Kantrowitz Limit
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Kantrowitz Limit
In gas dynamics, the Kantrowitz limit refers to a theoretical concept describing choked flow at supersonic or near-supersonic velocities. When an initially subsonic fluid flow experiences a reduction in cross-section area, the flow speeds up in order to maintain the same mass-flow rate, per the continuity equation. If a near supersonic flow experiences an area contraction, the velocity of the flow will increase until it reaches the local speed of sound, and the flow will be choked. This is the principle behind the Kantrowitz limit: it is the maximum amount of contraction a flow can experience before the flow chokes, and the flow speed can no longer be increased above this limit, independent of changes in upstream or downstream pressure. Derivation of Kantrowitz limit Assume a fluid enters an internally contracting nozzle at cross-section 0, and passes through a throat of smaller area at cross-section 4. A normal shock is assumed to start at the beginning of the nozzle contractio ...
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Arthur Kantrowitz
Arthur Robert Kantrowitz (October 20, 1913 – November 29, 2008) was an American scientist, engineer, and educator. Kantrowitz grew up in The Bronx and graduated from DeWitt Clinton High School.Overbye, Dennis"Arthur R. Kantrowitz, Whose Wide-Ranging Research Had Many Applications, Is Dead at 95" ''The New York Times'', December 9, 2008. Accessed December 9, 2008. He earned his B.S., M.A. and, in 1947, his Ph.D. degrees in physics from Columbia University. Early life Kantrowitz was born in New York City on October 28, 1913. His mother was a costume designer and his father ran a clinic in the Bronx. As a child, Arthur built an electrocardiograph from old radio parts, working with his brother Adrian (who would go on to perform the first heart transplant in the United States.)Hoffman, Jascha"Dr. Adrian Kantrowitz, Cardiac Pioneer, Dies at 90" ''The New York Times'', November 19, 2008. Accessed November 19, 2008. Career During his graduate studies at Columbia, Kantrowitz s ...
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Jet Engine
A jet engine is a type of reaction engine discharging a fast-moving jet of heated gas (usually air) that generates thrust by jet propulsion. While this broad definition can include rocket, Pump-jet, water jet, and hybrid propulsion, the term typically refers to an internal combustion airbreathing jet engine such as a turbojet, turbofan, ramjet, or pulse jet engine, pulse jet. In general, jet engines are internal combustion engines. Airbreathing jet engines typically feature a Axial compressor, rotating air compressor powered by a turbine, with the leftover power providing thrust through the propelling nozzle—this process is known as the Brayton cycle, Brayton thermodynamic cycle. Jet aircraft use such engines for long-distance travel. Early jet aircraft used turbojet engines that were relatively inefficient for subsonic flight. Most modern subsonic jet aircraft use more complex High-bypass turbofan, high-bypass turbofan engines. They give higher speed and greater fuel eff ...
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Adiabatic Index
In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume (). It is sometimes also known as the ''isentropic expansion factor'' and is denoted by ( gamma) for an ideal gasγ first appeared in an article by the French mathematician, engineer, and physicist Siméon Denis Poisson: * On p. 332, Poisson defines γ merely as a small deviation from equilibrium which causes small variations of the equilibrium value of the density ρ. In Poisson's article of 1823 – * γ was expressed as a function of density D (p. 8) or of pressure P (p. 9). Meanwhile, in 1816 the French mathematician and physicist Pierre-Simon Laplace had found that the speed of sound depends on the ratio of the specific heats. * However, he didn't denote the ratio as γ. In 1825, Laplace stated that the speed of sound is ...
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Suspension System
Suspension is the system of tires, tire air, springs, shock absorbers and linkages that connects a vehicle to its wheels and allows relative motion between the two. Suspension systems must support both road holding/ handling and ride quality, which are at odds with each other. The tuning of suspensions involves finding the right compromise. It is important for the suspension to keep the road wheel in contact with the road surface as much as possible, because all the road or ground forces acting on the vehicle do so through the contact patches of the tires. The suspension also protects the vehicle itself and any cargo or luggage from damage and wear. The design of front and rear suspension of a car may be different. History An early form of suspension on ox-drawn carts had the platform swing on iron chains attached to the wheeled frame of the carriage. This system remained the basis for most suspension systems until the turn of the 19th century, although the iron cha ...
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Air Bearing
Air bearings (also known as aerostatic or aerodynamic bearings) are fluid bearings that use a thin film of pressurized gas to provide a low friction load-bearing interface between surfaces. The two surfaces do not touch, thus avoiding the traditional bearing-related problems of friction, wear, particulates, and lubricant handling, and offer distinct advantages in precision positioning, such as lacking backlash and static friction, as well as in high-speed applications. Space craft simulators now most often use air bearings and 3-D printers are now used to make air-bearing-based attitude simulators for CubeSat satellites.Nemanja Jovanovic, et al. Design and Testing of a Low-Cost, Open Source, 3-D Printed Air-Bearing-Based Altitude Simulator for CubeSat Satellites. ''Journal of Small Satellites'' Vol. 8, No. 2, pp. 859–880 (2019). https://jossonline.com/letters/design-and-testing-of-a-low-cost-open-source-3-d-printed-air-bearing-based-attitude-simulator-for-cubesat-satellites/ ...
