1.
Field line
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A field line is a locus that is defined by a vector field and a starting location within the field. Field lines are useful for visualizing vector fields, which are hard to depict. A vector field defines a direction at all points in space, more precisely, the tangent line to the path at each point is required to be parallel to the vector field at that point. A complete description of the geometry of all the lines of a vector field is sufficient to completely specify the direction of the vector field everywhere. In order to depict the magnitude, a selection of field lines is drawn such that the density of field lines at any location is proportional to the magnitude of the vector field at that point. As a result of the theorem, field lines start at sources. In physics, drawings of field lines are useful in cases where the sources and sinks, if any, have a physical meaning. They can also form closed loops, or extend to or from infinity, a gravitational field has no sources, it has sinks at masses, and it has neither elsewhere, gravitational field lines come from infinity and end at masses. Note that for this kind of drawing, where the density is intended to be proportional to the field magnitude. For example, consider the electric field arising from a single, the electric field lines in this case are straight lines that emanate from the charge uniformly in all directions in three-dimensional space. This means that their density is proportional to 1 / r 2, however, if the electric field lines for this setup were just drawn on a two-dimensional plane, their two-dimensional density would be proportional to 1 / r, an incorrect result for this situation. If the vector field describes a velocity field, then the lines follow stream lines in the flow. Perhaps the most familiar example of a field described by field lines is the magnetic field. In this case, the divergence may be seen as the beginning and ending of field lines, in a solenoidal vector field, the field lines neither begin nor end, they either form closed loops, or go off to infinity in both directions. If a vector field has positive divergence in some area, there will be field lines starting from points in that area, if a vector field has negative divergence in some area, there will be field lines ending at points in that area. The Kelvin–Stokes theorem shows that field lines of a field with zero curl cannot be closed loops. In other words, curl is always present when a field line forms a closed loop and it may be present in other situations too, such as a helical shape of field lines. While field lines are a mathematical construction, in some circumstances they take on physical significance
2.
Fluid dynamics
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In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids. It has several subdisciplines, including aerodynamics and hydrodynamics, before the twentieth century, hydrodynamics was synonymous with fluid dynamics. This is still reflected in names of some fluid dynamics topics, like magnetohydrodynamics and hydrodynamic stability, the foundational axioms of fluid dynamics are the conservation laws, specifically, conservation of mass, conservation of linear momentum, and conservation of energy. These are based on mechanics and are modified in quantum mechanics. They are expressed using the Reynolds transport theorem, in addition to the above, fluids are assumed to obey the continuum assumption. Fluids are composed of molecules that collide with one another and solid objects, however, the continuum assumption assumes that fluids are continuous, rather than discrete. The fact that the fluid is made up of molecules is ignored. The unsimplified equations do not have a general solution, so they are primarily of use in Computational Fluid Dynamics. The equations can be simplified in a number of ways, all of which make them easier to solve, some of the simplifications allow some simple fluid dynamics problems to be solved in closed form. Three conservation laws are used to solve fluid dynamics problems, the conservation laws may be applied to a region of the flow called a control volume. A control volume is a volume in space through which fluid is assumed to flow. The integral formulations of the laws are used to describe the change of mass, momentum. Mass continuity, The rate of change of fluid mass inside a control volume must be equal to the net rate of flow into the volume. Mass flow into the system is accounted as positive, and since the vector to the surface is opposite the sense of flow into the system the term is negated. The first term on the right is the net rate at which momentum is convected into the volume, the second term on the right is the force due to pressure on the volumes surfaces. The first two terms on the right are negated since momentum entering the system is accounted as positive, the third term on the right is the net acceleration of the mass within the volume due to any body forces. Surface forces, such as forces, are represented by F surf. The following is the form of the momentum conservation equation
3.
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
4.
Vector field
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In vector calculus, a vector field is an assignment of a vector to each point in a subset of space. A vector field in the plane, can be visualised as, the elements of differential and integral calculus extend naturally to vector fields. Vector fields can usefully be thought of as representing the velocity of a flow in space. In coordinates, a field on a domain in n-dimensional Euclidean space can be represented as a vector-valued function that associates an n-tuple of real numbers to each point of the domain. This representation of a vector field depends on the coordinate system, vector fields are often discussed on open subsets of Euclidean space, but also make sense on other subsets such as surfaces, where they associate an arrow tangent to the surface at each point. More generally, vector fields are defined on manifolds, which are spaces that look like Euclidean space on small scales. In this setting, a field gives a tangent vector at each point of the manifold. Vector fields are one kind of tensor field, given a subset S in Rn, a vector field is represented by a vector-valued function V, S → Rn in standard Cartesian coordinates. If each component of V is continuous, then V is a vector field. A vector field can be visualized as assigning a vector to individual points within an n-dimensional space, in physics, a vector is additionally distinguished by how its coordinates change when one measures the same vector with respect to a different background coordinate system. The transformation properties of vectors distinguish a vector as a distinct entity from a simple list of scalars. Thus, suppose that is a choice of Cartesian coordinates, in terms of which the components of the vector V are V x =, then the components of the vector V in the new coordinates are required to satisfy the transformation law Such a transformation law is called contravariant. Given a differentiable manifold M, a field on M is an assignment of a tangent vector to each point in M. More precisely, a vector field F is a mapping from M into the tangent bundle TM so that p ∘ F is the identity mapping where p denotes the projection from TM to M, in other words, a vector field is a section of the tangent bundle. If the manifold M is smooth or analytic—that is, the change of coordinates is smooth —then one can make sense of the notion of vector fields. The collection of all vector fields on a smooth manifold M is often denoted by Γ or C∞. A vector field for the movement of air on Earth will associate for every point on the surface of the Earth a vector with the wind speed and direction for that point. This can be drawn using arrows to represent the wind, the length of the arrow will be an indication of the wind speed
5.
Three-dimensional space
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Three-dimensional space is a geometric setting in which three values are required to determine the position of an element. This is the meaning of the term dimension. In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space, when n =3, the set of all such locations is called three-dimensional Euclidean space. It is commonly represented by the symbol ℝ3 and this serves as a three-parameter model of the physical universe in which all known matter exists. However, this space is one example of a large variety of spaces in three dimensions called 3-manifolds. Furthermore, in case, these three values can be labeled by any combination of three chosen from the terms width, height, depth, and breadth. In mathematics, analytic geometry describes every point in space by means of three coordinates. Three coordinate axes are given, each perpendicular to the two at the origin, the point at which they cross. They are usually labeled x, y, and z, below are images of the above-mentioned systems. Two distinct points determine a line. Three distinct points are either collinear or determine a unique plane, four distinct points can either be collinear, coplanar or determine the entire space. Two distinct lines can intersect, be parallel or be skew. Two parallel lines, or two intersecting lines, lie in a plane, so skew lines are lines that do not meet. Two distinct planes can either meet in a line or are parallel. Three distinct planes, no pair of which are parallel, can meet in a common line. In the last case, the three lines of intersection of each pair of planes are mutually parallel, a line can lie in a given plane, intersect that plane in a unique point or be parallel to the plane. In the last case, there will be lines in the plane that are parallel to the given line, a hyperplane is a subspace of one dimension less than the dimension of the full space. The hyperplanes of a space are the two-dimensional subspaces, that is
6.
Continuum mechanics
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Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century, research in the area continues till today. Modeling an object as a continuum assumes that the substance of the object completely fills the space it occupies, Continuum mechanics deals with physical properties of solids and fluids which are independent of any particular coordinate system in which they are observed. These physical properties are represented by tensors, which are mathematical objects that have the required property of being independent of coordinate system. These tensors can be expressed in coordinate systems for computational convenience, Materials, such as solids, liquids and gases, are composed of molecules separated by space. On a microscopic scale, materials have cracks and discontinuities, a continuum is a body that can be continually sub-divided into infinitesimal elements with properties being those of the bulk material. More specifically, the continuum hypothesis/assumption hinges on the concepts of an elementary volume. This condition provides a link between an experimentalists and a viewpoint on constitutive equations as well as a way of spatial and statistical averaging of the microstructure. The latter then provide a basis for stochastic finite elements. The levels of SVE and RVE link continuum mechanics to statistical mechanics, the RVE may be assessed only in a limited way via experimental testing, when the constitutive response becomes spatially homogeneous. Specifically for fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made, consider car traffic on a highway---with just one lane for simplicity. Somewhat surprisingly, and in a tribute to its effectiveness, continuum mechanics effectively models the movement of cars via a differential equation for the density of cars. The familiarity of this situation empowers us to understand a little of the continuum-discrete dichotomy underlying continuum modelling in general. To start modelling define that, x measure distance along the highway, t is time, ρ is the density of cars on the highway, cars do not appear and disappear. Consider any group of cars, from the car at the back of the group located at x = a to the particular car at the front located at x = b. The total number of cars in this group N = ∫ a b ρ d x, since cars are conserved d N / d t =0. The only way an integral can be zero for all intervals is if the integrand is zero for all x, consequently, conservation derives the first order nonlinear conservation PDE ∂ ρ ∂ t + ∂ ∂ x =0 for all positions on the highway. This conservation PDE applies not only to car traffic but also to fluids, solids, crowds, animals, plants, bushfires, financial traders and this PDE is one equation with two unknowns, so another equation is needed to form a well posed problem
7.
