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Drag Equation
In fluid dynamics, the drag equation is a formula used to calculate the force of drag experienced by an object due to movement through a fully enclosing fluid. The equation is: F_\, =\, \tfrac12\, \rho\, u^2\, c_\, A where *F_ is the drag force, which is by definition the force component in the direction of the flow velocity, *\rho is the mass density of the fluid, *u is the flow velocity relative to the object, *A is the reference area, and *c_ is the drag coefficient – a dimensionless coefficient related to the object's geometry and taking into account both skin friction and form drag. If the fluid is a liquid, c_ depends on the Reynolds number; if the fluid is a gas, c_ depends on both the Reynolds number and the Mach number. The equation is attributed to Lord Rayleigh, who originally used ''L''2 in place of ''A'' (with ''L'' being some linear dimension). The reference area ''A'' is typically defined as the area of the orthographic projection of the object o ...
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Fluid Dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and ti ...
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Mach Number
Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after the Moravian physicist and philosopher Ernst Mach. : \mathrm = \frac, where: : is the local Mach number, : is the local flow velocity with respect to the boundaries (either internal, such as an object immersed in the flow, or external, like a channel), and : is the speed of sound in the medium, which in air varies with the square root of the thermodynamic temperature. By definition, at Mach1, the local flow velocity is equal to the speed of sound. At Mach0.65, is 65% of the speed of sound (subsonic), and, at Mach1.35, is 35% faster than the speed of sound (supersonic). Pilots of high-altitude aerospace vehicles use flight Mach number to express a vehicle's true airspeed, but the flow field around a vehicle varies in three dimensions, with corresponding variations in local Mach number. The loc ...
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Momentum
In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and is its velocity (also a vector quantity), then the object's momentum is : \mathbf = m \mathbf. In the International System of Units (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is equivalent to the newton-second. Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame it is a ''conserved'' quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, ...
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Mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementary particles, theoretically with the same amount of matter, have nonetheless different masses. Mass in modern physics has multiple definitions which are conceptually distinct, but physically equivalent. Mass can be experimentally defined as a measure of the body's inertia, meaning the resistance to acceleration (change of velocity) when a net force is applied. The object's mass also determines the strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon ...
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Pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and even by industry. Further, both spellings are often used ''within'' a particular industry or country. Industries in British English-speaking countries typically use the "gauge" spelling. is the pressure relative to the ambient pressure. Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre (N/m2); similarly, the pound-force per square inch ( psi) is the traditional unit of pressure in the imperial and U.S. customary systems. Pressure may also be expressed in terms of standard atmospheric pressure; the atmosphere (atm) is equal to this pressure, and the torr is defined as of this. Man ...
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Bluff Body
In fluid dynamics, the drag coefficient (commonly denoted as: c_\mathrm, c_x or c_) 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 drag equation in which a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area. The drag coefficient of any object comprises the effects of the two basic contributors to fluid dynamic drag: skin friction and form drag. The drag coefficient of a lifting airfoil or hydrofoil also includes the effects of lift-induced drag. The drag coefficient of a complete structure such as an aircraft also includes the effects of interference drag. Definition The drag coefficient c_\mathrm d is defined as c_\mathrm d = \dfrac where: * F_\mathrm d is the drag force, which is by definition the force component in the direction of the flow velocity; * \ ...
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Solid Of Revolution
In geometry, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the '' axis of revolution'') that lies on the same plane. The surface created by this revolution and which bounds the solid is the surface of revolution. Assuming that the curve does not cross the axis, the solid's volume is equal to the length of the circle described by the figure's centroid multiplied by the figure's area ( Pappus's second centroid theorem). A representative disc is a three-dimensional volume element of a solid of revolution. The element is created by rotating a line segment (of length ) around some axis (located units away), so that a cylindrical volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ... of units is enclosed. Finding the ...
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Airship
An airship or dirigible balloon is a type of aerostat or lighter-than-air aircraft that can navigate through the air under its own power. Aerostats gain their lift from a lifting gas that is less dense than the surrounding air. In early dirigibles, the lifting gas used was hydrogen, due to its high lifting capacity and ready availability. Helium gas has almost the same lifting capacity and is not flammable, unlike hydrogen, but is rare and relatively expensive. Significant amounts were first discovered in the United States and for a while helium was only available for airships in that country. Most airships built since the 1960s have used helium, though some have used hot air.A few airships after World War II used hydrogen. The first British airship to use helium was the ''Chitty Bang Bang'' of 1967. The envelope of an airship may form the gasbag, or it may contain a number of gas-filled cells. An airship also has engines, crew, and optionally also payload accommodatio ...
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Lift (force)
A fluid flowing around an object exerts a force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity, but it can act in any direction at right angles to the flow. If the surrounding fluid is air, the force is called an aerodynamic force. In water or any other liquid, it is called a hydrodynamic force. Dynamic lift is distinguished from other kinds of lift in fluids. Aerostatic lift or buoyancy, in which an internal fluid is lighter than the surrounding fluid, does not require movement and is used by balloons, blimps, dirigibles, boats, and submarines. Planing lift, in which only the lower portion of the body is immersed in a liquid flow, is used by motorboats, surfboards, windsurfers, sailboats, and water-skis. Overview A fluid flowing arou ...
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Chord (aircraft)
In aeronautics, the chord is an imaginary straight line joining the leading edge and trailing edge of an aerofoil. The chord length is the distance between the trailing edge and the point where the chord intersects the leading edge.L. J. Clancy (1975), ''Aerodynamics'', Section 5.2, Pitman Publishing Limited, London. The point on the leading edge used to define the chord may be the surface point of minimum radius. p.18 For a turbine aerofoil the chord may be defined by the line between points where the front and rear of a 2-dimensional blade section would touch a flat surface when laid convex-side up. The wing, horizontal stabilizer, vertical stabilizer and propeller/rotor blades of an aircraft are all based on aerofoil sections, and the term ''chord'' or ''chord length'' is also used to describe their width. The chord of a wing, stabilizer and propeller is determined by measuring the distance between leading and trailing edges in the direction of the airflow. (If a win ...
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Airfoils
An airfoil (American English) or aerofoil (British English) is the cross-sectional shape of an object whose motion through a gas is capable of generating significant lift, such as a wing, a sail, or the blades of propeller, rotor, or turbine. A solid body moving through a fluid produces an aerodynamic force. The component of this force perpendicular to the relative freestream velocity is called lift. The component parallel to the relative freestream velocity is called drag. An airfoil is a streamlined shape that is capable of generating significantly more lift than drag. Airfoils can be designed for use at different speeds by modifying their geometry: those for subsonic flight generally have a rounded leading edge, while those designed for supersonic flight tend to be slimmer with a sharp leading edge. All have a sharp trailing edge. Foils of similar function designed with water as the working fluid are called hydrofoils. The lift on an airfoil is primarily the result of ...
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Cross Section (geometry)
In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections. The boundary of a cross-section in three-dimensional space that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space showing points on the surface of the mountains of equal elevation. In technical drawing a cross-section, being a projection of an object onto a plane that intersects it, is a common tool used to depict the internal arrangement of a 3-dimensional object in two dimensions. It is traditionally crosshatched with the style of crosshatching often indicating the types of materials being used. With com ...
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