and clocks simultaneously. The number that marks the occurrence of an event as to hour or date is obtained by counting from a fiducial epoch—a central reference point. Artifacts from the Paleolithic suggest that the moon was used to time as early as 6,000 years ago. Lunar calendars were among the first to appear, either 12 or 13 lunar months, without intercalation to add days or months to some years, seasons quickly drift in a calendar based solely on twelve lunar months
5.
Drag (physics)
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In fluid dynamics, drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two layers or a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are independent of velocity. Drag force is proportional to the velocity for a laminar flow, even though the ultimate cause of a drag is viscous friction, the turbulent drag is independent of viscosity. Drag forces always decrease fluid velocity relative to the object in the fluids path. In the case of viscous drag of fluid in a pipe, in physics of sports, the drag force is necessary to explain the performance of runners, particularly of sprinters. Types of drag are generally divided into the categories, parasitic drag, consisting of form drag, skin friction, interference drag, lift-induced drag. The phrase parasitic drag is used in aerodynamics, since for lifting wings drag it is in general small compared to lift. For flow around bluff bodies, form and interference drags often dominate, further, lift-induced drag is only relevant when wings or a lifting body are present, and is therefore usually discussed either in aviation or in the design of semi-planing or planing hulls. Wave drag occurs either when an object is moving through a fluid at or near the speed of sound or when a solid object is moving along a fluid boundary. Drag depends on the properties of the fluid and on the size, shape, at low R e, C D is asymptotically proportional to R e −1, which means that the drag is linearly proportional to the speed. At high R e, C D is more or less constant, the graph to the right shows how C D varies with R e for the case of a sphere. As mentioned, the equation with a constant drag coefficient gives the force experienced by an object moving through a fluid at relatively large velocity. This is also called quadratic drag, the equation is attributed to Lord Rayleigh, who originally used L2 in place of A. Sometimes a body is a composite of different parts, each with a different reference areas, in the case of a wing the reference areas are the same and the drag force is in the same ratio to the lift force as the ratio of drag coefficient to lift coefficient. Therefore, the reference for a wing is often the area rather than the frontal area. For an object with a surface, and non-fixed separation points—like a sphere or circular cylinder—the drag coefficient may vary with Reynolds number Re. For an object with well-defined fixed separation points, like a disk with its plane normal to the flow direction
6.
Shear stress
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A shear stress, often denoted τ, is defined as the component of stress coplanar with a material cross section. Shear stress arises from the vector component parallel to the cross section. Normal stress, on the hand, arises from the force vector component perpendicular to the material cross section on which it acts. The formula to calculate average shear stress is force per unit area, τ = F A, where, τ = the shear stress, F = the force applied, A = the cross-sectional area of material with area parallel to the applied force vector. Pure shear stress is related to shear strain, denoted γ, by the following equation, τ = γ G where G is the shear modulus of the isotropic material. Here E is Youngs modulus and ν is Poissons ratio, beam shear is defined as the internal shear stress of a beam caused by the shear force applied to the beam. The beam shear formula is known as Zhuravskii shear stress formula after Dmitrii Ivanovich Zhuravskii who derived it in 1855. Shear stresses within a structure may be calculated by idealizing the cross-section of the structure into a set of stringers. Dividing the shear flow by the thickness of a portion of the semi-monocoque structure yields the shear stress. Any real fluids moving along solid boundary will incur a shear stress on that boundary, the no-slip condition dictates that the speed of the fluid at the boundary is zero, but at some height from the boundary the flow speed must equal that of the fluid. The region between two points is aptly named the boundary layer. For all Newtonian fluids in laminar flow the shear stress is proportional to the rate in the fluid where the viscosity is the constant of proportionality. However, for non-Newtonian fluids, this is no longer the case as for these fluids the viscosity is not constant, the shear stress is imparted onto the boundary as a result of this loss of velocity. Specifically, the shear stress is defined as, τ w ≡ τ = μ ∂ u ∂ y | y =0. For an isotropic Newtonian flow it is a scalar, while for anisotropic Newtonian flows it can be a second-order tensor too. On the other hand, given a shear stress as function of the flow velocity, the constant one finds in this case is the dynamic viscosity of the flow. On the other hand, a flow in which the viscosity were and this nonnewtonian flow is isotropic, so the viscosity is simply a scalar, μ =1 u. This relationship can be exploited to measure the shear stress
7.
Stress (mechanics)
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For example, when a solid vertical bar is supporting a weight, each particle in the bar pushes on the particles immediately below it. When a liquid is in a container under pressure, each particle gets pushed against by all the surrounding particles. The container walls and the pressure-inducing surface push against them in reaction and these macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the particles in those molecules. Strain inside a material may arise by various mechanisms, such as stress as applied by external forces to the material or to its surface. Any strain of a material generates an internal elastic stress, analogous to the reaction force of a spring. In liquids and gases, only deformations that change the volume generate persistent elastic stress, however, if the deformation is gradually changing with time, even in fluids there will usually be some viscous stress, opposing that change. Elastic and viscous stresses are usually combined under the mechanical stress. Significant stress may exist even when deformation is negligible or non-existent, stress may exist in the absence of external forces, such built-in stress is important, for example, in prestressed concrete and tempered glass. Stress may also be imposed on a material without the application of net forces, for example by changes in temperature or chemical composition, stress that exceeds certain strength limits of the material will result in permanent deformation or even change its crystal structure and chemical composition. In some branches of engineering, the stress is occasionally used in a looser sense as a synonym of internal force. For example, in the analysis of trusses, it may refer to the total traction or compression force acting on a beam, since ancient times humans have been consciously aware of stress inside materials. Until the 17th century the understanding of stress was largely intuitive and empirical, with those tools, Augustin-Louis Cauchy was able to give the first rigorous and general mathematical model for stress in a homogeneous medium. Cauchy observed that the force across a surface was a linear function of its normal vector, and, moreover. The understanding of stress in liquids started with Newton, who provided a formula for friction forces in parallel laminar flow. Stress is defined as the force across a small boundary per unit area of that boundary, following the basic premises of continuum mechanics, stress is a macroscopic concept. In a fluid at rest the force is perpendicular to the surface, in a solid, or in a flow of viscous liquid, the force F may not be perpendicular to S, hence the stress across a surface must be regarded a vector quantity, not a scalar. Moreover, the direction and magnitude depend on the orientation of S. Thus the stress state of the material must be described by a tensor, called the stress tensor, with respect to any chosen coordinate system, the Cauchy stress tensor can be represented as a symmetric matrix of 3×3 real numbers
8.
Honey
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Honey /ˈhʌni/ is a sugary food substance produced and stored by certain social hymenopteran insects. It is produced from the secretions of plants or insects, such as floral nectar or aphid honeydew, through regurgitation, enzymatic activity. The variety of honey produced by bees is the most well-known, due to its worldwide commercial production. Honey gets its sweetness from the monosaccharides fructose and glucose, and has about the relative sweetness as granulated sugar. It has attractive properties for baking and a distinctive flavor that leads some people to prefer it to sugar. Most microorganisms do not grow in honey, so sealed honey does not spoil, however, honey sometimes contains dormant endospores of the bacterium Clostridium botulinum, which can be dangerous to babies, as it may result in botulism. People who have an immune system should not eat honey because of the risk of bacterial or fungal infection. Although some evidence indicates honey may be effective in treating diseases and other conditions, such as wounds and burns. Providing 64 calories in a serving of one tablespoon equivalent to 1272 kj per 100 g. Honey is generally safe, but may have various, potential adverse effects or interactions with excessive consumption, existing disease conditions, or drugs. Honey use and production have a long and varied history as an ancient activity, depicted in Valencia, in cold weather or when other food sources are scarce, adult and larval bees use stored honey as food. By contriving for bee swarms to nest in man-made hives, people have been able to semidomesticate the insects, Bee digestive enzymes - invertase, amylase, and diastase - and gastric acid hydrolyze sucrose to a mixture of glucose and fructose. The bees work together as a group with the regurgitation and digestion for as long as 20 minutes until the product reaches storage quality. It is then placed in honeycomb cells left unsealed while still high in content and natural yeasts. The bees then cap the cells with wax to seal them, as removed from the hive by a beekeeper, honey has a long shelf life and will not ferment if properly sealed. Another source of honey is from a number of species, such as the wasps Brachygastra lecheguana and Brachygastra mellifica. These species are known to feed on nectar and produce honey, Honey is collected from wild bee colonies, or from domesticated beehives. The honey is stored in honeycombs, wild bee nests are sometimes located by following a honeyguide bird
9.
Water
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Water is a transparent and nearly colorless chemical substance that is the main constituent of Earths streams, lakes, and oceans, and the fluids of most living organisms. Its chemical formula is H2O, meaning that its molecule contains one oxygen, Water strictly refers to the liquid state of that substance, that prevails at standard ambient temperature and pressure, but it often refers also to its solid state or its gaseous state. It also occurs in nature as snow, glaciers, ice packs and icebergs, clouds, fog, dew, aquifers, Water covers 71% of the Earths surface. It is vital for all forms of life. Only 2. 5% of this water is freshwater, and 98. 8% of that water is in ice and groundwater. Less than 0. 3% of all freshwater is in rivers, lakes, and the atmosphere, a greater quantity of water is found in the earths interior. Water on Earth moves continually through the cycle of evaporation and transpiration, condensation, precipitation. Evaporation and transpiration contribute to the precipitation over land, large amounts of water are also chemically combined or adsorbed in hydrated minerals. Safe drinking water is essential to humans and other even though it provides no calories or organic nutrients. There is a correlation between access to safe water and gross domestic product per capita. However, some observers have estimated that by 2025 more than half of the population will be facing water-based vulnerability. A report, issued in November 2009, suggests that by 2030, in developing regions of the world. Water plays an important role in the world economy, approximately 70% of the freshwater used by humans goes to agriculture. Fishing in salt and fresh water bodies is a source of food for many parts of the world. Much of long-distance trade of commodities and manufactured products is transported by boats through seas, rivers, lakes, large quantities of water, ice, and steam are used for cooling and heating, in industry and homes. Water is an excellent solvent for a variety of chemical substances, as such it is widely used in industrial processes. Water is also central to many sports and other forms of entertainment, such as swimming, pleasure boating, boat racing, surfing, sport fishing, Water is a liquid at the temperatures and pressures that are most adequate for life. Specifically, at atmospheric pressure of 1 bar, water is a liquid between the temperatures of 273.15 K and 373.15 K
10.