Curve
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In mathematics, a curve is, generally speaking, an object similar to a line but that need not be straight. Thus, a curve is a generalization of a line, in that curvature is not necessarily zero, various disciplines within mathematics have given the term different meanings depending on the area of study, so the precise meaning depends on context. However, many of these meanings are special instances of the definition which follows, a curve is a topological space which is locally homeomorphic to a line. In everyday language, this means that a curve is a set of points which, near each of its points, looks like a line, a simple example of a curve is the parabola, shown to the right. A large number of curves have been studied in multiple mathematical fields. A closed curve is a curve that forms a path whose starting point is also its ending point—that is, closely related meanings include the graph of a function and a two-dimensional graph. Interest in curves began long before they were the subject of mathematical study and this can be seen in numerous examples of their decorative use in art and on everyday objects dating back to prehistoric times. Curves, or at least their graphical representations, are simple to create, historically, the term line was used in place of the more modern term curve. Hence the phrases straight line and right line were used to distinguish what are called lines from curved lines. For example, in Book I of Euclids Elements, a line is defined as a breadthless length, Euclids idea of a line is perhaps clarified by the statement The extremities of a line are points. Later commentators further classified according to various schemes. For example, Composite lines Incomposite lines Determinate Indeterminate The Greek geometers had studied many kinds of curves. One reason was their interest in solving problems that could not be solved using standard compass. These curves include, The conic sections, deeply studied by Apollonius of Perga The cissoid of Diocles, studied by Diocles, the conchoid of Nicomedes, studied by Nicomedes as a method to both double the cube and to trisect an angle. The Archimedean spiral, studied by Archimedes as a method to trisect an angle, the spiric sections, sections of tori studied by Perseus as sections of cones had been studied by Apollonius. A fundamental advance in the theory of curves was the advent of analytic geometry in the seventeenth century and this enabled a curve to be described using an equation rather than an elaborate geometrical construction. Previously, curves had been described as geometrical or mechanical according to how they were, or supposedly could be, conic sections were applied in astronomy by Kepler. Newton also worked on an example in the calculus of variations
8.
Tangent
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In geometry, the tangent line to a plane curve at a given point is the straight line that just touches the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve, a similar definition applies to space curves and curves in n-dimensional Euclidean space. Similarly, the tangent plane to a surface at a point is the plane that just touches the surface at that point. The concept of a tangent is one of the most fundamental notions in geometry and has been extensively generalized. The word tangent comes from the Latin tangere, to touch, euclid makes several references to the tangent to a circle in book III of the Elements. In Apollonius work Conics he defines a tangent as being a line such that no other straight line could fall between it and the curve, archimedes found the tangent to an Archimedean spiral by considering the path of a point moving along the curve. Independently Descartes used his method of normals based on the observation that the radius of a circle is always normal to the circle itself and these methods led to the development of differential calculus in the 17th century. Many people contributed, Roberval discovered a method of drawing tangents. René-François de Sluse and Johannes Hudde found algebraic algorithms for finding tangents, further developments included those of John Wallis and Isaac Barrow, leading to the theory of Isaac Newton and Gottfried Leibniz. An 1828 definition of a tangent was a line which touches a curve. This old definition prevents inflection points from having any tangent and it has been dismissed and the modern definitions are equivalent to those of Leibniz who defined the tangent line as the line through a pair of infinitely close points on the curve. The tangent at A is the limit when point B approximates or tends to A, the existence and uniqueness of the tangent line depends on a certain type of mathematical smoothness, known as differentiability. At most points, the tangent touches the curve without crossing it, a point where the tangent crosses the curve is called an inflection point. Circles, parabolas, hyperbolas and ellipses do not have any point, but more complicated curves do have, like the graph of a cubic function. Conversely, it may happen that the curve lies entirely on one side of a line passing through a point on it. This is the case, for example, for a passing through the vertex of a triangle. In convex geometry, such lines are called supporting lines, the geometrical idea of the tangent line as the limit of secant lines serves as the motivation for analytical methods that are used to find tangent lines explicitly. The question of finding the tangent line to a graph, or the tangent line problem, was one of the central questions leading to the development of calculus in the 17th century, suppose that a curve is given as the graph of a function, y = f
9.
Locus (mathematics)
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In geometry, a locus is a set of points, whose location satisfies or is determined by one or more specified conditions. Until the beginning of 20th century, a shape was not considered as an infinite set of points, rather. Thus a circle in the Euclidean plane was defined as the locus of a point that is at a distance of a fixed point. In contrast to the view, the old formulation avoids considering infinite collections. Once set theory became the universal basis over which the mathematics is built. Examples from plane geometry include, The set of points equidistant from two points is a perpendicular bisector to the segment connecting the two points. The set of points equidistant from two lines cross is the angle bisector. All conic sections are loci, Parabola, the set of points equidistant from a single point, Circle, the set of points for which the distance from a single point is constant. The set of points for each of which the ratio of the distances to two given foci is a constant is referred to as a Circle of Apollonius. Hyperbola, the set of points for each of which the value of the difference between the distances to two given foci is a constant. Ellipse, the set of points for each of which the sum of the distances to two given foci is a constant, the circle is the special case in which the two foci coincide with each other. Other examples of loci appear in areas of mathematics. For example, in dynamics, the Mandelbrot set is a subset of the complex plane that may be characterized as the connectedness locus of a family of polynomial maps. Proof that all the points on the given shape satisfy the conditions and we find the locus of the points P that have a given ratio of distances k = d1/d2 to two given points. In this example we choose k=3, A and B as the fixed points and it is the circle of Apollonius defined by these values of k, A, and B. A triangle ABC has a side with length c. We determine the locus of the third vertex C such that the medians from A and C are orthogonal and we choose an orthonormal coordinate system such that A, B. C is the third vertex
10.
Trajectory
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A trajectory or flight path is the path that a moving object follows through space as a function of time. The object might be a projectile or a satellite, for example, it can be an orbit—the path of a planet, an asteroid, or a comet as it travels around a central mass. A trajectory can be described either by the geometry of the path or as the position of the object over time. In control theory a trajectory is a set of states of a dynamical system. In discrete mathematics, a trajectory is a sequence k ∈ N of values calculated by the application of a mapping f to an element x of its source. A familiar example of a trajectory is the path of a projectile, in a significantly simplified model, the object moves only under the influence of a uniform gravitational force field. This can be an approximation for a rock that is thrown for short distances. In this simple approximation, the trajectory takes the shape of a parabola, generally when determining trajectories, it may be necessary to account for nonuniform gravitational forces and air resistance. This is the focus of the discipline of ballistics, one of the remarkable achievements of Newtonian mechanics was the derivation of the laws of Kepler. In the gravitational field of a point mass or an extended mass. Newtons theory later developed into the branch of physics known as classical mechanics. It employs the mathematics of differential calculus, over the centuries, countless scientists have contributed to the development of these two disciplines. Classical mechanics became a most prominent demonstration of the power of thought, i. e. reason. It helps to understand and predict an enormous range of phenomena, trajectories are, consider a particle of mass m, moving in a potential field V. Physically speaking, mass represents inertia, and the field V represents external forces of a kind known as conservative. Given V at every relevant position, there is a way to infer the associated force that would act at that position, not all forces can be expressed in this way, however. The motion of the particle is described by the differential equation m d 2 x → d t 2 = − ∇ V with x → =. On the right-hand side, the force is given in terms of ∇ V and this is the mathematical form of Newtons second law of motion, force equals mass times acceleration, for such situations
11.
Contour line
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A contour line of a function of two variables is a curve along which the function has a constant value. It is a cross-section of the graph of the function f parallel to the x, y plane. In cartography, a contour line joins points of elevation above a given level. A contour map is a map illustrated with contour lines, for example a map, which thus shows valleys and hills. The contour interval of a map is the difference in elevation between successive contour lines. More generally, a line for a function of two variables is a curve connecting points where the function has the same particular value. The gradient of the function is always perpendicular to the contour lines, when the lines are close together the magnitude of the gradient is large, the variation is steep. A level set is a generalization of a line for functions of any number of variables. Contour lines are curved, straight or a mixture of lines on a map describing the intersection of a real or hypothetical surface with one or more horizontal planes. The configuration of these contours allows map readers to infer relative gradient of a parameter, in the latter case, the method of interpolation affects the reliability of individual isolines and their portrayal of slope, pits and peaks. Contour lines are given specific names beginning iso- according to the nature of the variable being mapped. Specific names are most common in meteorology, where multiple maps with different variables may be viewed simultaneously, the prefix iso- can be replaced with isallo- to specify a contour line connecting points where a variable changes at the same rate during a given time period. The words isoline and isarithm are general terms covering all types of contour line, an isogon is a contour line for a variable which measures direction. In meteorology and in geomagnetics, the term isogon has specific meanings which are described below, an isocline is a line joining points with equal slope. In population dynamics and in geomagnetics, the terms isocline and isoclinic line have specific meanings which are described below, equidistant is a line of equal distance from a given point, line, polyline. In geography, the word isopleth is used for lines that depict a variable which cannot be measured at a point. An example is population density, which can be calculated by dividing the population of a district by the surface area of that district. Each calculated value is presumed to be the value of the variable at the centre of the area, the idea of an isopleth map can be compared with that of a choropleth map
12.
