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Vortex Software Games
In fluid dynamics, a vortex (: vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado or dust devil. Vortices are a major component of turbulent flow. The distribution of velocity, vorticity (the curl of the flow velocity), as well as the concept of circulation are used to characterise vortices. In most vortices, the fluid flow velocity is greatest next to its axis and decreases in inverse proportion to the distance from the axis. In the absence of external forces, viscous friction within the fluid tends to organise the flow into a collection of irrotational vortices, possibly superimposed to larger-scale flows, including larger-scale vortices. Once formed, vortices can move, stretch, twist, and interact in complex ways. A moving vortex carries so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Airplane Vortex Edit
An airplane (American English), or aeroplane (Commonwealth English), informally plane, is a fixed-wing aircraft that is propelled forward by thrust from a jet engine, Propeller (aircraft), propeller, or rocket engine. Airplanes come in a variety of sizes, shapes, and wing configurations. The broad spectrum of uses for airplanes includes recreation, air transportation, transportation of goods and people, military aviation, military, and Experimental aircraft, research. Worldwide, commercial aviation transports more than four billion passengers annually on airliners and transports more than 200 billion tonne-kilometersMeasured in RTKs—an RTK is one tonne of revenue freight carried one kilometer. of cargo annually, which is less than 1% of the world's cargo movement. Most airplanes are flown by a pilot on board the aircraft, but some are designed to be unmanned aerial vehicle, remotely or computer-controlled such as drones. The Wright brothers invented and flew the Wright Flyer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turbulent Flow
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by Chaos theory, chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disruption between those layers. Turbulence is commonly observed in everyday phenomena such as Breaking wave, surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent. Turbulence is caused by excessive kinetic energy in parts of a fluid flow, which overcomes the damping effect of the fluid's viscosity. For this reason, turbulence is commonly realized in low viscosity fluids. In general terms, in turbulent flow, unsteady vortices appear of many sizes which interact with each other, consequently Drag (physics), drag due to friction effects increases. The onset of turbulence can be predicted by the dimensionless Reynolds number, the rati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circulation (fluid Dynamics)
In physics, circulation is the line integral of a vector field around a closed curve embedded in the field. In fluid dynamics, the field is the fluid velocity field. In electrodynamics, it can be the electric or the magnetic field. In aerodynamics, it finds applications in the calculation of lift, for which circulation was first used independently by Frederick Lanchester, Ludwig Prandtl, Martin Kutta and Nikolay Zhukovsky. It is usually denoted (uppercase gamma). Definition and properties If is a vector field and is a vector representing the differential length of a small element of a defined curve, the contribution of that differential length to circulation is : \mathrm\Gamma = \mathbf \cdot \mathrm\mathbf = \left, \mathbf\ \left, \mathrm\mathbf\ \cos \theta. Here, is the angle between the vectors and . The circulation of a vector field around a closed curve is the line integral: \Gamma = \oint_\mathbf \cdot \mathrm d \mathbf. In a conservative vector field ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irrotational Vortex
In fluid dynamics, a vortex (: vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado or dust devil. Vortices are a major component of turbulent flow. The distribution of velocity, vorticity (the curl of the flow velocity), as well as the concept of circulation are used to characterise vortices. In most vortices, the fluid flow velocity is greatest next to its axis and decreases in inverse proportion to the distance from the axis. In the absence of external forces, viscous friction within the fluid tends to organise the flow into a collection of irrotational vortices, possibly superimposed to larger-scale flows, including larger-scale vortices. Once formed, vortices can move, stretch, twist, and interact in complex ways. A moving vortex carri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotational Vortex
Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a '' center of rotation''. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a axis. The special case of a rotation with an internal axis passing through the body's own center of mass is known as a spin (or ''autorotation''). In that case, the surface intersection of the internal ''spin axis'' can be called a ''pole''; for example, Earth's rotation defines the geographical poles. A rotation around an axis completely external to the moving body is called a revolution (or ''orbit''), e.g. Earth's orbit around the Sun. The ends of the external ''axis of revolution'' ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University
Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. The institution moved to Newark, New Jersey, Newark in 1747 and then to its Mercer County, New Jersey, Mercer County campus in Princeton nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest List of colleges and universities in the United States by endowment, endowment per student in the United States. Princeton provides undergraduate education, undergraduate and graduate education, graduate instruction in the hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nabla Operator
Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol ∇. When applied to a function defined on a one-dimensional domain, it denotes the standard derivative of the function as defined in calculus. When applied to a ''field'' (a function defined on a multi-dimensional domain), it may denote any one of three operations depending on the way it is applied: the gradient or (locally) steepest slope of a scalar field (or sometimes of a vector field, as in the Navier–Stokes equations); the divergence of a vector field; or the curl (rotation) of a vector field. Del is a very convenient mathematical notation for those three operations (gradient, divergence, and curl) that makes many equations easier to write and remember. The del symbol (or nabla) can be formally defined as a vector operator whose components are the corresponding partial derivative operators. As a ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Analysis
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, \mathbb^3. The term ''vector calculus'' is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields, and fluid flow. Vector calculus was developed from the theory of quaternions by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, '' Vector Analysis'', though earlier mathematicians such as Isaac Newton pioneered the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Velocity Field
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is scalar, the ''flow speed''. It is also called velocity field; when evaluated along a line, it is called a velocity profile (as in, e.g., law of the wall). Definition The flow velocity ''u'' of a fluid is a vector field : \mathbf=\mathbf(\mathbf,t), which gives the velocity of an '' element of fluid'' at a position \mathbf\, and time t.\, The flow speed ''q'' is the length of the flow velocity vector :q = \, \mathbf \, and is a scalar field. Uses The flow velocity of a fluid effectively describes everything about the motion of a fluid. Many physical properties of a fluid can be expressed mathematically in terms of the flow velocity. Some common examples follow: Steady flow The flow of a fluid is sai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Velocity
In physics, angular velocity (symbol or \vec, the lowercase Greek letter omega), also known as the angular frequency vector,(UP1) is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction. The magnitude of the pseudovector, \omega=\, \boldsymbol\, , represents the '' angular speed'' (or ''angular frequency''), the angular rate at which the object rotates (spins or revolves). The pseudovector direction \hat\boldsymbol=\boldsymbol/\omega is normal to the instantaneous plane of rotation or angular displacement. There are two types of angular velocity: * Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. * Spin angular velocity refers to how fast a rigid body rotates around a f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right-hand Rule
In mathematics and physics, the right-hand rule is a Convention (norm), convention and a mnemonic, utilized to define the orientation (vector space), orientation of Cartesian coordinate system, axes in three-dimensional space and to determine the direction of the cross product of two Euclidean vector, vectors, as well as to establish the direction of the force on a Electric current, current-carrying conductor in a magnetic field. The various right- and left-hand rules arise from the fact that the three axes of three-dimensional space have two possible orientations. This can be seen by holding your hands together with palms up and fingers curled. If the curl of the fingers represents a movement from the first or x-axis to the second or y-axis, then the third or z-axis can point along either right thumb or left thumb. History The right-hand rule dates back to the 19th century when it was implemented as a way for identifying the positive direction of coordinate axes in three dime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
