Momentum Theory
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Momentum Theory
In fluid dynamics, momentum theory or disk actuator theory is a theory describing a mathematical model of an ideal actuator disk, such as a propeller or helicopter rotor, by W.J.M. Rankine (1865), Alfred George Greenhill (1888) and (1889). The rotor is modeled as an infinitely thin disc, inducing a constant velocity along the axis of rotation. The basic state of a helicopter is hovering. This disc creates a flow around the rotor. Under certain mathematical premises of the fluid, there can be extracted a mathematical connection between power, radius of the rotor, torque and induced velocity. Friction is not included. For a stationary open rotor with no outer duct, such as a helicopter in hover, the power required to produce a given thrust is: :P = \sqrt where: * T is the thrust * \rho is the density of air (or other medium) * A is the area of the rotor disc * P is power A device which converts the translational energy of the fluid into rotational energy of the axis or vice v ...
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Actuator Disk
In fluid dynamics, momentum theory or disk actuator theory is a theory describing a mathematical model of an ideal actuator disk, such as a propeller or helicopter rotor, by W.J.M. Rankine (1865), Alfred George Greenhill (1888) and (1889). The rotor is modeled as an infinitely thin disc, inducing a constant velocity along the axis of rotation. The basic state of a helicopter is hovering. This disc creates a flow around the rotor. Under certain mathematical premises of the fluid, there can be extracted a mathematical connection between power, radius of the rotor, torque and induced velocity. Friction is not included. For a stationary open rotor with no outer duct, such as a helicopter in hover, the power required to produce a given thrust is: :P = \sqrt where: * T is the thrust * \rho is the density of air (or other medium) * A is the area of the rotor disc * P is power A device which converts the translational energy of the fluid into rotational energy of the axis or vice v ...
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Windmill
A windmill is a structure that converts wind power into rotational energy using vanes called windmill sail, sails or blades, specifically to mill (grinding), mill grain (gristmills), but the term is also extended to windpumps, wind turbines, and other applications, in some parts of the English speaking world. The term wind engine is sometimes used to describe such devices. Windmills were used throughout the High Middle Ages, high medieval and early modern periods; the horizontal or panemone windmill first appeared in Persia during the 9th century, and the vertical windmill first appeared in northwestern Europe in the 12th century. Regarded as an icon of Culture of the Netherlands, Dutch culture, there are approximately 1,000 windmills in the Netherlands today. Forerunners Wind-powered machines may have been known earlier, but there is no clear evidence of windmills before the 9th century. Hero of Alexandria (Heron) in first-century Roman Egypt described what appears to be a ...
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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 time. ...
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Kutta–Joukowski Theorem
The Kutta–Joukowski theorem is a fundamental theorem in aerodynamics used for the calculation of lift of an airfoil (and any two-dimensional body including circular cylinders) translating in a uniform fluid at a constant speed large enough so that the flow seen in the body-fixed frame is steady and unseparated. The theorem relates the lift generated by an airfoil to the speed of the airfoil through the fluid, the density of the fluid and the circulation around the airfoil. The circulation is defined as the line integral around a closed loop enclosing the airfoil of the component of the velocity of the fluid tangent to the loop. It is named after Martin Kutta and Nikolai Zhukovsky (or Joukowski) who first developed its key ideas in the early 20th century. Kutta–Joukowski theorem is an inviscid theory, but it is a good approximation for real viscous flow in typical aerodynamic applications. Kutta–Joukowski theorem relates lift to circulation much like the Magnus effe ...
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Disk Loading
In fluid dynamics, disk loading or disc loading is the average pressure change across an actuator disk, such as an airscrew. Airscrews with a relatively low disk loading are typically called rotors, including helicopter main rotors and tail rotors; propellers typically have a higher disk loading. The V-22 Osprey tiltrotor aircraft has a high disk loading relative to a helicopter in the hover mode, but a relatively low disk loading in fixed-wing mode compared to a turboprop aircraft. Rotors Disc loading of a hovering helicopter is the ratio of its weight to the total main rotor disc area. It is determined by dividing the total helicopter weight by the rotor disc area, which is the area swept by the blades of a rotor. Disc area can be found by using the span of one rotor blade as the radius of a circle and then determining the area the blades encompass during a complete rotation. When a helicopter is being maneuvered, its disc loading changes. The higher the loading, the more pow ...
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Circulation (fluid Dynamics)
In physics, circulation is the line integral of a vector field around a closed curve. In fluid dynamics, the field is the fluid velocity field. In electrodynamics, it can be the electric or the magnetic field. Circulation was first used independently by Frederick Lanchester, Martin Kutta and Nikolay Zhukovsky. It is usually denoted Γ (Greek uppercase gamma). Definition and properties If V is a vector field and dl is a vector representing the differential length of a small element of a defined curve, the contribution of that differential length to circulation is dΓ: :\mathrm\Gamma=\mathbf\cdot \mathrm\mathbf=, \mathbf, , \mathrm\mathbf, \cos \theta. Here, ''θ'' is the angle between the vectors V and dl. The circulation Γ of a vector field V around a closed curve ''C'' is the line integral: :\Gamma=\oint_\mathbf\cdot \mathrm d \mathbf. In a conservative vector field this integral evaluates to zero for every closed curve. That means that a line integral between any two ...
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Blade Element Theory
Blade element theory (BET) is a mathematical process originally designed by William Froude (1878), David W. Taylor (1893) and Stefan Drzewiecki to determine the behavior of propellers. It involves breaking a blade down into several small parts then determining the forces on each of these small blade elements. These forces are then integrated along the entire blade and over one rotor revolution in order to obtain the forces and moments produced by the entire propeller or rotor. One of the key difficulties lies in modelling the induced velocity on the rotor disk. Because of this the blade element theory is often combined with momentum theory to provide additional relationships necessary to describe the induced velocity on the rotor disk, producing blade element momentum theory. At the most basic level of approximation a uniform induced velocity on the disk is assumed: :v_i = \sqrt. Alternatively the variation of the induced velocity along the radius can be modeled by breaking the b ...
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Agitator (device)
An agitator is a device or mechanism to put something into motion by shaking or stirring. There are several types of agitation machines, including washing machine agitators (which rotate back and forth) and magnetic agitators (which contain a magnetic bar rotating in a magnetic field). Agitators can come in many sizes and varieties, depending on the application. In general, agitators usually consist of an impeller and a shaft. An impeller is a rotor located within a tube or conduit attached to the shaft. It helps enhance the pressure in order for the flow of a fluid be done. Modern industrial agitators incorporate process control to maintain better control over the mixing process. Washing machine agitator In a top load washing machine the agitator projects from the bottom of the wash basket and creates the wash action by rotating back and forth, rolling garments from the top of the load, down to the bottom, then back up again. There are several types of agitators with the m ...
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Turbocharger
In an internal combustion engine, a turbocharger (often called a turbo) is a forced induction device that is powered by the flow of exhaust gases. It uses this energy to compress the intake gas, forcing more air into the engine in order to produce more power for a given displacement.
The current categorisation is that a turbocharger is powered by the kinetic energy of the exhaust gasses, whereas a supercharger is mechanically powered (usually by a belt from the engine's crankshaft). However, up until the mid-20th century, a turbocharger was called a "turbosupercharger" and was considered a type of supercharger.