Stream function
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The stream function is defined for incompressible flows in two dimensions – as well as in three dimensions with axisymmetry. The flow velocity components can then be expressed as the derivatives of the stream function. The stream function can be used to plot streamlines, which represent the trajectories of particles in a steady flow, the two-dimensional Lagrange stream function was introduced by Joseph Louis Lagrange in 1781. The Stokes stream function is for axisymmetrical three-dimensional flow, and is named after George Gabriel Stokes, considering the particular case of fluid dynamics, the difference between the stream function values at any two points gives the volumetric flow rate through a line connecting the two points. Since streamlines are tangent to the velocity vector of the flow. A stream function may be defined for any flow of dimensions greater than or equal to two, however the case is generally the easiest to visualize and derive. For two-dimensional potential flow, streamlines are perpendicular to equipotential lines, taken together with the velocity potential, the stream function may be used to derive a complex potential. In other words, the stream function accounts for the part of a two-dimensional Helmholtz decomposition. Lamb and Batchelor define the stream function ψ – in the point P with two-dimensional coordinates and as a function of time t – for a flow by. So the stream function ψ is the flux through the curve A P, that is, the integral of the dot product of the flow velocity vector. The point A is a reference point defining where the function is zero. This is the condition of zero divergence resulting from flow incompressibility, the sign of the stream function depends on the definition used. One way is to define the stream function ψ for a two-dimensional flow such that the velocity can be expressed through the vector potential ψ, u = ∇ × ψ Where ψ = if the flow velocity vector u =. In Cartesian coordinate system this is equivalent to u = ∂ ψ ∂ y, v = − ∂ ψ ∂ x Where u and v are the velocity components in the cartesian x and y coordinate directions. Another definition is u = z × ∇ ψ ′ ≡, where z = is a vector in the + z direction. Note that this definition has the sign to that given above. Note that ψ = ψ z in this two-dimensional flow, Consider two points A and B in two-dimensional plane flow. Suppose an observer looks along an axis in the direction of increase
13.
Potential flow
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In fluid dynamics, potential flow describes the velocity field as the gradient of a scalar function, the velocity potential. As a result, a flow is characterized by an irrotational velocity field. The irrotationality of a flow is due to the curl of the gradient of a scalar always being equal to zero. In the case of an incompressible flow the velocity potential satisfies Laplaces equation, however, potential flows also have been used to describe compressible flows. The potential flow approach occurs in the modeling of both stationary as well as nonstationary flows, applications of potential flow are for instance, the outer flow field for aerofoils, water waves, electroosmotic flow, and groundwater flow. For flows with strong vorticity effects, the potential flow approximation is not applicable, in fluid dynamics, a potential flow is described by means of a velocity potential φ, being a function of space and time. The flow velocity v is a field equal to the gradient, ∇. Sometimes, also the definition v = −∇φ, with a sign, is used. But here we use the definition above, without the minus sign. From vector calculus it is known, that the curl of a gradient is equal to zero, ∇ × ∇ φ =0, and consequently the vorticity and this implies that a potential flow is an irrotational flow. This has direct consequences for the applicability of potential flow, in flow regions where vorticity is known to be important, such as wakes and boundary layers, potential flow theory is not able to provide reasonable predictions of the flow. Fortunately, there are often large regions of a flow where the assumption of irrotationality is valid, for instance in, flow around aircraft, groundwater flow, acoustics, water waves, and electroosmotic flow. As a result, the velocity potential φ has to satisfy Laplaces equation ∇2 φ =0, in this case the flow can be determined completely from its kinematics, the assumptions of irrotationality and zero divergence of flow. Dynamics only have to be applied afterwards, if one is interested in computing pressures, in two dimensions, potential flow reduces to a very simple system that is analyzed using complex analysis. Potential flow theory can also be used to model irrotational compressible flow, the flow velocity v is again equal to ∇Φ, with Φ the velocity potential. The full potential equation is valid for sub-, trans- and supersonic flow at arbitrary angle of attack and this linear equation is much easier to solve than the full potential equation, it may be recast into Laplaces equation by a simple coordinate stretching in the x-direction. Small-amplitude sound waves can be approximated with the following model, ∂2 φ ∂ t 2 = a ¯2 Δ φ. Note that also the parts of the pressure p and density ρ each individually satisfy the wave equation
14.
NACA airfoil
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The NACA airfoils are airfoil shapes for aircraft wings developed by the National Advisory Committee for Aeronautics. The shape of the NACA airfoils is described using a series of following the word NACA. The parameters in the code can be entered into equations to precisely generate the cross-section of the airfoil. The NACA four-digit wing sections define the profile by, For example, the NACA0015 airfoil is symmetrical, the 00 indicating that it has no camber. The 15 indicates that the airfoil has a 15% thickness to chord length ratio and this equation gives the thickness as percentage of the chord length, to get the thickness the above equation should be multiplied with c. Note that in this equation, at =1, the thickness is not quite zero, if a zero-thickness trailing edge is required, for example for computational work, one of the coefficients should be modified such that they sum to zero. Modifying the last coefficient will result in the smallest change to the shape of the airfoil. The leading edge approximates a cylinder with a radius of, r =1.1019 t 2 c. Now the coordinates of the airfoil surface, and of the lower airfoil surface are, x U = x L = x, y U = + y t. Symmetrical 4-digit series airfoils by default have maximum thickness at 30% of the chord from the leading edge. The simplest asymmetric foils are the NACA 4-digit series foils, which use the formula as that used to generate the 00xx symmetric foils. The constant m is chosen so that the maximum occurs at x = p, for example, for the 230 camber-line, p =0.3 /2 =0.15. Finally, constant k 1 is determined to give the lift coefficient. For a 230 camber-line profile, k 1 =15.957 is used,3 digit camber lines provide a very far forward location for the maximum camber. The first digit is 2/3 of the lift coefficient. The second digit is twice the location of the maximum camber location. The third digit indicates a non-reflexed or reflexed trailing edge and this results in a theoretical pitching moment of 0. From x c <= r y c = k 16 from r < x c <=1, one digit describing the distance of maximum thickness from the leading edge in tens of percent of the chord
15.
Angle of attack
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In fluid dynamics, angle of attack is the angle between a reference line on a body and the vector representing the relative motion between the body and the fluid through which it is moving. Angle of attack is the angle between the reference line and the oncoming flow. This article focuses on the most common application, the angle of attack of a wing or airfoil moving through air, since a wing can have twist, a chord line of the whole wing may not be definable, so an alternate reference line is simply defined. Often, the line of the root of the wing is chosen as the reference line. Another choice is to use a line on the fuselage as the reference line. Some authors do not use a chord line, but use the zero lift axis. Some British authors have used the angle of incidence instead of angle of attack. However, this can lead to confusion with the term angle of incidence meaning the angle between the chord of an airfoil and some fixed datum in the airplane. The lift coefficient of a fixed-wing aircraft varies with angle of attack, increasing angle of attack is associated with increasing lift coefficient up to the maximum lift coefficient, after which lift coefficient decreases. The figure shows a curve for a cambered straight wing. A symmetrical wing has zero lift at 0 degrees angle of attack, the lift curve is also influenced by the wing shape, including its airfoil section and wing planform. A swept wing has a lower, flatter curve with a critical angle. The critical angle of attack is the angle of attack which produces maximum lift coefficient and this is also called the stall angle of attack. Below the critical angle of attack, as the angle of attack increases, conversely, above the critical angle of attack, as angle of attack increases, the air begins to flow less smoothly over the upper surface of the airfoil and begins to separate from the upper surface. On most airfoil shapes, as the angle of attack increases, at the critical angle of attack, upper surface flow is more separated and the airfoil or wing is producing its maximum coefficient of lift. As angle of attack increases further, the surface flow becomes more and more fully separated. Above this critical angle of attack, the aircraft is said to be in a stall, a fixed-wing aircraft by definition is stalled at or above the critical angle of attack rather than at or below a particular airspeed. The airspeed at which the aircraft stalls varies with the weight of the aircraft, the load factor, however the aircraft always stalls at the same critical angle of attack
16.
Streamlines, streaklines, and pathlines
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Streamlines, streaklines and pathlines are field lines in a fluid flow. They differ only when the changes with time, that is. These show the direction in which a fluid element will travel at any point in time. Streaklines are the loci of points of all the particles that have passed continuously through a particular spatial point in the past. Dye steadily injected into the fluid at a fixed point extends along a streakline, Pathlines are the trajectories that individual fluid particles follow. These can be thought of as recording the path of an element in the flow over a certain period. The direction the path takes will be determined by the streamlines of the fluid at each moment in time. Timelines are the lines formed by a set of particles that were marked at a previous instant in time. By definition, different streamlines at the instant in a flow do not intersect. However, pathlines are allowed to intersect themselves or other pathlines, Streamlines and timelines provide a snapshot of some flowfield characteristics, whereas streaklines and pathlines depend on the full time-history of the flow. However, often sequences of timelines at different instants—being presented either in an image or with a video stream—may be used to provide insight in the flow. If a line, curve or closed curve is used as start point for a set of streamlines. In the case of a curve in a steady flow, fluid that is inside a stream surface must remain forever within that same stream surface. A scalar function whose contour lines define the streamlines is known as the stream function. Streamlines are defined by d x → S d s × u → =0, a streamtube consists of a bundle of streamlines, much like communication cable. Pathlines are defined by { d x → P d t = u → P x → P = x → P0 The suffix P indicates that we are following the motion of a fluid particle. Note that at point x → P the curve is parallel to the velocity vector u →. The parameter τ P, parametrizes the streakline x → P and 0 ≤ τ P ≤ t 0, in steady flow, the streamlines, pathlines, and streaklines coincide
17.