Velocity
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The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of its speed and direction of motion, Velocity is an important concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a vector quantity, both magnitude and direction are needed to define it. The scalar absolute value of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI system as metres per second or as the SI base unit of. For example,5 metres per second is a scalar, whereas 5 metres per second east is a vector, if there is a change in speed, direction or both, then the object has a changing velocity and is said to be undergoing an acceleration. To have a constant velocity, an object must have a constant speed in a constant direction, constant direction constrains the object to motion in a straight path thus, a constant velocity means motion in a straight line at a constant speed. For example, a car moving at a constant 20 kilometres per hour in a path has a constant speed. Hence, the car is considered to be undergoing an acceleration, Speed describes only how fast an object is moving, whereas velocity gives both how fast and in what direction the object is moving. If a car is said to travel at 60 km/h, its speed has been specified, however, if the car is said to move at 60 km/h to the north, its velocity has now been specified. The big difference can be noticed when we consider movement around a circle and this is because the average velocity is calculated by only considering the displacement between the starting and the end points while the average speed considers only the total distance traveled. Velocity is defined as the rate of change of position with respect to time, average velocity can be calculated as, v ¯ = Δ x Δ t. The average velocity is less than or equal to the average speed of an object. This can be seen by realizing that while distance is always strictly increasing, from this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs. time is the displacement, x. In calculus terms, the integral of the velocity v is the displacement function x. In the figure, this corresponds to the area under the curve labeled s. Since the derivative of the position with respect to time gives the change in position divided by the change in time, although velocity is defined as the rate of change of position, it is often common to start with an expression for an objects acceleration. As seen by the three green tangent lines in the figure, an objects instantaneous acceleration at a point in time is the slope of the tangent to the curve of a v graph at that point. In other words, acceleration is defined as the derivative of velocity with respect to time, from there, we can obtain an expression for velocity as the area under an a acceleration vs. time graph
11.
Stress (physics)
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For example, when a solid vertical bar is supporting a weight, each particle in the bar pushes on the particles immediately below it. When a liquid is in a container under pressure, each particle gets pushed against by all the surrounding particles. The container walls and the pressure-inducing surface push against them in reaction and these macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the particles in those molecules. Strain inside a material may arise by various mechanisms, such as stress as applied by external forces to the material or to its surface. Any strain of a material generates an internal elastic stress, analogous to the reaction force of a spring. In liquids and gases, only deformations that change the volume generate persistent elastic stress, however, if the deformation is gradually changing with time, even in fluids there will usually be some viscous stress, opposing that change. Elastic and viscous stresses are usually combined under the mechanical stress. Significant stress may exist even when deformation is negligible or non-existent, stress may exist in the absence of external forces, such built-in stress is important, for example, in prestressed concrete and tempered glass. Stress may also be imposed on a material without the application of net forces, for example by changes in temperature or chemical composition, stress that exceeds certain strength limits of the material will result in permanent deformation or even change its crystal structure and chemical composition. In some branches of engineering, the stress is occasionally used in a looser sense as a synonym of internal force. For example, in the analysis of trusses, it may refer to the total traction or compression force acting on a beam, since ancient times humans have been consciously aware of stress inside materials. Until the 17th century the understanding of stress was largely intuitive and empirical, with those tools, Augustin-Louis Cauchy was able to give the first rigorous and general mathematical model for stress in a homogeneous medium. Cauchy observed that the force across a surface was a linear function of its normal vector, and, moreover. The understanding of stress in liquids started with Newton, who provided a formula for friction forces in parallel laminar flow. Stress is defined as the force across a small boundary per unit area of that boundary, following the basic premises of continuum mechanics, stress is a macroscopic concept. In a fluid at rest the force is perpendicular to the surface, in a solid, or in a flow of viscous liquid, the force F may not be perpendicular to S, hence the stress across a surface must be regarded a vector quantity, not a scalar. Moreover, the direction and magnitude depend on the orientation of S. Thus the stress state of the material must be described by a tensor, called the stress tensor, with respect to any chosen coordinate system, the Cauchy stress tensor can be represented as a symmetric matrix of 3×3 real numbers
12.
Pressure
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Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the relative to the ambient pressure. Various units are used to express pressure, Pressure may also be expressed in terms of standard atmospheric pressure, the atmosphere is equal to this pressure and the torr is defined as 1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, Pressure is the amount of force acting per unit area. The symbol for it is p or P, the IUPAC recommendation for pressure is a lower-case p. However, upper-case P is widely used. The usage of P vs p depends upon the field in one is working, on the nearby presence of other symbols for quantities such as power and momentum. Mathematically, p = F A where, p is the pressure, F is the normal force and it relates the vector surface element with the normal force acting on it. It is incorrect to say the pressure is directed in such or such direction, the pressure, as a scalar, has no direction. The force given by the relationship to the quantity has a direction. If we change the orientation of the element, the direction of the normal force changes accordingly. Pressure is distributed to solid boundaries or across arbitrary sections of normal to these boundaries or sections at every point. It is a parameter in thermodynamics, and it is conjugate to volume. The SI unit for pressure is the pascal, equal to one newton per square metre and this name for the unit was added in 1971, before that, pressure in SI was expressed simply in newtons per square metre. Other units of pressure, such as pounds per square inch, the CGS unit of pressure is the barye, equal to 1 dyn·cm−2 or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre, but using the names kilogram, gram, kilogram-force, or gram-force as units of force is expressly forbidden in SI. The technical atmosphere is 1 kgf/cm2, since a system under pressure has potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume. It is therefore related to density and may be expressed in units such as joules per cubic metre. Similar pressures are given in kilopascals in most other fields, where the prefix is rarely used
13.
Friction
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Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction, Dry friction resists relative lateral motion of two surfaces in contact. Dry friction is subdivided into static friction between non-moving surfaces, and kinetic friction between moving surfaces, fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other. Lubricated friction is a case of fluid friction where a lubricant fluid separates two solid surfaces, skin friction is a component of drag, the force resisting the motion of a fluid across the surface of a body. Internal friction is the force resisting motion between the making up a solid material while it undergoes deformation. When surfaces in contact move relative to other, the friction between the two surfaces converts kinetic energy into thermal energy. This property can have consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to thermal energy whenever motion with friction occurs, another important consequence of many types of friction can be wear, which may lead to performance degradation and/or damage to components. Friction is a component of the science of tribology, Friction is not itself a fundamental force. Dry friction arises from a combination of adhesion, surface roughness, surface deformation. The complexity of interactions makes the calculation of friction from first principles impractical and necessitates the use of empirical methods for analysis. Friction is a non-conservative force - work done against friction is path dependent, in the presence of friction, some energy is always lost in the form of heat. Thus mechanical energy is not conserved, the Greeks, including Aristotle, Vitruvius, and Pliny the Elder, were interested in the cause and mitigation of friction. They were aware of differences between static and kinetic friction with Themistius stating in 350 A. D. that it is easier to further the motion of a moving body than to move a body at rest. The classic laws of sliding friction were discovered by Leonardo da Vinci in 1493, a pioneer in tribology and these laws were rediscovered by Guillaume Amontons in 1699. Amontons presented the nature of friction in terms of surface irregularities, the understanding of friction was further developed by Charles-Augustin de Coulomb. Coulomb further considered the influence of sliding velocity, temperature and humidity, the distinction between static and dynamic friction is made in Coulombs friction law, although this distinction was already drawn by Johann Andreas von Segner in 1758. Leslie was equally skeptical about the role of adhesion proposed by Desaguliers, in Leslies view, friction should be seen as a time-dependent process of flattening, pressing down asperities, which creates new obstacles in what were cavities before
14.