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Gas Compressor
A compressor is a mechanical device that increases the pressure of a gas by reducing its volume. An air compressor is a specific type of gas compressor. Compressors are similar to pumps: both increase the pressure on a fluid and both can transport the fluid through a pipe. The main distinction is that the focus of a compressor is to change the density or volume of the fluid, which is mostly only achievable on gases. Gases are compressible, while liquids are relatively incompressible, so compressors are rarely used for liquids. The main action of a pump is to pressurize and transport liquids. Many compressors can be staged, that is, the fluid is compressed several times in steps or stages, to increase discharge pressure. Often, the second stage is physically smaller than the primary stage, to accommodate the already compressed gas without reducing its pressure. Each stage further compresses the gas and increases its pressure and also temperature (if inter cooling between stages i ...
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Elon Musk
Elon Reeve Musk ( ; born June 28, 1971) is a business magnate and investor. He is the founder, CEO and chief engineer of SpaceX; angel investor, CEO and product architect of Tesla, Inc.; owner and CEO of Twitter, Inc.; founder of The Boring Company; co-founder of Neuralink and OpenAI; and president of the philanthropic Musk Foundation. With an estimated net worth of around $139 billion as of December 23, 2022, primarily from his ownership stakes in Tesla and SpaceX, Musk is the second-wealthiest person in the world according to both the ''Bloomberg Billionaires Index'' and ''Forbes'' real-time billionaires list. Musk was born in Pretoria, South Africa and briefly attended at the University of Pretoria before moving to Canada at age 18, acquiring citizenship through his Canadian-born mother. Two years later, he matriculated at Queen's University and transferred to the University of Pennsylvania, where he received bachelor's degrees in economics and physics. He moved ...
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Continuity Principle
A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described using continuity equations. Continuity equations are a stronger, local form of conservation laws. For example, a weak version of the law of conservation of energy states that energy can neither be created nor destroyed—i.e., the total amount of energy in the universe is fixed. This statement does not rule out the possibility that a quantity of energy could disappear from one point while simultaneously appearing at another point. A stronger statement is that energy is ''locally'' conserved: energy can neither be created nor destroyed, ''nor'' can it " ...
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Hyperloop
A hyperloop is a proposed high-speed transportion system for both public and goods transport. The idea was picked up by Elon Musk to describe a modern project based on the vactrain concept (first appearance in 1799). Hyperloop systems comprise three essential elements: tubes, pods, and terminals. The tube is a large, sealed and low-pressure system (usually a long tunnel). The pod is a coach pressurized at atmospheric pressure that runs substantially free of air resistance or friction inside this tube using magnetic propulsion (in some cases augmented by a ducted fan). The terminal handles pod arrivals and departures. The Hyperloop, in the initial form proposed by Musk, differs from vactrains by relying on residual air pressure inside the tube to provide lift by aerofoils and propulsion by fans. The hyperloop has its roots in a concept by George Medhurst in 1799 and subsequently developed under the names pneumatic railway, atmospheric railway or vactrain. Elon Musk renewed in ...
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Supersonic
Supersonic speed is the speed of an object that exceeds the speed of sound ( Mach 1). For objects traveling in dry air of a temperature of 20 °C (68 °F) at sea level, this speed is approximately . Speeds greater than five times the speed of sound (Mach 5) are often referred to as hypersonic. Flights during which only some parts of the air surrounding an object, such as the ends of rotor blades, reach supersonic speeds are called transonic. This occurs typically somewhere between Mach 0.8 and Mach 1.2. Sounds are traveling vibrations in the form of pressure waves in an elastic medium. Objects move at supersonic speed when the objects move faster than the speed at which sound propagates through the medium. In gases, sound travels longitudinally at different speeds, mostly depending on the molecular mass and temperature of the gas, and pressure has little effect. Since air temperature and composition varies significantly with altitude, the speed of s ...
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Launch Vehicle
A launch vehicle or carrier rocket is a rocket designed to carry a payload (spacecraft or satellites) from the Earth's surface to outer space. Most launch vehicles operate from a launch pad, launch pads, supported by a missile launch control center, launch control center and systems such as vehicle assembly and fueling. Launch vehicles are engineered with advanced aerodynamics and technologies, which contribute to large operating costs. An orbital spaceflight, orbital launch vehicle must lift its payload at least to the boundary of space, approximately and accelerate it to a horizontal velocity of at least . Suborbital spaceflight, Suborbital vehicles launch their payloads to lower velocity or are launched at elevation angles greater than horizontal. Practical orbital launch vehicles are multistage rockets which use chemical propellants such as Solid-propellant rocket, solid fuel, liquid hydrogen, kerosene, liquid oxygen, or Hypergolic propellants. Launch vehicles are cla ...
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Gas Dynamics
Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the ratio of the speed of the flow to the speed of sound) is smaller than 0.3 (since the density change due to velocity is about 5% in that case).Anderson, J.D., ''Fundamentals of Aerodynamics'', 4th Ed., McGraw–Hill, 2007. The study of compressible flow is relevant to high-speed aircraft, jet engines, rocket motors, high-speed entry into a planetary atmosphere, gas pipelines, commercial applications such as abrasive blasting, and many other fields. History The study of gas dynamics is often associated with the flight of modern high-speed aircraft and atmospheric reentry of space-exploration vehicles; however, its origins lie with simpler machines. At the beginning of the 19th century, investigation into the behaviour of fired bullets led to ...
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