Euclidean vector
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In mathematics, physics, and engineering, a Euclidean vector is a geometric object that has magnitude and direction. Vectors can be added to other vectors according to vector algebra, a Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by A B →. A vector is what is needed to carry the point A to the point B and it was first used by 18th century astronomers investigating planet rotation around the Sun. The magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from A to B. These operations and associated laws qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space. Vectors play an important role in physics, the velocity and acceleration of a moving object, many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances, their magnitude and direction can still be represented by the length, the mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the system include pseudovectors and tensors. The concept of vector, as we know it today, evolved gradually over a period of more than 200 years, about a dozen people made significant contributions. Giusto Bellavitis abstracted the basic idea in 1835 when he established the concept of equipollence, working in a Euclidean plane, he made equipollent any pair of line segments of the same length and orientation. Essentially he realized an equivalence relation on the pairs of points in the plane, the term vector was introduced by William Rowan Hamilton as part of a quaternion, which is a sum q = s + v of a Real number s and a 3-dimensional vector. Like Bellavitis, Hamilton viewed vectors as representative of classes of equipollent directed segments, grassmanns work was largely neglected until the 1870s. Peter Guthrie Tait carried the standard after Hamilton. His 1867 Elementary Treatise of Quaternions included extensive treatment of the nabla or del operator ∇, in 1878 Elements of Dynamic was published by William Kingdon Clifford. Clifford simplified the quaternion study by isolating the dot product and cross product of two vectors from the complete quaternion product and this approach made vector calculations available to engineers and others working in three dimensions and skeptical of the fourth. Josiah Willard Gibbs, who was exposed to quaternions through James Clerk Maxwells Treatise on Electricity and Magnetism, the first half of Gibbss Elements of Vector Analysis, published in 1881, presents what is essentially the modern system of vector analysis. In 1901 Edwin Bidwell Wilson published Vector Analysis, adapted from Gibbs lectures, in physics and engineering, a vector is typically regarded as a geometric entity characterized by a magnitude and a direction. It is formally defined as a line segment, or arrow
18.
Cross product
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In mathematics and vector algebra, the cross product or vector product is a binary operation on two vectors in three-dimensional space and is denoted by the symbol ×. Given two linearly independent vectors a and b, the product, a × b, is a vector that is perpendicular to both a and b and therefore normal to the plane containing them. It has many applications in mathematics, physics, engineering, and it should not be confused with dot product. If two vectors have the direction or if either one has zero length, then their cross product is zero. The cross product is anticommutative and is distributive over addition, the space R3 together with the cross product is an algebra over the real numbers, which is neither commutative nor associative, but is a Lie algebra with the cross product being the Lie bracket. Like the dot product, it depends on the metric of Euclidean space, but if the product is limited to non-trivial binary products with vector results, it exists only in three and seven dimensions. If one adds the further requirement that the product be uniquely defined, the cross product of two vectors a and b is defined only in three-dimensional space and is denoted by a × b. In physics, sometimes the notation a ∧ b is used, if the vectors a and b are parallel, by the above formula, the cross product of a and b is the zero vector 0. Then, the n is coming out of the thumb. Using this rule implies that the cross-product is anti-commutative, i. e. b × a = −. By pointing the forefinger toward b first, and then pointing the finger toward a. Using the cross product requires the handedness of the system to be taken into account. If a left-handed coordinate system is used, the direction of the n is given by the left-hand rule. This, however, creates a problem because transforming from one arbitrary reference system to another, the problem is clarified by realizing that the cross product of two vectors is not a vector, but rather a pseudovector. See cross product and handedness for more detail, in 1881, Josiah Willard Gibbs, and independently Oliver Heaviside, introduced both the dot product and the cross product using a period and an x, respectively, to denote them. These alternative names are widely used in the literature. Both the cross notation and the cross product were possibly inspired by the fact that each scalar component of a × b is computed by multiplying non-corresponding components of a and b. Conversely, a dot product a ⋅ b involves multiplications between corresponding components of a and b, as explained below, the cross product can be expressed in the form of a determinant of a special 3 ×3 matrix
19.
Parametric equation
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In mathematics, parametric equations define a group of quantities as functions of one or more independent variables called parameters. For example, the equations x = cos t y = sin t form a representation of the unit circle. Parametric equations are used in kinematics, where the trajectory of an object is represented by equations depending on time as the parameter. Because of this application, a parameter is often labeled t, however. Parameterizations are non-unique, more than one set of equations can specify the same curve. In kinematics, objects paths through space are described as parametric curves. Used in this way, the set of equations for the objects coordinates collectively constitute a vector-valued function for position. Such parametric curves can then be integrated and differentiated termwise, thus, if a particles position is described parametrically as r = then its velocity can be found as v = r ′ = and its acceleration as a = r ″ =. Another important use of equations is in the field of computer-aided design. For example, consider the three representations, all of which are commonly used to describe planar curves. These problems can be addressed by rewriting the non-parametric equations in parametric form, numerous problems in integer geometry can be solved using parametric equations. A classical such solution is Euclids parametrization of right triangles such that the lengths of their sides a, b, by multiplying a, b and c by an arbitrary positive integer, one gets a parametrization of all right triangles whose three sides have integer lengths. Converting a set of equations to a single equation involves eliminating the variable t from the simultaneous equations x = x, y = y. If one of these equations can be solved for t, the expression obtained can be substituted into the equation to obtain an equation involving x and y only. If the parametrization is given by rational functions x = p r, y = q r, where p, q, r are set-wise coprime polynomials, in some cases there is no single equation in closed form that is equivalent to the parametric equations. The simplest equation for a parabola, y = x 2 can be parameterized by using a free parameter t, and setting x = t, y = t 2 f o r − ∞ < t < ∞. More generally, any given by an explicit equation y = f can be parameterized by using a free parameter t. A more sophisticated example is the following, consider the unit circle which is described by the ordinary equation x 2 + y 2 =1
20.
Field (physics)
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In physics, a field is a physical quantity, typically a number or tensor, that has a value for each point in space and time. For example, on a map, the surface wind velocity is described by assigning a vector to each point on a map. Each vector represents the speed and direction of the movement of air at that point, as another example, an electric field can be thought of as a condition in space emanating from an electric charge and extending throughout the whole of space. When a test electric charge is placed in this electric field, physicists have found the notion of a field to be of such practical utility for the analysis of forces that they have come to think of a force as due to a field. In the modern framework of the theory of fields, even without referring to a test particle, a field occupies space, contains energy. This led physicists to consider electromagnetic fields to be a physical entity, the fact that the electromagnetic field can possess momentum and energy makes it very real. A particle makes a field, and a field acts on another particle, in practice, the strength of most fields has been found to diminish with distance to the point of being undetectable. One consequence is that the Earths gravitational field quickly becomes undetectable on cosmic scales, a field has a unique tensorial character in every point where it is defined, i. e. a field cannot be a scalar field somewhere and a vector field somewhere else. For example, the Newtonian gravitational field is a vector field, moreover, within each category, a field can be either a classical field or a quantum field, depending on whether it is characterized by numbers or quantum operators respectively. In fact in this theory an equivalent representation of field is a field particle, to Isaac Newton his law of universal gravitation simply expressed the gravitational force that acted between any pair of massive objects. In the eighteenth century, a new quantity was devised to simplify the bookkeeping of all these gravitational forces and this quantity, the gravitational field, gave at each point in space the total gravitational force which would be felt by an object with unit mass at that point. The development of the independent concept of a field began in the nineteenth century with the development of the theory of electromagnetism. In the early stages, André-Marie Ampère and Charles-Augustin de Coulomb could manage with Newton-style laws that expressed the forces between pairs of electric charges or electric currents. However, it became more natural to take the field approach and express these laws in terms of electric and magnetic fields. The independent nature of the field became more apparent with James Clerk Maxwells discovery that waves in these fields propagated at a finite speed, Maxwell, at first, did not adopt the modern concept of a field as fundamental quantity that could independently exist. Instead, he supposed that the field expressed the deformation of some underlying medium—the luminiferous aether—much like the tension in a rubber membrane. If that were the case, the velocity of the electromagnetic waves should depend upon the velocity of the observer with respect to the aether. Despite much effort, no evidence of such an effect was ever found
21.
Spark (fire)
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A spark is an incandescent particle. Such sparks may be produced by pyrotechnics, by metalworking or as a by-product of fires, in pyrotechnics, iron filings and metal alloys such as magnalium may be used to create sparks. The quantity and style of sparks produced depends on the composition and pyrophoricity of the metal, in the case of iron, the presence of carbon is required, as in carbon steel — about 0. 7% is best for large sparks. The carbon burns explosively in the hot iron and this produces pretty, the duration of the existence of a spark is determined by the initial size of the particle, with a larger size leading to a longer-lasting spark. Metals with low thermal conductivity are especially good at producing sparks, titanium and zirconium are especially good in this respect and so are now used in fireworks. Copper, on the hand, has a high conductivity. For this reason, alloys of copper such as beryllium bronze are used to make safety tools which will not spark so easily, robert Hooke studied the sparks created by striking a piece of flint and steel together. He found that the sparks were usually particles of the steel which had become red hot and these sparks can be used to ignite tinder and so start a fire. In colonial America, flint and steel were used to light fires when easier methods failed, scorched linen was commonly used as tinder to catch the spark and start the fire but producing a good spark could take much time. A spinning steel wheel provided a stream of sparks when it engaged the flint. In a modern lighter or firesteel, iron is mixed with cerium and this readily produces sparks when scraped and burns hotter than steel would. This higher temperature is needed to ignite the vapour of the lighter fluid, molten metal sparks can be created when metal is heated by processes such as Bessemer conversion of iron to steel or arc welding. Arc welding uses a low voltage and high current electric arc between an electrode and the material to melt the metals at the welding point, which often creates sparks. To reduce the risk of burns, welders wear heavy leather gloves and long sleeve jackets to avoid exposure to heat, flames. In spot welding, metal surfaces that are held in contact are joined by the heat resistance to electric current flow. It is common for a spray of sparks in the form of metal droplets to be ejected from the parts being joined. Or the resistance heating of spot welding, fires may produce sparks as updrafts carry particles of the burning fuel aloft. This was a problem with steam locomotives as the sparks might set fire to the adjacent landscape or even to the train itself
22.