Cryogenics
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In physics, cryogenics is the study of the production and behaviour of materials at very low temperatures. It is not well-defined at what point on the temperature scale refrigeration ends and cryogenics begins, but scientists assume a gas to be cryogenic if it can be liquefied at or below −150 °C. The U. S. National Institute of Standards and Technology has chosen to consider the field of cryogenics as that involving temperatures below −180 °C or −292.00 °F or 93.15 K. A person who studies elements that have been subjected to cold temperatures is called a cryogenicist. Cryogenicists use the Kelvin or Rankine temperature scales present in nature, Cryogenics The branches of physics and engineering that involve the study of very low temperatures, how to produce them, and how materials behave at those temperatures. Cryobiology The branch of biology involving the study of the effects of low temperatures on organisms, cryoconservation of animal genetic resources The conservation of genetic material with the intention of conserving a breed. Cryosurgery The branch of surgery applying very low temperatures to destroy malignant tissue, cryoelectronics The field of research regarding superconductivity at low temperatures. Cryotronics The practical application of cryoelectronics, Cryonics Cryopreserving humans and animals with the intention of future revival. Cryogenics is sometimes used to mean Cryonics in popular culture. The word cryogenics stems from Greek kρύο – cold + genic – having to do with production, Cryogenic fluids with their boiling point in kelvins Liquefied gases, such as liquid nitrogen and liquid helium, are used in many cryogenic applications. Liquid nitrogen is the most commonly used element in cryogenics and is legally purchasable around the world, Liquid helium is also commonly used and allows for the lowest attainable temperatures to be reached. These liquids may be stored in Dewar flasks, which are double-walled containers with a vacuum between the walls to reduce heat transfer into the liquid. Typical laboratory Dewar flasks are spherical, made of glass and protected in a metal outer container, Dewar flasks for extremely cold liquids such as liquid helium have another double-walled container filled with liquid nitrogen. Dewar flasks are named after their inventor, James Dewar, the man who first liquefied hydrogen, thermos bottles are smaller vacuum flasks fitted in a protective casing. Cryogenic barcode labels are used to mark dewar flasks containing these liquids, Cryogenic transfer pumps are the pumps used on LNG piers to transfer liquefied natural gas from LNG carriers to LNG storage tanks, as are cryogenic valves. The field of cryogenics advanced during World War II when scientists found that metals frozen to low temperatures showed more resistance to wear, based on this theory of cryogenic hardening, the commercial cryogenic processing industry was founded in 1966 by Ed Busch. This evolved in the late 1990s into the treatment of other parts, cryogens, such as liquid nitrogen, are further used for specialty chilling and freezing applications. Some chemical reactions, like those used to produce the active ingredients for the popular statin drugs, special cryogenic chemical reactors are used to remove reaction heat and provide a low temperature environment
15.
Superfluidity
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Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without loss of kinetic energy. When stirred a superfluid forms cellular vortices that continue to rotate indefinitely, superfluidity occurs in two isotopes of helium when they are liquified by cooling to cryogenic temperatures. It is also a property of other exotic states of matter theorized to exist in astrophysics, high-energy physics. Superfluidity was originally discovered in liquid helium, by Pyotr Kapitsa and it has since been described through phenomenology and microscopic theories. In liquid helium-4, the superfluidity occurs at far higher temperatures than it does in helium-3, each atom of helium-4 is a boson particle, by virtue of its integer spin. A helium-3 atom is a particle, it can form bosons only by pairing with itself at much lower temperatures. The discovery of superfluidity in helium-3 was the basis for the award of the 1996 Nobel Prize in Physics and this process is similar to the electron pairing in superconductivity. Superfluidity in an ultracold fermionic gas was experimentally proven by Wolfgang Ketterle, such vortices had previously been observed in an ultracold bosonic gas using 87Rb in 2000, and more recently in two-dimensional gases. As early as 1999 Lene Hau created such a condensate using sodium atoms for the purpose of slowing light, with a double light-roadblock setup, we can generate controlled collisions between shock waves resulting in completely unexpected, nonlinear excitations. We have observed hybrid structures consisting of vortex rings embedded in dark solitonic shells, the vortex rings act as phantom propellers leading to very rich excitation dynamics. The idea that superfluidity exists inside neutron stars was first proposed by Arkady Migdal, superfluid vacuum theory is an approach in theoretical physics and quantum mechanics where the physical vacuum is viewed as superfluid. The ultimate goal of the approach is to develop scientific models that unify quantum mechanics with gravity and this makes SVT a candidate for the theory of quantum gravity and an extension of the Standard Model. Boojum Condensed matter physics Macroscopic quantum phenomena Quantum hydrodynamics Slow light Supersolid Guénault, annett, James F. Superconductivity, superfluids, and condensates. The Universe in a helium droplet
16.
Pitch (resin)
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Pitch is a name for any of a number of viscoelastic polymers. Pitch can be natural or manufactured, derived from petroleum, coal tar or plants, various forms of pitch may also be called tar, bitumen or asphalt. Pitch produced from plants is known as resin. Some products made from plant resin are also known as rosin, Pitch was traditionally used to help caulk the seams of wooden sailing vessels. Pitch may also be used to waterproof wooden containers and in the making of torches, petroleum-derived pitch is black in colour, hence the adjectival phrase, pitch-black. Naturally occurring asphalt/bitumen, a type of pitch, is a viscoelastic polymer and this means that even though it seems to be solid at room temperature and can be shattered with a hard impact, it is actually fluid and will flow over time, but extremely slowly. The pitch drop experiment taking place at University of Queensland is an experiment which demonstrates the flow of a piece of pitch over many years. For the experiment, pitch was put in a glass funnel, since the pitch was allowed to start dripping in 1930, only nine drops have fallen. It was calculated in the 1980s that the pitch in the experiment has a viscosity approximately 230 billion times that of water, the eighth drop fell on 28 November 2000, and the ninth drop fell on 17 April 2014. Another experiment was begun by a colleague of Nobel Prize winner Ernest Walton in the department of Trinity College in Ireland in 1944. Over the years, the pitch had produced several drops, on Thursday, July 11,2013 scientists at Trinity College caught pitch dripping from a funnel on camera for the first time. The viscoelastic properties of pitch make it the vehicle of choice for polishing high-quality optical lenses, in use the pitch is formed into a lap or polishing surface, which is charged with iron oxide or cerium oxide. The surface to be polished is pressed into the pitch, then rubbed against the surface so formed, the ability of pitch to flow, albeit slowly, keeps it in constant uniform contact with the optical surface. The heating of wood tar and pitch to drip away from the wood. Birchbark is used to make birch-tar, a particularly fine tar, the terms tar and pitch are often used interchangeably. However, pitch is considered solid, while tar is more liquid. Traditionally, pitch that was used for waterproofing buckets, barrels and it is used to make Cutlers resin. Asphaltene Tar The Pitch Drop Experiment Pine Tar Production Primitive tar and charcoal production
17.
Solid
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Solid is one of the four fundamental states of matter. It is characterized by structural rigidity and resistance to changes of shape or volume, unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a gas does. The atoms in a solid are tightly bound to other, either in a regular geometric lattice or irregularly. The branch of physics deals with solids is called solid-state physics. Materials science is concerned with the physical and chemical properties of solids. Solid-state chemistry is concerned with the synthesis of novel materials, as well as the science of identification. The atoms, molecules or ions which make up solids may be arranged in a repeating pattern. Materials whose constituents are arranged in a regular pattern are known as crystals, in some cases, the regular ordering can continue unbroken over a large scale, for example diamonds, where each diamond is a single crystal. Almost all common metals, and many ceramics, are polycrystalline, in other materials, there is no long-range order in the position of the atoms. These solids are known as amorphous solids, examples include polystyrene, whether a solid is crystalline or amorphous depends on the material involved, and the conditions in which it was formed. Solids which are formed by slow cooling will tend to be crystalline, likewise, the specific crystal structure adopted by a crystalline solid depends on the material involved and on how it was formed. While many common objects, such as an ice cube or a coin, are chemically identical throughout, for example, a typical rock is an aggregate of several different minerals and mineraloids, with no specific chemical composition. Wood is an organic material consisting primarily of cellulose fibers embedded in a matrix of organic lignin. In materials science, composites of more than one constituent material can be designed to have desired properties, the forces between the atoms in a solid can take a variety of forms. For example, a crystal of sodium chloride is made up of sodium and chlorine. In diamond or silicon, the atoms share electrons and form covalent bonds, in metals, electrons are shared in metallic bonding. Some solids, particularly most organic compounds, are together with van der Waals forces resulting from the polarization of the electronic charge cloud on each molecule. The dissimilarities between the types of solid result from the differences between their bonding, metals typically are strong, dense, and good conductors of both electricity and heat
18.
Latin
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Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets, Latin was originally spoken in Latium, in the Italian Peninsula. Through the power of the Roman Republic, it became the dominant language, Vulgar Latin developed into the Romance languages, such as Italian, Portuguese, Spanish, French, and Romanian. Latin, Italian and French have contributed many words to the English language, Latin and Ancient Greek roots are used in theology, biology, and medicine. By the late Roman Republic, Old Latin had been standardised into Classical Latin, Vulgar Latin was the colloquial form spoken during the same time and attested in inscriptions and the works of comic playwrights like Plautus and Terence. Late Latin is the language from the 3rd century. Later, Early Modern Latin and Modern Latin evolved, Latin was used as the language of international communication, scholarship, and science until well into the 18th century, when it began to be supplanted by vernaculars. Ecclesiastical Latin remains the language of the Holy See and the Roman Rite of the Catholic Church. Today, many students, scholars and members of the Catholic clergy speak Latin fluently and it is taught in primary, secondary and postsecondary educational institutions around the world. The language has been passed down through various forms, some inscriptions have been published in an internationally agreed, monumental, multivolume series, the Corpus Inscriptionum Latinarum. Authors and publishers vary, but the format is about the same, volumes detailing inscriptions with a critical apparatus stating the provenance, the reading and interpretation of these inscriptions is the subject matter of the field of epigraphy. The works of several hundred ancient authors who wrote in Latin have survived in whole or in part and they are in part the subject matter of the field of classics. The Cat in the Hat, and a book of fairy tales, additional resources include phrasebooks and resources for rendering everyday phrases and concepts into Latin, such as Meissners Latin Phrasebook. The Latin influence in English has been significant at all stages of its insular development. From the 16th to the 18th centuries, English writers cobbled together huge numbers of new words from Latin and Greek words, dubbed inkhorn terms, as if they had spilled from a pot of ink. Many of these words were used once by the author and then forgotten, many of the most common polysyllabic English words are of Latin origin through the medium of Old French. Romance words make respectively 59%, 20% and 14% of English, German and those figures can rise dramatically when only non-compound and non-derived words are included. Accordingly, Romance words make roughly 35% of the vocabulary of Dutch, Roman engineering had the same effect on scientific terminology as a whole
19.