History

Prior to the invention of the turbocharger,

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Wind Turbine
A wind turbine is a device that converts the kinetic energy of wind into electrical energy. Hundreds of thousands of large turbines, in installations known as wind farms, now generate over 650 gigawatts of power, with 60 GW added each year. Wind turbines are an increasingly important source of intermittent renewable energy, and are used in many countries to lower energy costs and reduce reliance on fossil fuels. One study claimed that, wind had the "lowest relative greenhouse gas emissions, the least water consumption demands and the most favorable social impacts" compared to photovoltaic, hydro, geothermal, coal and gas energy sources. Smaller wind turbines are used for applications such as battery charging for auxiliary power for boats or caravans, and to power traffic warning signs. Larger turbines can contribute to a domestic power supply while selling unused power back to the utility supplier via the electrical grid. Wind turbines are manufactured in a wide range of ...
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Centrifugal Pump
Centrifugal pumps are used to transport fluids by the conversion of rotational kinetic energy to the hydrodynamic energy of the fluid flow. The rotational energy typically comes from an engine or electric motor. They are a sub-class of dynamic axisymmetric work-absorbing turbomachinery. The fluid enters the pump impeller along or near to the rotating axis and is accelerated by the impeller, flowing radially outward into a diffuser or volute chamber (casing), from which it exits. Common uses include water, sewage, agriculture, petroleum, and petrochemical pumping. Centrifugal pumps are often chosen for their high flow rate capabilities, abrasive solution compatibility, mixing potential, as well as their relatively simple engineering. A centrifugal fan is commonly used to implement an air handling unit or vacuum cleaner. The reverse function of the centrifugal pump is a water turbine converting potential energy of water pressure into mechanical rotational energy. His ...
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Density Of Air
The density of air or atmospheric density, denoted '' ρ'', is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature and humidity. At 101.325 kPa (abs) and 20 °C (68 °F), air has a density of approximately , according to the International Standard Atmosphere (ISA). At 101.325kPa (abs) and , air has a density of approximately , which is about that of water, according to the International Standard Atmosphere (ISA). Pure liquid water is . Air density is a property used in many branches of science, engineering, and industry, including aeronautics;Olson, Wayne M. (2000) AFFTC-TIH-99-01, Aircraft Performance FlightICAO, Manual of the ICAO Standard Atmosphere (extended to 80 kilometres (262 500 feet)), Doc 7488-CD, Third Edition, 1993, .Grigorie, T.L., Dinca, L., Corcau J-I. and Grigorie, O. (2010) Aircrafts' Altitude Measurement Using Pressure Information:Ba ...
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