Inertial frame of reference
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In classical physics and special relativity, an inertial frame of reference is a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner. The physics of a system in an inertial frame have no causes external to the system, all inertial frames are in a state of constant, rectilinear motion with respect to one another, an accelerometer moving with any of them would detect zero acceleration. Measurements in one frame can be converted to measurements in another by a simple transformation. In general relativity, in any region small enough for the curvature of spacetime and tidal forces to be negligible, systems in non-inertial frames in general relativity dont have external causes because of the principle of geodesic motion. Physical laws take the form in all inertial frames. For example, a ball dropped towards the ground does not go straight down because the Earth is rotating. Someone rotating with the Earth must account for the Coriolis effect—in this case thought of as a force—to predict the horizontal motion, another example of such a fictitious force associated with rotating reference frames is the centrifugal effect, or centrifugal force. The motion of a body can only be described relative to something else—other bodies, observers and these are called frames of reference. If the coordinates are chosen badly, the laws of motion may be more complex than necessary, for example, suppose a free body that has no external forces on it is at rest at some instant. In many coordinate systems, it would begin to move at the next instant, however, a frame of reference can always be chosen in which it remains stationary. Similarly, if space is not described uniformly or time independently, indeed, an intuitive summary of inertial frames can be given as, In an inertial reference frame, the laws of mechanics take their simplest form. In an inertial frame, Newtons first law, the law of inertia, is satisfied, Any free motion has a constant magnitude, the force F is the vector sum of all real forces on the particle, such as electromagnetic, gravitational, nuclear and so forth. The extra terms in the force F′ are the forces for this frame. The first extra term is the Coriolis force, the second the centrifugal force, also, fictitious forces do not drop off with distance. For example, the force that appears to emanate from the axis of rotation in a rotating frame increases with distance from the axis. All observers agree on the forces, F, only non-inertial observers need fictitious forces. The laws of physics in the frame are simpler because unnecessary forces are not present. In Newtons time the stars were invoked as a reference frame
23.
Aircraft
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An aircraft is a machine that is able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the lift of an airfoil. The human activity that surrounds aircraft is called aviation, crewed aircraft are flown by an onboard pilot, but unmanned aerial vehicles may be remotely controlled or self-controlled by onboard computers. Aircraft may be classified by different criteria, such as type, aircraft propulsion, usage. Each of the two World Wars led to technical advances. Consequently, the history of aircraft can be divided into five eras, Pioneers of flight, first World War,1914 to 1918. Aviation between the World Wars,1918 to 1939, Second World War,1939 to 1945. Postwar era, also called the jet age,1945 to the present day, aerostats use buoyancy to float in the air in much the same way that ships float on the water. They are characterized by one or more large gasbags or canopies, filled with a relatively low-density gas such as helium, hydrogen, or hot air, which is less dense than the surrounding air. When the weight of this is added to the weight of the aircraft structure, a balloon was originally any aerostat, while the term airship was used for large, powered aircraft designs – usually fixed-wing. In 1919 Frederick Handley Page was reported as referring to ships of the air, in the 1930s, large intercontinental flying boats were also sometimes referred to as ships of the air or flying-ships. – though none had yet been built, the advent of powered balloons, called dirigible balloons, and later of rigid hulls allowing a great increase in size, began to change the way these words were used. Huge powered aerostats, characterized by an outer framework and separate aerodynamic skin surrounding the gas bags, were produced. There were still no fixed-wing aircraft or non-rigid balloons large enough to be called airships, then several accidents, such as the Hindenburg disaster in 1937, led to the demise of these airships. Nowadays a balloon is an aerostat and an airship is a powered one. A powered, steerable aerostat is called a dirigible, sometimes this term is applied only to non-rigid balloons, and sometimes dirigible balloon is regarded as the definition of an airship. Non-rigid dirigibles are characterized by a moderately aerodynamic gasbag with stabilizing fins at the back and these soon became known as blimps. During the Second World War, this shape was adopted for tethered balloons, in windy weather
24.
Wing
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A wing is a type of fin that produces lift, while moving through air or some other fluid. As such, wings have a shape, a streamlined cross-sectional shape. A wings aerodynamic efficiency is expressed as its lift-to-drag ratio, the lift a wing generates at a given speed and angle of attack can be one to two orders of magnitude greater than the total drag on the wing. A high lift-to-drag ratio requires a significantly smaller thrust to propel the wings through the air at sufficient lift, lifting structures used in water, include various foils, including hydrofoils. Hydrodynamics is the science, rather than aerodynamics. Applications of underwater foils occur in hydroplanes, sailboats and submarines, the word wing from the Old Norse vængr for many centuries referred mainly to the foremost limbs of birds. In nature wings have evolved in dinosaurs, birds, mammals, fish, reptiles, Wing forms in nature The design and analysis of the wings of aircraft is one of the principal applications of the science of aerodynamics, which is a branch of fluid mechanics. The properties of the airflow around any moving object can - in principle - be found by solving the Navier-Stokes equations of fluid dynamics, however, except for simple geometries these equations are notoriously difficult to solve. Fortunately, simpler explanations can be described, for a wing to produce lift, it must be oriented at a suitable angle of attack relative to the flow of air past the wing. When this occurs the wing deflects the airflow downwards, turning the air as it passes the wing, since the wing exerts a force on the air to change its direction, the air must exert a force on the wing, equal in size but opposite in direction. This force manifests itself as differing air pressures at different points on the surface of the wing, a region of lower-than-normal air pressure is generated over the top surface of the wing, with a higher pressure on the bottom of the wing. The lower air pressure on the top of the wing generates a smaller force on the top of the wing than the upward force generated by the higher air pressure on the bottom of the wing. Hence, a net force acts on the wing. This force is called the lift generated by the wing, the different velocities of the air passing by the wing, the air pressure differences, the change in direction of the airflow, and the lift on the wing are intrinsically one phenomenon. It is, therefore, possible to lift from any of the other three. For example, the lift can be calculated from the differences, or from different velocities of the air above and below the wing. Fluid dynamics offers other approaches to solving these problems—and all produce the same answers if done correctly, air velocity on the bottom of a wing is higher than that on the top, while the wing is generating lift. Wings with a cross section are the norm in subsonic flight
25.
Bernoulli's principle
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In fluid dynamics, Bernoullis principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a decrease in the fluids potential energy. The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738, Bernoullis principle can be applied to various types of fluid flow, resulting in various forms of Bernoullis equation, there are different forms of Bernoullis equation for different types of flow. The simple form of Bernoullis equation is valid for incompressible flows, more advanced forms may be applied to compressible flows at higher Mach numbers. Bernoullis principle can be derived from the principle of conservation of energy and this states that, in a steady flow, the sum of all forms of energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of energy, potential energy. If the fluid is flowing out of a reservoir, the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per volume is the same everywhere. Bernoullis principle can also be derived directly from Isaac Newtons Second Law of Motion, if a small volume of fluid is flowing horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than in front. This gives a net force on the volume, accelerating it along the streamline, fluid particles are subject only to pressure and their own weight. Consequently, within a fluid flowing horizontally, the highest speed occurs where the pressure is lowest, and the lowest speed occurs where the pressure is highest. In most flows of liquids, and of gases at low Mach number, therefore, the fluid can be considered to be incompressible and these flows are called incompressible flows. Bernoulli performed his experiments on liquids, so his equation in its form is valid only for incompressible flow. The constant on the side of the equation depends only on the streamline chosen. For conservative force fields, Bernoullis equation can be generalized as, E. g. for the Earths gravity Ψ = gz. The constant in the Bernoulli equation can be normalised, most often, gases and liquids are not capable of negative absolute pressure, or even zero pressure, so clearly Bernoullis equation ceases to be valid before zero pressure is reached. In liquids – when the pressure becomes too low – cavitation occurs, the above equations use a linear relationship between flow speed squared and pressure. At higher flow speeds in gases, or for sound waves in liquid, in many applications of Bernoullis equation, the change in the ρgz term along the streamline is so small compared with the other terms that it can be ignored. For example, in the case of aircraft in flight, the change in height z along a streamline is so small the ρgz term can be omitted. This allows the equation to be presented in the following simplified form, p + q = p 0 where p0 is called total pressure
26.
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
27.