Mistletoe
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Mistletoe is the common name for most obligate hemiparasitic plants in the order Santalales. Mistletoes attach to and penetrate the branches of a tree or shrub by a called the haustorium, through which they absorb water. The name mistletoe originally referred to the species Viscum album, it was the species native to Great Britain. A separate species, Viscum cruciatum, occurs in Southwest Spain and Southern Portugal, as well as North Africa, in particular, the Eastern mistletoe native to North America, Phoradendron leucarpum, belongs to a distinct genus of the Santalaceae family. The genus Viscum is not native to North America, but Viscum album has been introduced to California, european mistletoe has smooth-edged, oval, evergreen leaves borne in pairs along the woody stem, and waxy, white berries that it bears in clusters of two to six. The Eastern mistletoe of North America is similar, but has shorter, broader leaves, the word mistletoe derives from the older form mistle, adding the Old English word tān. Further etymology is uncertain, but may be related to the Germanic base for mash, although Viscaceae and Eremolepidaceae were placed in a broadly defined Santalaceae by Angiosperm Phylogeny Group II, DNA data indicate they evolved independently. The largest family of mistletoes, the Loranthaceae, has 73 genera, subtropical and tropical climates have markedly more mistletoe species, Australia has 85, of which 71 are in Loranthaceae, and 14 in Santalaceae. Mistletoe plants grow on a range of host trees, they commonly reduce their growth. A heavy infestation may kill the entire host plant, Viscum album successfully parasitizes more than 200 tree and shrub species. Technically, all species are hemiparasites, because they do perform at least a little photosynthesis for at least a short period of their life cycle. However, this is academic in some species whose contribution is nearly zero. Once they have germinated and attached to the system of the host. Most of the Viscaceae bear evergreen leaves that photosynthesise effectively, and photosynthesis proceeds within their green, some species, such as Viscum capense, are adapted to semi-arid conditions and their leaves are vestigial scales, hardly visible without detailed morphological investigation. Accordingly their contribution to the hosts metabolic balance becomes trivial and the parasite may become quite yellow as it grows. At another extreme other species have green leaves. In such a tree the host is relegated purely to the supply of water and mineral nutrients and the physical support of the trunk. Such a tree may survive as a Viscum community for years, it resembles a totally unknown species unless one examines it closely, an example of a species that behaves like that is Viscum continuum
20.
Glue
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The use of adhesives offers many advantages over binding techniques such as sewing, mechanical fastening, thermal bonding, etc. Adhesives are typically organized by the method of adhesion and these are then organized into reactive and non-reactive adhesives, which refers to whether the adhesive chemically reacts in order to harden. Alternatively they can be organized by whether the raw stock is of natural or synthetic origin, Adhesives may be found naturally or produced synthetically. The earliest human use of substances was approximately 200,000 years ago. The first references to adhesives in literature first appeared in approximately 2000 BCE, the Greeks and Romans made great contributions to the development of adhesives. In Europe, glue was not widely used until the period 1500–1700 CE, from then until the 1900s increases in adhesive use and discovery were relatively gradual. Only since the last century has the development of synthetic adhesives accelerated rapidly, the earliest use of adhesives was discovered in central Italy when two stone flakes partially covered with birch-bark tar and a third uncovered stone from the Middle Pleistocene era were found. This is thought to be the oldest discovered human use of tar-hafted stones, the birch-bark-tar adhesive is a simple, one-component adhesive. Although sticky enough, plant-based adhesives are brittle and vulnerable to environmental conditions, the first use of compound adhesives was discovered in Sibudu, South Africa. The ability to produce stronger adhesives allowed middle stone age humans to attach stone segments to sticks in greater variations, more recent examples of adhesive use by prehistoric humans have been found at the burial sites of ancient tribes. Archaeologists studying the sites found that approximately 6,000 years ago the tribesmen had buried their dead together with food found in clay pots repaired with tree resins. The glue was analyzed as pitch, which requires the heating of tar during its production, the retrieval of this tar requires a transformation of birch bark by means of heat, in a process known as pyrolysis. The first references to adhesives in literature first appeared in approximately 2000 BCE, further historical records of adhesive use are found from the period spanning 1500–1000 BCE. Artifacts from this period include paintings depicting wood gluing operations and a made of wood. Other ancient Egyptian artifacts employ animal glue for bonding or lamination, such lamination of wood for bows and furniture is thought to have extended their life and was accomplished using casein -based glues. The ancient Egyptians also developed starch-based pastes for the bonding of papyrus to clothing, from 1 to 500 AD the Greeks and Romans made great contributions to the development of adhesives. Wood veneering and marquetry were developed, the production of animal and fish glues refined, egg-based pastes were used to bond gold leaves incorporated various natural ingredients such as blood, bone, hide, milk, cheese, vegetables, and grains. The Greeks began the use of slaked lime as mortar while the Romans furthered mortar development by mixing lime with volcanic ash and this material, known as pozzolanic cement, was used in the construction of the Roman Colosseum and Pantheon
21.
Couette flow
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In fluid dynamics, Couette flow is the laminar flow of a viscous fluid in the space between two parallel plates, one of which is moving relative to the other. The flow is driven by virtue of viscous drag force acting on the fluid and this type of flow is named in honor of Maurice Marie Alfred Couette, a Professor of Physics at the French University of Angers in the late 19th century. Couette flow is used in undergraduate physics and engineering courses to illustrate shear-driven fluid motion. The simplest conceptual configuration finds two infinite, parallel plates separated by a distance h, one plate, say the top one, translates with a constant velocity U in its own plane. Neglecting pressure gradients, the Navier–Stokes equations simplify to d 2 u d y 2 =0 and this equation reflects the assumption that the flow is uni-directional. That is, only one of the three velocity components is non-trivial, if y originates at the lower plate, the boundary conditions are u =0 and u = U. The exact solution u = U y h can be found by integrating twice, a notable aspect of the flow is that shear stress is constant throughout the flow domain. In particular, the first derivative of the velocity, U / h, is constant, according to Newtons Law of Viscosity, the shear stress is the product of this expression and the fluid viscosity. In reality, the Couette solution cant be reached instantaneously, as t → ∞, the steady Couette solution is recovered. At times t ∼ h 2 / ν, steady Couette solution will be almost reached as shown in the figure. The time required to reach the solution depends only on the spacing between the plates h and the kinematic viscosity of the fluid, but not on how fast the top plate is moved U. A more general Couette flow situation arises when a constant pressure gradient G = − d p / d x = c o n s t a n t is imposed in a parallel to the plates. The Navier–Stokes equations, in case, simplify to d 2 u d y 2 = − G μ. Integrating the above equation twice and applying the conditions to yield the following exact solution u = G2 μ y + U y h. The pressure gradient can be positive or negative and it may be noted that in the limiting case of stationary plates, the flow is referred to as plane Poiseuille flow with a symmetric parabolic velocity profile. This problem was first addressed by C. R. Illingworth in 1950, in incompressible flow, the velocity profile is linear because the fluid temperature is constant. When the upper and lower walls are maintained at different temperatures, the velocity profile is complicated, consider the plane Couette flow with lower wall at rest and properties denoted with suffix w and let the upper wall move with constant velocity U with properties denoted with suffix ∞. The properties and the pressure at the wall are prescribed
22.
Linear function
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In linear algebra and functional analysis, a linear function is a linear map. In calculus, analytic geometry and related areas, a function is a polynomial of degree one or less. When the function is of one variable, it is of the form f = a x + b. The graph of such a function of one variable is a nonvertical line, a is frequently referred to as the slope of the line, and b as the intercept. For a function f of any number of independent variables, the general formula is f = b + a 1 x 1 + … + a k x k. A constant function is also considered linear in this context, as it is a polynomial of degree zero or is the zero polynomial and its graph, when there is only one independent variable, is a horizontal line. In this context, the meaning may be referred to as a homogeneous linear function or a linear form. In the context of linear algebra, this meaning is a kind of affine map. In linear algebra, a function is a map f between two vector spaces that preserves vector addition and scalar multiplication, f = f + f f = a f. Here a denotes a constant belonging to some field K of scalars and x and y are elements of a vector space, some authors use linear function only for linear maps that take values in the scalar field, these are also called linear functionals. The linear functions of calculus qualify as linear maps when f =0, or, equivalently, geometrically, the graph of the function must pass through the origin. Homogeneous function Nonlinear system Piecewise linear function Linear interpolation Discontinuous linear map Izrail Moiseevich Gelfand, Lectures on Linear Algebra, Interscience Publishers, ISBN 0-486-66082-6 Thomas S. Shores, Applied Linear Algebra and Matrix Analysis, Undergraduate Texts in Mathematics, Springer. ISBN 0-387-33195-6 James Stewart, Calculus, Early Transcendentals, edition 7E, ISBN 978-0-538-49790-9 Leonid N. Vaserstein, Linear Programming, in Leslie Hogben, ed. Handbook of Linear Algebra, Discrete Mathematics and Its Applications, Chapman and Hall/CRC, chap
23.