Engineering
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The term Engineering is derived from the Latin ingenium, meaning cleverness and ingeniare, meaning to contrive, devise. Engineering has existed since ancient times as humans devised fundamental inventions such as the wedge, lever, wheel, each of these inventions is essentially consistent with the modern definition of engineering. The term engineering is derived from the engineer, which itself dates back to 1390 when an engineer originally referred to a constructor of military engines. In this context, now obsolete, a referred to a military machine. Notable examples of the obsolete usage which have survived to the present day are military engineering corps, the word engine itself is of even older origin, ultimately deriving from the Latin ingenium, meaning innate quality, especially mental power, hence a clever invention. The earliest civil engineer known by name is Imhotep, as one of the officials of the Pharaoh, Djosèr, he probably designed and supervised the construction of the Pyramid of Djoser at Saqqara in Egypt around 2630–2611 BC. Ancient Greece developed machines in both civilian and military domains, the Antikythera mechanism, the first known mechanical computer, and the mechanical inventions of Archimedes are examples of early mechanical engineering. In the Middle Ages, the trebuchet was developed, the first steam engine was built in 1698 by Thomas Savery. The development of this gave rise to the Industrial Revolution in the coming decades. With the rise of engineering as a profession in the 18th century, similarly, in addition to military and civil engineering, the fields then known as the mechanic arts became incorporated into engineering. The inventions of Thomas Newcomen and the Scottish engineer James Watt gave rise to mechanical engineering. The development of specialized machines and machine tools during the revolution led to the rapid growth of mechanical engineering both in its birthplace Britain and abroad. John Smeaton was the first self-proclaimed civil engineer and is regarded as the father of civil engineering. He was an English civil engineer responsible for the design of bridges, canals, harbours and he was also a capable mechanical engineer and an eminent physicist. Smeaton designed the third Eddystone Lighthouse where he pioneered the use of hydraulic lime and his lighthouse remained in use until 1877 and was dismantled and partially rebuilt at Plymouth Hoe where it is known as Smeatons Tower. The United States census of 1850 listed the occupation of engineer for the first time with a count of 2,000, there were fewer than 50 engineering graduates in the U. S. before 1865. In 1870 there were a dozen U. S. mechanical engineering graduates, in 1890 there were 6,000 engineers in civil, mining, mechanical and electrical. There was no chair of applied mechanism and applied mechanics established at Cambridge until 1875, the theoretical work of James Maxwell and Heinrich Hertz in the late 19th century gave rise to the field of electronics
28.
Dye
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A dye is a colored substance that has an affinity to the substrate to which it is being applied. The dye is applied in an aqueous solution, and may require a mordant to improve the fastness of the dye on the fiber. Both dyes and pigments are colored because they absorb some wavelengths of light more than others, in contrast to dyes, pigments are insoluble and have no affinity for the substrate. Some dyes can be precipitated with a salt to produce a lake pigment. The majority of natural dyes are from plant sources, roots, berries, bark, leaves, and wood, fungi, textile dyeing dates back to the Neolithic period. Throughout history, people have dyed their textiles using common, locally available materials, scarce dyestuffs that produced brilliant and permanent colors such as the natural invertebrate dyes Tyrian purple and crimson kermes were highly prized luxury items in the ancient and medieval world. Plant-based dyes such as woad, indigo, saffron, and madder were raised commercially and were important trade goods in the economies of Asia, across Asia and Africa, patterned fabrics were produced using resist dyeing techniques to control the absorption of color in piece-dyed cloth. Dyes from the New World such as cochineal and logwood were brought to Europe by the Spanish treasure fleets, dyed flax fibers have been found in the Republic of Georgia in a prehistoric cave dated to 36,000 BP. Archaeological evidence shows that, particularly in India and Phoenicia, dyeing has been carried out for over 5,000 years. The dyes were obtained from animal, vegetable or mineral origin, by far the greatest source of dyes has been from the plant kingdom, notably roots, berries, bark, leaves and wood, but only a few have ever been used on a commercial scale. The discovery of synthetic dyes late in the 19th century ended the large-scale market for natural dyes. These dyes are made from synthetic resources such as petroleum by-products, the first human-made organic aniline dye, mauveine, was discovered serendipitously by William Henry Perkin in 1856, the result of a failed attempt at the total synthesis of quinine. Other aniline dyes followed, such as fuchsine, safranine, many thousands of synthetic dyes have since been prepared. These may be natural or synthetic, other than pigmentation, they have a range of applications including organic dye lasers, optical media and camera sensors. This is the basic classification Dyes are classified according to their solubility, acid dyes are water-soluble anionic dyes that are applied to fibers such as silk, wool, nylon and modified acrylic fibers using neutral to acid dye baths. Attachment to the fiber is attributed, at least partly, to salt formation between anionic groups in the dyes and cationic groups in the fiber, acid dyes are not substantive to cellulosic fibers. Most synthetic food colors fall in this category, basic dyes are water-soluble cationic dyes that are mainly applied to acrylic fibers, but find some use for wool and silk. Usually acetic acid is added to the dye bath to help the uptake of the dye onto the fiber, basic dyes are also used in the coloration of paper
29.
Smoke
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It is commonly an unwanted by-product of fires, but may also be used for pest control, communication, defensive and offensive capabilities in the military, cooking, or smoking. Smoke is used in rituals where incense, sage, or resin is burned to produce a smell for spiritual purposes, smoke is sometimes used as a flavoring agent, and preservative for various foodstuffs. Smoke is also a component of internal combustion engine exhaust gas, smoke inhalation is the primary cause of death in victims of indoor fires. The smoke kills by a combination of damage, poisoning and pulmonary irritation caused by carbon monoxide, hydrogen cyanide. Smoke is an aerosol of solid particles and liquid droplets that are close to the range of sizes for Mie scattering of visible light. This effect has been likened to three-dimensional textured privacy glass — a smoke cloud does not obstruct an image, the composition of smoke depends on the nature of the burning fuel and the conditions of combustion. High temperature also leads to production of nitrogen oxides, sulfur content yields sulfur dioxide, or in case of incomplete combustion, hydrogen sulfide. Carbon and hydrogen are almost completely oxidized to carbon dioxide and water, fires burning with lack of oxygen produce a significantly wider palette of compounds, many of them toxic. Partial oxidation of carbon produces carbon monoxide, nitrogen-containing materials can yield hydrogen cyanide, ammonia, hydrogen gas can be produced instead of water. Content of halogens such as chlorine may lead to production of e. g. hydrogen chloride, phosgene, dioxin, hydrogen fluoride can be formed from fluorocarbons, whether fluoropolymers subjected to fire or halocarbon fire suppression agents. Phosphorus and antimony oxides and their products can be formed from some fire retardant additives. Heterocyclic compounds may be also present, heavier hydrocarbons may condense as tar, smoke with significant tar content is yellow to brown. Partial oxidation of the released hydrocarbons yields in a palette of other compounds, aldehydes, ketones, alcohols. The visible particulate matter in such smokes is most commonly composed of carbon, other particulates may be composed of drops of condensed tar, or solid particles of ash. The presence of metals in the fuel yields particles of metal oxides, particles of inorganic salts may also be formed, e. g. ammonium sulfate, ammonium nitrate, or sodium chloride. Inorganic salts present on the surface of the particles may make them hydrophilic. Many organic compounds, typically the aromatic hydrocarbons, may be adsorbed on the surface of the solid particles. Metal oxides can be present when metal-containing fuels are burned, e. g. solid rocket fuels containing aluminium, depleted uranium projectiles after impacting the target ignite, producing particles of uranium oxides
30.
Steam locomotive
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A steam locomotive is a railway locomotive that produces its pulling power through a steam engine. These locomotives are fueled by burning combustible material—usually coal, wood, the steam moves reciprocating pistons which are mechanically connected to the locomotives main wheels. Both fuel and water supplies are carried with the locomotive, either on the locomotive itself or in wagons pulled behind, the first steam locomotive, made by Richard Trevithick, first operated on 21 February 1804, three years after the road locomotive he made in 1801. The first practical steam locomotive was built in 1812-13 by John Blenkinsop, Steam locomotives were first developed in Great Britain during the early 19th century and used for railway transport until the middle of the 20th century. From the early 1900s they were superseded by electric and diesel locomotives, with full conversions to electric. The majority of locomotives were retired from regular service by the 1980s, though several continue to run on tourist. The earliest railways employed horses to draw carts along railway tracks, in 1784, William Murdoch, a Scottish inventor, built a small-scale prototype of a steam road locomotive. An early working model of a rail locomotive was designed and constructed by steamboat pioneer John Fitch in the US during 1794. His steam locomotive used interior bladed wheels guided by rails or tracks, the model still exists at the Ohio Historical Society Museum in Columbus. The authenticity and date of this locomotive is disputed by some experts, accompanied by Andrew Vivian, it ran with mixed success. The design incorporated a number of important innovations that included using high-pressure steam which reduced the weight of the engine, Trevithick visited the Newcastle area in 1804 and had a ready audience of colliery owners and engineers. The visit was so successful that the railways in north-east England became the leading centre for experimentation. Trevithick continued his own steam propulsion experiments through another trio of locomotives, Four years later, the successful twin-cylinder locomotive Salamanca by Matthew Murray for the edge railed rack and pinion Middleton Railway debuted in 1812. Another well known early locomotive was Puffing Billy built 1813–14 by engineer William Hedley and it was intended to work on the Wylam Colliery near Newcastle upon Tyne. This locomotive is the oldest preserved, and is on display in the Science Museum. George Stephenson built Locomotion No.1 for the Stockton and Darlington Railway, north-east England, in 1829, his son Robert built in Newcastle The Rocket which was entered in and won the Rainhill Trials. This success led to the company emerging as the pre-eminent builder of locomotives used on railways in the UK, US. The Liverpool and Manchester Railway opened a year later making exclusive use of power for passenger
31.