Force
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In physics, a force is any interaction that, when unopposed, will change the motion of an object. In other words, a force can cause an object with mass to change its velocity, force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity and it is measured in the SI unit of newtons and represented by the symbol F. The original form of Newtons second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. In an extended body, each part usually applies forces on the adjacent parts, such internal mechanical stresses cause no accelation of that body as the forces balance one another. Pressure, the distribution of small forces applied over an area of a body, is a simple type of stress that if unbalanced can cause the body to accelerate. Stress usually causes deformation of materials, or flow in fluids. In part this was due to an understanding of the sometimes non-obvious force of friction. A fundamental error was the belief that a force is required to maintain motion, most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Isaac Newton formulated laws of motion that were not improved-on for nearly three hundred years, the Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known, in order of decreasing strength, they are, strong, electromagnetic, weak, high-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction. Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was famous for formulating a treatment of buoyant forces inherent in fluids. Aristotle provided a discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotles view, the sphere contained four elements that come to rest at different natural places therein. Aristotle believed that objects on Earth, those composed mostly of the elements earth and water, to be in their natural place on the ground. He distinguished between the tendency of objects to find their natural place, which led to natural motion, and unnatural or forced motion
24.
Pascal (unit)
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The pascal is the SI derived unit of pressure used to quantify internal pressure, stress, Youngs modulus and ultimate tensile strength. It is defined as one newton per square meter and it is named after the French polymath Blaise Pascal. Common multiple units of the pascal are the hectopascal which is equal to one millibar, the unit of measurement called standard atmosphere is defined as 101,325 Pa and approximates to the average pressure at sea-level at the latitude 45° N. Meteorological reports typically state atmospheric pressure in hectopascals, the unit is named after Blaise Pascal, noted for his contributions to hydrodynamics and hydrostatics, and experiments with a barometer. The name pascal was adopted for the SI unit newton per square metre by the 14th General Conference on Weights, one pascal is the pressure exerted by a force of magnitude one newton perpendicularly upon an area of one square metre. The unit of measurement called atmosphere or standard atmosphere is 101325 Pa and this value is often used as a reference pressure and specified as such in some national and international standards, such as ISO2787, ISO2533 and ISO5024. In contrast, IUPAC recommends the use of 100 kPa as a standard pressure when reporting the properties of substances, geophysicists use the gigapascal in measuring or calculating tectonic stresses and pressures within the Earth. Medical elastography measures tissue stiffness non-invasively with ultrasound or magnetic resonance imaging, in materials science and engineering, the pascal measures the stiffness, tensile strength and compressive strength of materials. In engineering use, because the pascal represents a small quantity. The pascal is also equivalent to the SI unit of energy density and this applies not only to the thermodynamics of pressurised gases, but also to the energy density of electric, magnetic, and gravitational fields. In measurements of sound pressure, or loudness of sound, one pascal is equal to 94 decibels SPL, the quietest sound a human can hear, known as the threshold of hearing, is 0 dB SPL, or 20 µPa. The airtightness of buildings is measured at 50 Pa, the units of atmospheric pressure commonly used in meteorology were formerly the bar, which was close to the average air pressure on Earth, and the millibar. Since the introduction of SI units, meteorologists generally measure pressures in hectopascals unit, exceptions include Canada and Portugal, which use kilopascals. In many other fields of science, the SI is preferred, many countries also use the millibar or hectopascal to give aviation altimeter settings. In practically all fields, the kilopascal is used instead. Centimetre of water Metric prefix Orders of magnitude Pascals law
25.
Second
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The second is the base unit of time in the International System of Units. It is qualitatively defined as the division of the hour by sixty. SI definition of second is the duration of 9192631770 periods of the corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. Seconds may be measured using a mechanical, electrical or an atomic clock, SI prefixes are combined with the word second to denote subdivisions of the second, e. g. the millisecond, the microsecond, and the nanosecond. Though SI prefixes may also be used to form multiples of the such as kilosecond. The second is also the unit of time in other systems of measurement, the centimetre–gram–second, metre–kilogram–second, metre–tonne–second. Absolute zero implies no movement, and therefore zero external radiation effects, the second thus defined is consistent with the ephemeris second, which was based on astronomical measurements. The realization of the second is described briefly in a special publication from the National Institute of Standards and Technology. 1 international second is equal to, 1⁄60 minute 1⁄3,600 hour 1⁄86,400 day 1⁄31,557,600 Julian year 1⁄, more generally, = 1⁄, the Hellenistic astronomers Hipparchus and Ptolemy subdivided the day into sixty parts. They also used an hour, simple fractions of an hour. No sexagesimal unit of the day was used as an independent unit of time. The modern second is subdivided using decimals - although the third remains in some languages. The earliest clocks to display seconds appeared during the last half of the 16th century, the second became accurately measurable with the development of mechanical clocks keeping mean time, as opposed to the apparent time displayed by sundials. The earliest spring-driven timepiece with a hand which marked seconds is an unsigned clock depicting Orpheus in the Fremersdorf collection. During the 3rd quarter of the 16th century, Taqi al-Din built a clock with marks every 1/5 minute, in 1579, Jost Bürgi built a clock for William of Hesse that marked seconds. In 1581, Tycho Brahe redesigned clocks that displayed minutes at his observatory so they also displayed seconds, however, they were not yet accurate enough for seconds. In 1587, Tycho complained that his four clocks disagreed by plus or minus four seconds, in 1670, London clockmaker William Clement added this seconds pendulum to the original pendulum clock of Christiaan Huygens. From 1670 to 1680, Clement made many improvements to his clock and this clock used an anchor escapement mechanism with a seconds pendulum to display seconds in a small subdial
26.
Derivative
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The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a tool of calculus. For example, the derivative of the position of an object with respect to time is the objects velocity. The derivative of a function of a variable at a chosen input value. The tangent line is the best linear approximation of the function near that input value, for this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives may be generalized to functions of real variables. In this generalization, the derivative is reinterpreted as a transformation whose graph is the best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of independent and dependent variables and it can be calculated in terms of the partial derivatives with respect to the independent variables. For a real-valued function of variables, the Jacobian matrix reduces to the gradient vector. The process of finding a derivative is called differentiation, the reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration, differentiation and integration constitute the two fundamental operations in single-variable calculus. Differentiation is the action of computing a derivative, the derivative of a function y = f of a variable x is a measure of the rate at which the value y of the function changes with respect to the change of the variable x. It is called the derivative of f with respect to x, If x and y are real numbers, and if the graph of f is plotted against x, the derivative is the slope of this graph at each point. The simplest case, apart from the case of a constant function, is when y is a linear function of x. This formula is true because y + Δ y = f = m + b = m x + m Δ x + b = y + m Δ x. Thus, since y + Δ y = y + m Δ x and this gives an exact value for the slope of a line. If the function f is not linear, however, then the change in y divided by the change in x varies, differentiation is a method to find an exact value for this rate of change at any given value of x. The idea, illustrated by Figures 1 to 3, is to compute the rate of change as the value of the ratio of the differences Δy / Δx as Δx becomes infinitely small
27.
Perpendicular
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In elementary geometry, the property of being perpendicular is the relationship between two lines which meet at a right angle. The property extends to other related geometric objects, a line is said to be perpendicular to another line if the two lines intersect at a right angle. Perpendicularity can be shown to be symmetric, meaning if a first line is perpendicular to a second line, for this reason, we may speak of two lines as being perpendicular without specifying an order. Perpendicularity easily extends to segments and rays, in symbols, A B ¯ ⊥ C D ¯ means line segment AB is perpendicular to line segment CD. A line is said to be perpendicular to an if it is perpendicular to every line in the plane that it intersects. This definition depends on the definition of perpendicularity between lines, two planes in space are said to be perpendicular if the dihedral angle at which they meet is a right angle. Perpendicularity is one instance of the more general mathematical concept of orthogonality, perpendicularity is the orthogonality of classical geometric objects. Thus, in advanced mathematics, the perpendicular is sometimes used to describe much more complicated geometric orthogonality conditions. The word foot is used in connection with perpendiculars. This usage is exemplified in the top diagram, above, the diagram can be in any orientation. The foot is not necessarily at the bottom, step 2, construct circles centered at A and B having equal radius. Let Q and R be the points of intersection of two circles. Step 3, connect Q and R to construct the desired perpendicular PQ, to prove that the PQ is perpendicular to AB, use the SSS congruence theorem for and QPB to conclude that angles OPA and OPB are equal. Then use the SAS congruence theorem for triangles OPA and OPB to conclude that angles POA, to make the perpendicular to the line g at or through the point P using Thales theorem, see the animation at right. The Pythagorean Theorem can be used as the basis of methods of constructing right angles, for example, by counting links, three pieces of chain can be made with lengths in the ratio 3,4,5. These can be out to form a triangle, which will have a right angle opposite its longest side. This method is useful for laying out gardens and fields, where the dimensions are large, the chains can be used repeatedly whenever required. If two lines are perpendicular to a third line, all of the angles formed along the third line are right angles
28.
Isaac Newton
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His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus. Newtons Principia formulated the laws of motion and universal gravitation that dominated scientists view of the universe for the next three centuries. Newtons work on light was collected in his influential book Opticks. He also formulated a law of cooling, made the first theoretical calculation of the speed of sound. Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge, politically and personally tied to the Whig party, Newton served two brief terms as Member of Parliament for the University of Cambridge, in 1689–90 and 1701–02. He was knighted by Queen Anne in 1705 and he spent the last three decades of his life in London, serving as Warden and Master of the Royal Mint and his father, also named Isaac Newton, had died three months before. Born prematurely, he was a child, his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Newtons mother had three children from her second marriage. From the age of twelve until he was seventeen, Newton was educated at The Kings School, Grantham which taught Latin and Greek. He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, Henry Stokes, master at the Kings School, persuaded his mother to send him back to school so that he might complete his education. Motivated partly by a desire for revenge against a bully, he became the top-ranked student. In June 1661, he was admitted to Trinity College, Cambridge and he started as a subsizar—paying his way by performing valets duties—until he was awarded a scholarship in 1664, which guaranteed him four more years until he would get his M. A. He set down in his notebook a series of Quaestiones about mechanical philosophy as he found it, in 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. Soon after Newton had obtained his B. A. degree in August 1665, in April 1667, he returned to Cambridge and in October was elected as a fellow of Trinity. Fellows were required to become ordained priests, although this was not enforced in the restoration years, however, by 1675 the issue could not be avoided and by then his unconventional views stood in the way. Nevertheless, Newton managed to avoid it by means of a special permission from Charles II. A and he was elected a Fellow of the Royal Society in 1672. Newtons work has been said to distinctly advance every branch of mathematics then studied and his work on the subject usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newtons mathematical papers
29.
Differential equation
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A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. In pure mathematics, differential equations are studied from different perspectives. Only the simplest differential equations are solvable by explicit formulas, however, if a self-contained formula for the solution is not available, the solution may be numerically approximated using computers. Differential equations first came into existence with the invention of calculus by Newton, jacob Bernoulli proposed the Bernoulli differential equation in 1695. This is a differential equation of the form y ′ + P y = Q y n for which the following year Leibniz obtained solutions by simplifying it. Historically, the problem of a string such as that of a musical instrument was studied by Jean le Rond dAlembert, Leonhard Euler, Daniel Bernoulli. In 1746, d’Alembert discovered the wave equation, and within ten years Euler discovered the three-dimensional wave equation. The Euler–Lagrange equation was developed in the 1750s by Euler and Lagrange in connection with their studies of the tautochrone problem. This is the problem of determining a curve on which a particle will fall to a fixed point in a fixed amount of time. Lagrange solved this problem in 1755 and sent the solution to Euler, both further developed Lagranges method and applied it to mechanics, which led to the formulation of Lagrangian mechanics. Contained in this book was Fouriers proposal of his heat equation for conductive diffusion of heat and this partial differential equation is now taught to every student of mathematical physics. For example, in mechanics, the motion of a body is described by its position. Newtons laws allow one to express these variables dynamically as an equation for the unknown position of the body as a function of time. In some cases, this equation may be solved explicitly. An example of modelling a real world problem using differential equations is the determination of the velocity of a ball falling through the air, considering only gravity, the balls acceleration towards the ground is the acceleration due to gravity minus the acceleration due to air resistance. Gravity is considered constant, and air resistance may be modeled as proportional to the balls velocity and this means that the balls acceleration, which is a derivative of its velocity, depends on the velocity. Finding the velocity as a function of time involves solving a differential equation, Differential equations can be divided into several types
30.
Defining equation (physics)
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In physics, defining equations are equations that define new quantities in terms of base quantities. This article uses the current SI system of units, not natural or characteristic units, physical quantities and units follow the same hierarchy, chosen base quantities have defined base units, from these any other quantities may be derived and have corresponding derived units. Defining quantities is analogous to mixing colours, and could be classified a similar way, primary colours are to base quantities, as secondary colours are to derived quantities. Mixing colours is analogous to combining quantities using mathematical operations, the choice of a base system of quantities and units is arbitrary, but once chosen it must be adhered to throughout all analysis which follows for consistency. It makes no sense to mix up different systems of units, choosing a system of units, one system out of the SI, CGS etc. is like choosing whether use paint or light colours. Much of physics requires definitions to be made for the equations to make sense, theoretical implications, Definitions are important since they can lead into new insights of a branch of physics. Two such examples occurred in classical physics, ease of comparison, They allow comparisons of measurements to be made when they might appear ambiguous and unclear otherwise. Example A basic example is mass density and it is not clear how compare how much matter constitutes a variety of substances given only their masses or only their volumes. Making such comparisons without using mathematics logically in this way would not be as systematic, functions may be incorporated into a definition, in for calculus this is necessary. Quantities may also be complex-valued for theoretical advantage, but for a measurement the real part is relevant. For more advanced treatments the equation may have to be written in an equivalent, often definitions can start from elementary algebra, then modify to vectors, then in the limiting cases calculus may be used. The various levels of maths used typically follows this pattern, for vector equations, sometimes the defining quantity is in a cross or dot product and cannot be solved for explicitly as a vector, but the components can. Examples Electric current density is an example spanning all of these methods, see the classical mechanics section below for nomenclature and diagrams to the right. Elementary algebra Operations are simply multiplication and division, equations may be written in a product or quotient form, both of course equivalent. Vector algebra There is no way to divide a vector by a vector, elementary calculus The arithmetic operations are modified to the limiting cases of differentiation and integration. Equations can be expressed in these equivalent and alternative ways, vector calculus Tensor analysis Vectors are rank-1 tensors. The formulae below are no more than the equations in the language of tensors. Sometimes there is still freedom within the chosen units system, to one or more quantities in more than one way
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IUPAC
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The International Union of Pure and Applied Chemistry /ˈaɪjuːpæk/ or /ˈjuːpæk/ is an international federation of National Adhering Organizations that represents chemists in individual countries. It is a member of the International Council for Science, IUPAC is registered in Zürich, Switzerland, and the administrative office, known as the IUPAC Secretariat, is in Research Triangle Park, North Carolina, United States. This administrative office is headed by IUPACs executive director, currently Lynn Soby, IUPAC was established in 1919 as the successor of the International Congress of Applied Chemistry for the advancement of chemistry. Its members, the National Adhering Organizations, can be national chemistry societies, national academies of sciences, there are fifty-four National Adhering Organizations and three Associate National Adhering Organizations. IUPACs Inter-divisional Committee on Nomenclature and Symbols is the world authority in developing standards for the naming of the chemical elements. Since its creation, IUPAC has been run by different committees with different responsibilities. These committees run different projects which include standardizing nomenclature, finding ways to bring chemistry to the world, IUPAC is best known for its works standardizing nomenclature in chemistry and other fields of science, but IUPAC has publications in many fields including chemistry, biology and physics. IUPAC is also known for standardizing the atomic weights of the elements through one of its oldest standing committees, the need for an international standard for chemistry was first addressed in 1860 by a committee headed by German scientist Friedrich August Kekulé von Stradonitz. This committee was the first international conference to create an international naming system for organic compounds, the ideas that were formulated in that conference evolved into the official IUPAC nomenclature of organic chemistry. IUPAC stands as a legacy of this meeting, making it one of the most important historical international collaborations of chemistry societies, since this time, IUPAC has been the official organization held with the responsibility of updating and maintaining official organic nomenclature. IUPAC as such was established in 1919, one notable country excluded from this early IUPAC is Germany. Germanys exclusion was a result of prejudice towards Germans by the Allied powers after World War I, Germany was finally admitted into IUPAC during 1929. However, Nazi Germany was removed from IUPAC during World War II, during World War II, IUPAC was affiliated with the Allied powers, but had little involvement during the war effort itself. After the war, East and West Germany were eventually readmitted to IUPAC, since World War II, IUPAC has been focused on standardizing nomenclature and methods in science without interruption. In 2016, IUPAC denounced the use of chlorine as a chemical weapon, the letter stated, Our organizations deplore the use of chlorine in this manner. According to the CWC, the use, stockpiling, distribution, IUPAC is governed by several committees that all have different responsibilities. Each committee is made up of members of different National Adhering Organizations from different countries, the steering committee hierarchy for IUPAC is as follows, All committees have an allotted budget to which they must adhere. Any committee may start a project, if a projects spending becomes too much for a committee to continue funding, it must take the issue to the Project Committee
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Density
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The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume, ρ = m V, where ρ is the density, m is the mass, and V is the volume. In some cases, density is defined as its weight per unit volume. For a pure substance the density has the numerical value as its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity, osmium and iridium are the densest known elements at standard conditions for temperature and pressure but certain chemical compounds may be denser. Thus a relative density less than one means that the floats in water. The density of a material varies with temperature and pressure and this variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object, increasing the temperature of a substance decreases its density by increasing its volume. In most materials, heating the bottom of a results in convection of the heat from the bottom to the top. This causes it to rise relative to more dense unheated material, the reciprocal of the density of a substance is occasionally called its specific volume, a term sometimes used in thermodynamics. Density is a property in that increasing the amount of a substance does not increase its density. Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass, upon this discovery, he leapt from his bath and ran naked through the streets shouting, Eureka. As a result, the term eureka entered common parlance and is used today to indicate a moment of enlightenment, the story first appeared in written form in Vitruvius books of architecture, two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time, from the equation for density, mass density has units of mass divided by volume. As there are units of mass and volume covering many different magnitudes there are a large number of units for mass density in use. The SI unit of kilogram per metre and the cgs unit of gram per cubic centimetre are probably the most commonly used units for density.1,000 kg/m3 equals 1 g/cm3. In industry, other larger or smaller units of mass and or volume are often more practical, see below for a list of some of the most common units of density