Streamliner
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A streamliner is a vehicle incorporating streamlining in a shape providing reduced air resistance. The term is applied to high-speed railway trainsets of the 1930s to 1950s, less commonly, the term is applied to fully faired recumbent bicycles. In land speed racing, it is a term applied to the long, slender, custom built, the first high-speed streamliner in Germany was the Schienenzeppelin, an experimental propeller driven single car, built 1930. On 21 June 1931, it set a record of 230.2 km/h on a run between Berlin and Hamburg. In 1932 the propeller was removed and a system installed. The Schienenzeppelin made 180 km/h in 1933, the Schienenzeppelin led to the construction of the diesel-electric DRG Class SVT877 Flying Hamburger. This two-car train set had 98 seats and a top speed of 160 km/h, during regular service starting on 15 May 1933, this train ran the 286 kilometres between Hamburg and Berlin in 138 minutes with an average speed of 124.4 km/h. The SVT877 was the prototype for the DRG Class SVT137, during test drives, the SVT137 Bauart Leipzig set a world speed record of 205 km/h in 1936. The fastest regular service with SVT137 was between Hannover and Hamm with an speed of 132.2 km/h. This service lasted until 22 August 1939, three examples were built during 1935-36. Built for top speeds of over 85 mph, they soon proved much faster in test runs, DRG 05-002 made seven runs during 1935-36 during which it attained top speeds of more than 177 km/h with trains up to 254 t weight. On 11 May 1936 it set the speed record for steam locomotives after reaching 200.4 km/h on the Berlin–Hamburg line hauling a 197 t train. The engine power was more than 2,535 kW ) and that record was broken two years later by the British LNER Class A44468 Mallard engine.4 km/h average between start and stop. In 1938 on a test run, the locomotive Mallard built for this set the official record for the highest top speed attained by a steam locomotive. That record stands to this day, the London Midland and Scottish Railway introduced streamline locomotives of the Princess Coronation Class shortly before the outbreak of war. The Ferrovie dello Stato developed the FS Class ETR200, a three-unit electric streamliner and these trains went into service in 1937. On 6 December 1937, an ETR200 made a top speed of 201 km/h between Campoleone and Cisterna on the run Rome-Naples, in 1939 the ETR212 even made 203 km/h. The 219-kilometre journeys from Bologna to Milan were made in 77 minutes, in the Netherlands, Nederlandse Spoorwegen introduced the Materieel 34, a three unit 140 km/h streamlined diesel-electric trainset in 1934
32.
Car
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A car is a wheeled, self-powered motor vehicle used for transportation and a product of the automotive industry. The year 1886 is regarded as the year of the modern car. In that year, German inventor Karl Benz built the Benz Patent-Motorwagen, cars did not become widely available until the early 20th century. One of the first cars that was accessible to the masses was the 1908 Model T, an American car manufactured by the Ford Motor Company. Cars were rapidly adopted in the United States of America, where they replaced animal-drawn carriages and carts, cars are equipped with controls used for driving, parking, passenger comfort and safety, and controlling a variety of lights. Over the decades, additional features and controls have been added to vehicles, examples include rear reversing cameras, air conditioning, navigation systems, and in car entertainment. Most cars in use in the 2010s are propelled by a combustion engine. Both fuels cause air pollution and are blamed for contributing to climate change. Vehicles using alternative fuels such as ethanol flexible-fuel vehicles and natural gas vehicles are also gaining popularity in some countries, electric cars, which were invented early in the history of the car, began to become commercially available in 2008. There are costs and benefits to car use, the costs of car usage include the cost of, acquiring the vehicle, interest payments, repairs and auto maintenance, fuel, depreciation, driving time, parking fees, taxes, and insurance. The costs to society of car use include, maintaining roads, land use, road congestion, air pollution, public health, health care, road traffic accidents are the largest cause of injury-related deaths worldwide. The benefits may include transportation, mobility, independence. The ability for humans to move flexibly from place to place has far-reaching implications for the nature of societies and it was estimated in 2010 that the number of cars had risen to over 1 billion vehicles, up from the 500 million of 1986. The numbers are increasing rapidly, especially in China, India, the word car is believed to originate from the Latin word carrus or carrum, or the Middle English word carre. In turn, these originated from the Gaulish word karros, the Gaulish language was a branch of the Brythoic language which also used the word Karr, the Brythonig language evolved into Welsh where Car llusg and car rhyfel still survive. It originally referred to any wheeled vehicle, such as a cart, carriage. Motor car is attested from 1895, and is the formal name for cars in British English. Autocar is a variant that is attested from 1895
33.
Dolphin
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Dolphins are a widely distributed and diverse group of aquatic mammals. They are a grouping within the order Cetacea, excluding whales and porpoises. The dolphins comprise the extant families Delphinidae, Platanistidae, Iniidae, and Pontoporiidae, there are 40 extant species of dolphins. Dolphins, alongside other cetaceans, belong to the clade Cetartiodactyla with even-toed ungulates and their closest living relatives are the hippopotamuses, having diverged about 40 million years ago. Dolphins range in size from the 1.7 m long and 50 kg Mauis dolphin to the 9.5 m and 10 t killer whale, several species exhibit sexual dimorphism, in that the males are larger than females. They have streamlined bodies and two limbs that are modified into flippers, though not quite as flexible as seals, some dolphins can travel at 55.5 km/h. Dolphins use their conical shaped teeth to capture fast moving prey and they have well-developed hearing which is adapted for both air and water and is so well developed that some can survive even if they are blind. Some species are adapted for diving to great depths. They have a layer of fat, or blubber, under the skin to keep warm in the cold water, although dolphins are widespread, most species prefer the warmer waters of the tropic zones, but some, like the right whale dolphin, prefer colder climates. Dolphins feed largely on fish and squid, but a few, like the killer whale, feed on large mammals, male dolphins typically mate with multiple females every year, but females only mate every two to three years. Calves are typically born in the spring and summer months and females bear all the responsibility for raising them, mothers of some species fast and nurse their young for a relatively long period of time. Dolphins produce a variety of vocalizations, usually in the form of clicks, Dolphins are sometimes hunted in places like Japan, in an activity known as dolphin drive hunting. Besides drive hunting, they face threats from bycatch, habitat loss. Dolphins have been depicted in cultures worldwide. Dolphins occasionally feature in literature and film, as in the film series Free Willy, Dolphins are sometimes kept in captivity and trained to perform tricks, but breeding success has been poor and the animals often die within a few months of capture. The most common dolphins kept are killer whales and bottlenose dolphins, the name is originally from Greek δελφίς, dolphin, which was related to the Greek δελφύς, womb. The animals name can therefore be interpreted as meaning a fish with a womb, the name was transmitted via the Latin delphinus, which in Medieval Latin became dolfinus and in Old French daulphin, which reintroduced the ph into the word. The term mereswine has also historically been used, the term dolphin can be used to refer to, under the parvorder Odontoceti, all the species in the family Delphinidae and the river dolphin families Iniidae, Pontoporiidae, Lipotidae and Platanistidae
34.
Streamline Moderne
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Streamline Moderne, or Art Moderne, is a late type of the Art Deco architecture and design that emerged in the 1930s. Its architectural style emphasized curving forms, long lines. The first streamline buildings evolved from the work of New Objectivity artists, a movement connected to the German Werkbund, as the Great Depression of the 1930s progressed, Americans saw a new aspect of Art Deco—i. e. Cylindrical forms and long horizontal windowing also may be influenced by constructivism, as a result, an array of designers quickly ultra-modernized and streamlined the designs of everyday objects. Manufacturers of clocks, radios, telephones, cars, furniture, the style was the first to incorporate electric light into architectural structure. In the first-class dining room of the SS Normandie, fitted out 1933–35, twelve pillars of Lalique glass. The Streamline Moderne was both a reaction to Art Deco and a reflection of austere economic times, Sharp angles were replaced with simple, exotic woods and stone were replaced with cement and glass. Art Deco and Streamline Moderne were not necessarily opposites, the Sterling Streamliner Diners were diners designed like streamlined trains. Although Streamline Moderne houses are less common than streamline commercial buildings, the Lydecker House in Los Angeles, built by Howard Lydecker, is an example of Streamline Moderne design in residential architecture. In tract development, elements of the style were used as a variation in postwar row housing in San Franciscos Sunset District. The style was applied to such as electric clocks, sewing machines, small radio receivers. Their manufacturing processes exploited developments in science including aluminium and bakelite. Compared to Europe, the United States in the 1930s had a focus on design as a means to increase sales of consumer products. Streamlining was associated with prosperity and an exciting future and this hope resonated with the American middle class, the major market for consumer products. A wide range of goods from refrigerators to pencil sharpeners was produced in streamlined designs, streamlining became a widespread design practice for automobiles, railroad cars, buses, and other vehicles in the 1930s. Streamline style can be contrasted with functionalism, which was a design style in Europe at the same time. One reason for the designs in functionalism was to lower the production costs of the items. Streamlining and functionalism represent two different schools in modernistic industrial design, but both reflecting the intended consumer
35.