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Nu (letter)
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Nu /njuː/, is the 13th letter of the Greek alphabet. In the system of Greek numerals it has a value of 50 and it is derived from the ancient Phoenician alphabet nun. Its Latin equivalent is N, though the lowercase resembles the Roman lowercase v, the name of the letter is written νῦ in Ancient Greek and traditional Modern Greek polytonic orthography, while in Modern Greek it is written νι. The uppercase nu is not used, because it is identical to Latin N. The lower-case letter ν is used as a symbol for, Degree of freedom in statistics, the frequency of a wave in physics and other fields, sometimes also spatial frequency. Poissons ratio, the ratio of strains perpendicular with and parallel with an applied force, any of three kinds of neutrino in particle physics. One of the Greeks in mathematical finance, known as vega, the number of neutrons released per fission of an atom in nuclear physics. A DNA polymerase found in eukaryotes and implicated in translesion synthesis. Molecular vibrational mode, νx where x is the number of the vibration, the greatest fixed point of a function, as commonly used in the μ-calculus. Free names of a process, as used in the π-calculus, the maximum conditioning possible for an unconditioned stimulus in the Rescorla-Wagner model. The true anomaly, a parameter that defines the position of a body moving along an orbit. Greek Nu/Coptic Ni Mathematical Nu These characters are used only as mathematical symbols, stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style
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Reynolds number
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The Reynolds number is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations. It has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. The concept was introduced by George Gabriel Stokes in 1851, but the Reynolds number was named by Arnold Sommerfeld in 1908 after Osborne Reynolds, who popularized its use in 1883. A similar effect is created by the introduction of a stream of higher velocity fluid and this relative movement generates fluid friction, which is a factor in developing turbulent flow. Counteracting this effect is the viscosity of the fluid, which as it increases, progressively inhibits turbulence, the Reynolds number quantifies the relative importance of these two types of forces for given flow conditions, and is a guide to when turbulent flow will occur in a particular situation. Such scaling is not linear and the application of Reynolds numbers to both situations allows scaling factors to be developed, the Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface. These definitions generally include the properties of density and viscosity, plus a velocity. This dimension is a matter of convention – for example radius and diameter are equally valid to describe spheres or circles, for aircraft or ships, the length or width can be used. For flow in a pipe or a sphere moving in a fluid the internal diameter is used today. Other shapes such as pipes or non-spherical objects have an equivalent diameter defined. For fluids of variable density such as gases or fluids of variable viscosity such as non-Newtonian fluids. The velocity may also be a matter of convention in some circumstances, in practice, matching the Reynolds number is not on its own sufficient to guarantee similitude. Fluid flow is chaotic, and very small changes to shape. Nevertheless, Reynolds numbers are an important guide and are widely used. Osborne Reynolds famously studied the conditions in which the flow of fluid in pipes transitioned from laminar flow to turbulent flow, when the velocity was low, the dyed layer remained distinct through the entire length of the large tube. When the velocity was increased, the broke up at a given point. The point at which this happened was the point from laminar to turbulent flow. From these experiments came the dimensionless Reynolds number for dynamic similarity—the ratio of forces to viscous forces
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Inertia
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Inertia is the resistance of any physical object to any change in its state of motion, this includes changes to its speed, direction, or state of rest. It is the tendency of objects to keep moving in a line at constant velocity. The principle of inertia is one of the principles of classical physics that are used to describe the motion of objects. Inertia comes from the Latin word, iners, meaning idle, Inertia is one of the primary manifestations of mass, which is a quantitative property of physical systems. In common usage, the inertia may refer to an objects amount of resistance to change in velocity, or sometimes to its momentum. Thus, an object will continue moving at its current velocity until some force causes its speed or direction to change. On the surface of the Earth, inertia is often masked by the effects of friction and air resistance, both of which tend to decrease the speed of moving objects, and gravity. Aristotle explained the continued motion of projectiles, which are separated from their projector, by the action of the surrounding medium, Aristotle concluded that such violent motion in a void was impossible. Despite its general acceptance, Aristotles concept of motion was disputed on several occasions by notable philosophers over nearly two millennia, for example, Lucretius stated that the default state of matter was motion, not stasis. Philoponus proposed that motion was not maintained by the action of a surrounding medium, although this was not the modern concept of inertia, for there was still the need for a power to keep a body in motion, it proved a fundamental step in that direction. This view was opposed by Averroes and by many scholastic philosophers who supported Aristotle. However, this view did not go unchallenged in the Islamic world, in the 14th century, Jean Buridan rejected the notion that a motion-generating property, which he named impetus, dissipated spontaneously. Buridans position was that an object would be arrested by the resistance of the air. Buridan also maintained that impetus increased with speed, thus, his idea of impetus was similar in many ways to the modern concept of momentum. Buridan also believed that impetus could be not only linear, but also circular in nature, buridans thought was followed up by his pupil Albert of Saxony and the Oxford Calculators, who performed various experiments that further undermined the classical, Aristotelian view. Their work in turn was elaborated by Nicole Oresme who pioneered the practice of demonstrating laws of motion in the form of graphs, benedetti cites the motion of a rock in a sling as an example of the inherent linear motion of objects, forced into circular motion. The law of inertia states that it is the tendency of an object to resist a change in motion. According to Newton, an object will stay at rest or stay in motion unless acted on by a net force, whether it results from gravity, friction, contact
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Compressible fluid
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Compressible flow is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number is less than 0.3. The study of gas dynamics is often associated with the flight of modern high-speed aircraft and atmospheric reentry of space-exploration vehicles, however, at the beginning of the 19th century, investigation into the behaviour of fired bullets led to improvement in the accuracy and capabilities of guns and artillery. As the century progressed, inventors such as Gustaf de Laval advanced the field, at the beginning of the 20th century, the focus of gas dynamics research shifted to what would eventually become the aerospace industry. Ludwig Prandtl and his students proposed important concepts ranging from the layer to supersonic shock waves, supersonic wind tunnels. Theodore von Kármán, a student of Prandtl, continued to improve the understanding of supersonic flow, other notable figures also contributed significantly to the principles considered fundamental to the study of modern gas dynamics. Many others also contributed to this field, in truth, the barrier to supersonic flight was merely a technological one, although it was a stubborn barrier to overcome. Amongst other factors, conventional aerofoils saw an increase in drag coefficient when the flow approached the speed of sound. Overcoming the larger drag proved difficult with contemporary designs, thus the perception of a sound barrier, however, aircraft design progressed sufficiently to produce the Bell X-1. Piloted by Chuck Yeager, the X-1 officially achieved supersonic speed in October 1947, historically, two parallel paths of research have been followed in order to further gas dynamics knowledge. Experimental gas dynamics undertakes wind tunnel experiments and experiments in shock tubes. Theoretical gas dynamics considers the equations of motion applied to a variable-density gas, there are several important assumptions involved in the underlying theory of compressible flow. All fluids are composed of molecules, but tracking a number of individual molecules in a flow is unnecessary. Instead, the assumption allows us to consider a flowing gas as a continuous substance except at low densities. This assumption provides a huge simplification which is accurate for most gas-dynamic problems, only in the low-density realm of rarefied gas dynamics does the motion of individual molecules become important. The no-slip condition implies that the flow is viscous, and as a result a boundary layer forms on bodies traveling through the air at high speeds, in compressible flow, however, the gas density and temperature also become variables. This requires two more equations in order to solve problems, an equation of state for the gas. For the majority of problems, the simple Ideal gas law is the appropriate state equation
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Sound
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In physics, sound is a vibration that propagates as a typically audible mechanical wave of pressure and displacement, through a transmission medium such as air or water. In physiology and psychology, sound is the reception of such waves, humans can hear sound waves with frequencies between about 20 Hz and 20 kHz. Sound above 20 kHz is ultrasound and below 20 Hz is infrasound, other animals have different hearing ranges. Acoustics is the science that deals with the study of mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound. A scientist who works in the field of acoustics is an acoustician, an audio engineer, on the other hand, is concerned with the recording, manipulation, mixing, and reproduction of sound. Auditory sensation evoked by the oscillation described in, sound can propagate through a medium such as air, water and solids as longitudinal waves and also as a transverse wave in solids. The sound waves are generated by a source, such as the vibrating diaphragm of a stereo speaker. The sound source creates vibrations in the surrounding medium, as the source continues to vibrate the medium, the vibrations propagate away from the source at the speed of sound, thus forming the sound wave. At a fixed distance from the source, the pressure, velocity, at an instant in time, the pressure, velocity, and displacement vary in space. Note that the particles of the medium do not travel with the sound wave and this is intuitively obvious for a solid, and the same is true for liquids and gases. During propagation, waves can be reflected, refracted, or attenuated by the medium, the behavior of sound propagation is generally affected by three things, A complex relationship between the density and pressure of the medium. This relationship, affected by temperature, determines the speed of sound within the medium, if the medium is moving, this movement may increase or decrease the absolute speed of the sound wave depending on the direction of the movement. For example, sound moving through wind will have its speed of propagation increased by the speed of the if the sound and wind are moving in the same direction. If the sound and wind are moving in opposite directions, the speed of the wave will be decreased by the speed of the wind. Medium viscosity determines the rate at which sound is attenuated, for many media, such as air or water, attenuation due to viscosity is negligible. When sound is moving through a medium that does not have constant physical properties, the mechanical vibrations that can be interpreted as sound can travel through all forms of matter, gases, liquids, solids, and plasmas. The matter that supports the sound is called the medium, sound cannot travel through a vacuum. Sound is transmitted through gases, plasma, and liquids as longitudinal waves and it requires a medium to propagate