Art Deco
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Art Deco, sometimes simply referred to as Deco, is a style of visual arts, architecture and design that first appeared in France just before World War I. It took its name, short for Arts Decorators, from the Exposition Internationale des Arts Décoratifs et Industriels Modernes held in Paris in 1925 and it combined modernist styles with fine craftsmanship and rich materials. During its heyday, Art Deco represented luxury, glamour, exuberance, Art Deco was a pastiche of many different styles, sometimes contradictory, united by a desire to be modern. It featured rare and expensive materials such as ebony and ivory, the Chrysler Building and other skyscrapers of New York were the most visible monuments of the new style. In the 1930s, during the Great Depression, the became more subdued. New materials arrived, including chrome plating, stainless steel and plastic, a more sleek form of the style, called Streamline Moderne, appeared in the 1930s, it featured curving forms and smooth, polished surfaces. Art Deco became one of the first truly international architectural styles, with examples found in European cities, the style came to an end with the beginning of World War II. Deco was replaced as the dominant global style by the functional and unadorned styles of modernism. The term arts décoratifs was first used in France in 1858, in 1868, Le Figaro newspaper used the term art décoratifs with respect to objects for stage scenery created for the Théâtre de lOpéra. In 1875, furniture designers, textile, jewelry and glass designers and it took its present name of ENSAD in 1927. The term Art déco was then used in a 1966 newspaper article by Hillary Gelson in the Times, describing the different styles at the exhibit. Art Deco gained currency as a broadly applied stylistic label in 1968 when historian Bevis Hillier published the first major book on the style. Hillier noted that the term was already being used by art dealers and cites The Times, in 1971, Hillier organized an exhibition at the Minneapolis Institute of Arts, which he details in his book about it, The World of Art Deco. The emergence of Art Deco was closely connected with the rise in status of decorative artists, the term arts décoratifs had been invented in 1875, giving the designers of furniture, textiles, and other decoration official status. The Société des artistes décorateurs, or SAD, was founded in 1901, a similar movement developed in Italy. The first international exhibition devoted entirely to the arts, the Esposizione international dArte decorative moderna, was held in Turin in 1902. Several new magazines devoted to decorative arts were founded in Paris, including Arts et décoration, Decorative arts sections were introduced into the annual salons of the Sociéte des artistes français, and later in the Salon dautomne. French nationalism also played a part in the resurgence of decorative arts, in 1911 the SAD proposed the holding of a major new international exposition of decorative arts in 1912
36.
Oval
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An oval is a closed curve in a plane which loosely resembles the outline of an egg. The term is not very specific, but in areas it is given a more precise definition. In common English, the term is used in a broader sense, the three-dimensional version of an oval is called an ovoid. The term oval when used to describe curves in geometry is not well-defined, many distinct curves are commonly called ovals or are said to have an oval shape. Generally, to be called an oval, a plane curve should resemble the outline of an egg or an ellipse, the adjectives ovoidal and ovate mean having the characteristic of being an ovoid, and are often used as synonyms for egg-shaped. In the theory of planes, an oval is a set of n +1 points in a projective plane of order n. An ovoid in the projective geometry PG is a set of q2 +1 points such that no three points are collinear. At each point of an all the tangent lines to the ovoid lie in a single plane. The shape of an egg is approximated by long half of a spheroid, joined to a short half of a roughly spherical ellipsoid. These are joined at the equator and sharing a principal axis of rotational symmetry, although the term egg-shaped usually implies a lack of reflection symmetry across the equatorial plane, it may also refer to true prolate ellipsoids. It can also be used to describe the 2-dimensional figure that, if revolved around its major axis, in technical drawing, an oval is a figure constructed from two pairs of arcs, with two different radii. The arcs are joined at a point in which lines tangential to both joining arcs lie on the line, thus making the joint smooth. Any point of an oval belongs to an arc with a constant radius, but in an ellipse, in common speech, oval means a shape rather like an egg or an ellipse, which may be two-dimensional or three-dimensional. It also often refers to a figure that resembles two semicircles joined by a rectangle, like a cricket infield, speed skating rink or an athletics track, however, this is more correctly called a stadium or archaically, an oblong. Sometimes, it can refer to any rectangle with rounded corners. The shape lends its name to many well-known places, ellipse Stadium Vesica piscis – a pointed oval
37.
Drag coefficient
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In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the equation in which a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is associated with a particular surface area. The drag coefficient of any object comprises the effects of the two contributors to fluid dynamic drag, skin friction and form drag. The drag coefficient of an airfoil or hydrofoil also includes the effects of lift-induced drag. The drag coefficient of a structure such as an aircraft also includes the effects of interference drag. The reference area depends on type of drag coefficient is being measured. For automobiles and many objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the sectional area of the vehicle. For example, for a sphere A = π r 2, for airfoils, the reference area is the nominal wing area. Since this tends to be compared to the frontal area, the resulting drag coefficients tend to be low, much lower than for a car with the same drag, frontal area. Airships and some bodies of revolution use the drag coefficient. Submerged streamlined bodies use the surface area. Two objects having the same reference area moving at the speed through a fluid will experience a drag force proportional to their respective drag coefficients. Coefficients for unstreamlined objects can be 1 or more, for streamlined objects much less, cd is not a constant but varies as a function of flow speed, flow direction, object position, object size, fluid density and fluid viscosity. Speed, kinematic viscosity and a length scale of the object are incorporated into a dimensionless quantity called the Reynolds number R e. C d is thus a function of R e, in a compressible flow, the speed of sound is relevant, and C d is also a function of Mach number M a. For certain body shapes, the drag coefficient C d only depends on the Reynolds number R e, Mach number M a, for low Mach number M a, the drag coefficient is independent of Mach number
38.
Equipotential
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Equipotential or isopotential in mathematics and physics refers to a region in space where every point in it is at the same potential. This usually refers to a potential, although it can also be applied to vector potentials. An equipotential of a potential function in n-dimensional space is typically an dimensional space. The del operator illustrates the relationship between a field and its associated scalar potential field. Note that an equipotential region might be referred as being of equipotential or simply be called an equipotential, an equipotential region of a scalar potential in three-dimensional space is often an equipotential surface, but it can also be a three-dimensional region in space. The gradient of the potential is everywhere perpendicular to the equipotential surface. Electrical conductors offer an intuitive example, thus, an equipotential would contain both points a and b as they have the same potential. Extending this definition, an isopotential is the locus of all points that are of the same potential, in gravity, a hollow sphere has a three-dimensional equipotential region inside, with no gravity. In electrostatics a conductor is an equipotential region. In the case of a conductor, the equipotential region includes the space inside. A ball will not be accelerated by the force of gravity if it is resting on a flat, horizontal surface, equipotential surface Potential gradient Isopotential map Scalar potential Electric Field Applet
39.
Flow visualization
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Flow visualization or flow visualisation in fluid dynamics is used to make the flow patterns visible, in order to get qualitative or quantitative information on them. Flow visualization is the art of making flow patterns visible, most fluids are transparent, thus their flow patterns are invisible to the naked eye without methods to make them visible. Historically, such methods included experimental methods, with the development of computer models and CFD simulating flow processes, purely computational methods have been developed. In experimental fluid dynamics, flows are visualized by three methods, Surface flow visualization, This reveals the flow streamlines in the limit as a surface is approached. Colored oil applied to the surface of a wind tunnel model provides one example, Particle tracer methods, Particles, such as smoke or microspheres, can be added to a flow to trace the fluid motion. We can illuminate the particles with a sheet of light in order to visualize a slice of a complicated fluid flow pattern. Particles with densities that match that of the flow will exhibit the most accurate visualization. Optical methods, Some flows reveal their patterns by way of changes in their optical refractive index and these are visualized by optical methods known as the shadowgraph, schlieren photography, and interferometry. More directly, dyes can be added to flows to measure concentrations, in scientific visualization flows are visualized with two main methods, Analytical methods, that analyse a given flow and show properties like streamlines, streaklines, and pathlines. The flow can either be given in a representation or as a smooth function. Texture advection methods that bend textures according to the flow, as the image is always finite, these methods will visualize approximations of the real flow. In computational fluid dynamics the numerical solution of the equations can yield all the fluid properties in space. This overwhelming amount of information must be displayed in a meaningful form, thus flow visualization is equally important in computational as in experimental fluid dynamics. Samimy, M. Breuer, K. S. Leal, L. G. Steen, settles, G. S. Schlieren and shadowgraph techniques, Visualizing phenomena in transparent media. Educational Particle Image Velocimetry - resources and demonstrations
40.
Scientific visualization
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Scientific visualization is an interdisciplinary branch of science. It is also considered a subset of computer graphics, a branch of computer science, the purpose of scientific visualization is to graphically illustrate scientific data to enable scientists to understand, illustrate, and glean insight from their data. One of the earliest examples of scientific visualisation was Maxwells thermodynamic surface. This prefigured modern scientific techniques that use computer graphics. Scientific visualization using computer graphics gained in popularity as graphics matured, primary applications were scalar fields and vector fields from computer simulations and also measured data. The primary methods for visualizing two-dimensional scalar fields are color mapping and drawing contour lines, 2D vector fields are visualized using glyphs and streamlines or line integral convolution methods. For 3D scalar fields the primary methods are volume rendering and isosurfaces, methods for visualizing vector fields include glyphs such as arrows, streamlines and streaklines, particle tracing, line integral convolution and topological methods. Later, visualization techniques such as hyperstreamlines were developed to visualize 2D, computer animation is the art, technique, and science of creating moving images via the use of computers. It is becoming common to be created by means of 3D computer graphics, though 2D computer graphics are still widely used for stylistic, low bandwidth. Sometimes the target of the animation is the computer itself, but sometimes the target is another medium and it is also referred to as CGI, especially when used in films. Computer simulation is a program, or network of computers. The simultaneous visualization and simulation of a system is called visulation, computer simulations vary from computer programs that run a few minutes, to network-based groups of computers running for hours, to ongoing simulations that run for months. Information visualization focused on the creation of approaches for conveying information in intuitive ways. The key difference between scientific visualization and information visualization is that information visualization is often applied to data that is not generated by scientific inquiry, some examples are graphical representations of data for business, government, news and social media. Interface technology and perception shows how new interfaces and an understanding of underlying perceptual issues create new opportunities for the scientific visualization community. Rendering is the process of generating an image from a model, the model is a description of three-dimensional objects in a strictly defined language or data structure. It would contain geometry, viewpoint, texture, lighting, the image is a digital image or raster graphics image. The term may be by analogy with a rendering of a scene
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