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Shock wave
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In physics, a shock wave, or shock, is a type of propagating disturbance. When a wave moves faster than the speed of sound in a fluid it is a shock wave. In supersonic flows, expansion is achieved through an expansion fan also known as a Prandtl-Meyer expansion fan, unlike solitons, the energy of a shock wave dissipates relatively quickly with distance. Also, the accompanying expansion wave approaches and eventually merges with the shock wave, when a shock wave passes through matter, energy is preserved but entropy increases. Shock waves can be, Normal, at 90° to the shock mediums flow direction, oblique, at an angle to the direction of flow. Bow, Occurs upstream of the front of a blunt object when the flow velocity exceeds Mach 1. Some other terms Shock Front, The boundary over which the physical conditions undergo a change because of a shock wave. Contact Front, in a wave caused by a driver gas. The Contact Front trails the Shock Front, when an object moves faster than the information about it can propagate into the surrounding fluid, fluid near the disturbance cannot react or get out of the way before the disturbance arrives. In a shock wave the properties of the fluid change almost instantaneously, measurements of the thickness of shock waves in air have resulted in values around 200 nm, which is on the same order of magnitude as the mean free gas molecule path. In reference to the continuum, this implies the shock wave can be treated as either a line or a plane if the field is two-dimensional or three-dimensional. Shock waves are formed when a pressure front moves at supersonic speeds, Shock waves are not conventional sound waves, a shock wave takes the form of a very sharp change in the gas properties. Shock waves in air are heard as a crack or snap noise. Over longer distances, a wave can change from a nonlinear wave into a linear wave, degenerating into a conventional sound wave as it heats the air. The sound wave is heard as the familiar thud or thump of a sonic boom, the shock wave is one of several different ways in which a gas in a supersonic flow can be compressed. Some other methods are isentropic compressions, including Prandtl-Meyer compressions, the method of compression of a gas results in different temperatures and densities for a given pressure ratio which can be analytically calculated for a non-reacting gas. A shock wave compression results in a loss of pressure, meaning that it is a less efficient method of compressing gases for some purposes. The appearance of pressure-drag on supersonic aircraft is due to the effect of shock compression on the flow
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Deformation (mechanics)
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Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration. A configuration is a set containing the positions of all particles of the body, a deformation may be caused by external loads, body forces, or changes in temperature, moisture content, or chemical reactions, etc. Strain is a description of deformation in terms of displacement of particles in the body that excludes rigid-body motions. In a continuous body, a deformation field results from a field induced by applied forces or is due to changes in the temperature field inside the body. The relation between stresses and induced strains is expressed by constitutive equations, e. g. Hookes law for linear elastic materials, deformations which are recovered after the stress field has been removed are called elastic deformations. In this case, the continuum completely recovers its original configuration, on the other hand, irreversible deformations remain even after stresses have been removed. Another type of deformation is viscous deformation, which is the irreversible part of viscoelastic deformation. In the case of elastic deformations, the response function linking strain to the stress is the compliance tensor of the material. Strain is a measure of deformation representing the displacement between particles in the relative to a reference length. A general deformation of a body can be expressed in the form x = F where X is the position of material points in the body. Such a measure does not distinguish between rigid body motions and changes in shape of the body, a deformation has units of length. We could, for example, define strain to be ε ≐ ∂ ∂ X = F ′ − I, hence strains are dimensionless and are usually expressed as a decimal fraction, a percentage or in parts-per notation. Strains measure how much a given deformation differs locally from a rigid-body deformation, a strain is in general a tensor quantity. Physical insight into strains can be gained by observing that a given strain can be decomposed into normal and this could be applied by elongation, shortening, or volume changes, or angular distortion. However, it is sufficient to know the normal and shear components of strain on a set of three perpendicular directions. In this case, the undeformed and deformed configurations of the continuum are significantly different and this is commonly the case with elastomers, plastically-deforming materials and other fluids and biological soft tissue. Infinitesimal strain theory, also called small strain theory, small deformation theory, small displacement theory, in this case, the undeformed and deformed configurations of the body can be assumed identical. Large-displacement or large-rotation theory, which assumes small strains but large rotations, in each of these theories the strain is then defined differently
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Elasticity (physics)
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In physics, elasticity is the ability of a body to resist a distorting influence or deforming force and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate forces are applied on them, if the material is elastic, the object will return to its initial shape and size when these forces are removed. The physical reasons for elastic behavior can be different for different materials. In metals, the atomic lattice changes size and shape when forces are applied, when forces are removed, the lattice goes back to the original lower energy state. For rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied, perfect elasticity is an approximation of the real world. The most elastic body in modern science found is Quartz fibre which is not even a perfect elastic body, so perfect elastic body is an ideal concept only. Most materials which possess elasticity in practice remain purely elastic only up to very small deformations. In engineering, the amount of elasticity of a material is determined by two types of material parameter, the first type of material parameter is called a modulus, which measures the amount of force per unit area needed to achieve a given amount of deformation. The SI unit of modulus is the pascal, a higher modulus typically indicates that the material is harder to deform. The second type of measures the elastic limit, the maximum stress that can arise in a material before the onset of permanent deformation. Its SI unit is also pascal, when describing the relative elasticities of two materials, both the modulus and the elastic limit have to be considered. Rubbers typically have a low modulus and tend to stretch a lot, of two rubber materials with the same elastic limit, the one with a lower modulus will appear to be more elastic, which is however not correct. When an elastic material is deformed due to a force, it experiences internal resistance to the deformation. The various moduli apply to different kinds of deformation, for instance, Youngs modulus applies to extension/compression of a body, whereas the shear modulus applies to its shear. The elasticity of materials is described by a curve, which shows the relation between stress and strain. The curve is nonlinear, but it can be approximated as linear for sufficiently small deformations. For even higher stresses, materials exhibit behavior, that is, they deform irreversibly. Elasticity is not exhibited only by solids, non-Newtonian fluids, such as viscoelastic fluids, in response to a small, rapidly applied and removed strain, these fluids may deform and then return to their original shape. Under larger strains, or strains applied for longer periods of time, because the elasticity of a material is described in terms of a stress-strain relation, it is essential that the terms stress and strain be defined without ambiguity
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Hydrostatics
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Fluid statics or hydrostatics is the branch of fluid mechanics that studies incompressible fluids at rest. It encompasses the study of the conditions under which fluids are at rest in stable equilibrium as opposed to fluid dynamics, hydrostatics are categorized as a part of the fluid statics, which is the study of all fluids, incompressible or not, at rest. Hydrostatics is fundamental to hydraulics, the engineering of equipment for storing, transporting and using fluids and it is also relevant to geophysics and astrophysics, to meteorology, to medicine, and many other fields. Some principles of hydrostatics have been known in an empirical and intuitive sense since antiquity, by the builders of boats, cisterns, aqueducts and fountains. Archimedes is credited with the discovery of Archimedes Principle, which relates the force on an object that is submerged in a fluid to the weight of fluid displaced by the object. The fair cup or Pythagorean cup, which dates from about the 6th century BC, is a technology whose invention is credited to the Greek mathematician. It was used as a learning tool, the cup consists of a line carved into the interior of the cup, and a small vertical pipe in the center of the cup that leads to the bottom. The height of this pipe is the same as the line carved into the interior of the cup, the cup may be filled to the line without any fluid passing into the pipe in the center of the cup. However, when the amount of fluid exceeds this fill line, due to the drag that molecules exert on one another, the cup will be emptied. Herons fountain is a device invented by Heron of Alexandria that consists of a jet of fluid being fed by a reservoir of fluid. The fountain is constructed in such a way that the height of the jet exceeds the height of the fluid in the reservoir, the device consisted of an opening and two containers arranged one above the other. The intermediate pot, which was sealed, was filled with fluid, trapped air inside the vessels induces a jet of water out of a nozzle, emptying all water from the intermediate reservoir. Pascal made contributions to developments in both hydrostatics and hydrodynamics, due to the fundamental nature of fluids, a fluid cannot remain at rest under the presence of a shear stress. However, fluids can exert pressure normal to any contacting surface, if a point in the fluid is thought of as an infinitesimally small cube, then it follows from the principles of equilibrium that the pressure on every side of this unit of fluid must be equal. If this were not the case, the fluid would move in the direction of the resulting force, thus, the pressure on a fluid at rest is isotropic, i. e. it acts with equal magnitude in all directions. This characteristic allows fluids to transmit force through the length of pipes or tubes, i. e. a force applied to a fluid in a pipe is transmitted, via the fluid, to the other end of the pipe. This principle was first formulated, in an extended form, by Blaise Pascal. In a fluid at rest, all frictional and inertial stresses vanish, when this condition of V =0 is applied to the Navier-Stokes equation, the gradient of pressure becomes a function of body forces only
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Newtonian fluid
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That is equivalent to saying that those forces are proportional to the rates of change of the fluids velocity vector as one moves away from the point in question in various directions. Newtonian fluids are the simplest mathematical models of fluids that account for viscosity, while no real fluid fits the definition perfectly, many common liquids and gases, such as water and air, can be assumed to be Newtonian for practical calculations under ordinary conditions. However, non-Newtonian fluids are relatively common, and include oobleck, other examples include many polymer solutions, molten polymers, many solid suspensions, blood, and most highly viscous fluids. Newtonian fluids are named after Isaac Newton, who first postulated the relation between the strain rate and shear stress for such fluids in differential form. An element of a liquid or gas will suffer forces from the surrounding fluid. These forces can be approximated to first order by a viscous stress tensor. The deformation of that element, relative to some previous state. The tensors τ and ∇ v can be expressed by 3×3 matrices, one also defines a total stress tensor σ ) that combines the shear stress with conventional pressure p. The diagonal components of viscosity tensor is molecular viscosity of a liquid, and not diagonal components – turbulence eddy viscosity