|
Shock Polar
The term ''shock polar'' is generally used with the graphical representation of the Rankine–Hugoniot equations in either the hodograph plane or the pressure ratio-flow deflection angle plane. The polar itself is the locus of all possible states after an oblique shock. Shock polar in the (''φ'', ''p'') plane The minimum angle, \theta, which an oblique shock can have is the Mach angle \mu =\sin^(1/M), where M is the initial Mach number before the shock and the greatest angle corresponds to a normal shock. The range of shock angles is therefore \sin^(1/M)\leq\theta\leq\pi /2. To calculate the pressures for this range of angles, the Rankine–Hugoniot equations are solved for pressure: \frac = 1 + \frac \left(M^\sin^\theta - 1\right) To calculate the possible flow deflection angles, the relationship between shock angle \theta and \varphi is used: \tan\varphi = 2\cot\theta\frac. Where \gamma is the ratio of specific heats and \varphi is the flow deflection angle. Uses of shock ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hodograph
A hodograph is a diagram that gives a vectorial visual representation of the movement of a body or a fluid. It is the locus of one end of a variable vector, with the other end fixed. The position of any plotted data on such a diagram is proportional to the velocity of the moving particle. It is also called a velocity diagram. It appears to have been used by James Bradley, but its practical development is mainly from Sir William Rowan Hamilton, who published an account of it in the ''Proceedings of the Royal Irish Academy'' in 1846. Applications It is used in physics, astronomy, solid and fluid mechanics to plot deformation of material, motion of planets or any other data that involves the velocities of different parts of a body. See Swinging Atwood's machine Meteorology In meteorology, hodographs are used to plot winds from soundings of the Earth's atmosphere. It is a polar diagram where wind direction is indicated by the angle from the center axis and its strength by the di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oblique Shock
An oblique shock wave is a shock wave that, unlike a normal shock, is inclined with respect to the incident upstream flow direction. It will occur when a supersonic flow encounters a corner that effectively turns the flow into itself and compresses. The upstream streamlines are uniformly deflected after the shock wave. The most common way to produce an oblique shock wave is to place a wedge into supersonic, compressible flow. Similar to a normal shock wave, the oblique shock wave consists of a very thin region across which nearly discontinuous changes in the thermodynamic properties of a gas occur. While the upstream and downstream flow directions are unchanged across a normal shock, they are different for flow across an oblique shock wave. It is always possible to convert an oblique shock into a normal shock by a Galilean transformation. Wave theory For a given Mach number, M1, and corner angle, θ, the oblique shock angle, β, and the downstream Mach number, M2, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shock Polar
The term ''shock polar'' is generally used with the graphical representation of the Rankine–Hugoniot equations in either the hodograph plane or the pressure ratio-flow deflection angle plane. The polar itself is the locus of all possible states after an oblique shock. Shock polar in the (''φ'', ''p'') plane The minimum angle, \theta, which an oblique shock can have is the Mach angle \mu =\sin^(1/M), where M is the initial Mach number before the shock and the greatest angle corresponds to a normal shock. The range of shock angles is therefore \sin^(1/M)\leq\theta\leq\pi /2. To calculate the pressures for this range of angles, the Rankine–Hugoniot equations are solved for pressure: \frac = 1 + \frac \left(M^\sin^\theta - 1\right) To calculate the possible flow deflection angles, the relationship between shock angle \theta and \varphi is used: \tan\varphi = 2\cot\theta\frac. Where \gamma is the ratio of specific heats and \varphi is the flow deflection angle. Uses of shock ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mach Angle
In fluid dynamics, a Mach wave is a pressure wave traveling with the speed of sound caused by a slight change of pressure added to a compressible flow. These weak waves can combine in supersonic flow to become a shock wave if sufficient Mach waves are present at any location. Such a shock wave is called a Mach stem or Mach front. Thus, it is possible to have shockless compression or expansion in a supersonic flow by having the production of Mach waves sufficiently spaced (''cf.'' isentropic compression in supersonic flows). A Mach wave is the weak limit of an oblique shock wave where time averages of flow quantities don't change; (a normal shock is the other limit). If the size of the object moving at the speed of sound is near 0, then this domain of influence of the wave is called a Mach cone. Mach angle A Mach wave propagates across the flow at the Mach angle ''μ'', which is the angle formed between the Mach wave wavefront and a vector that points opposite to the vector of mot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mach Reflection
Mach reflection is a supersonic fluid dynamics effect, named for Ernst Mach, and is a shock wave reflection pattern involving three shocks. Introduction Mach reflection can exist in steady, pseudo-steady and unsteady flows. When a shock wave, which is moving with a constant velocity, propagates over a solid wedge, the flow generated by the shock impinges on the wedge thus generating a second reflected shock, which ensures that the velocity of the flow is parallel to the wedge surface. Viewed in the frame of the reflection point, this flow is locally steady, and the flow is referred to as pseudosteady. When the angle between the wedge and the primary shock is sufficiently large, a single reflected shock is not able to turn the flow to a direction parallel to the wall and a transition to Mach reflection occurs. In a steady flow situation, if a wedge is placed into a steady supersonic flow in such a way that its oblique attached shock impinges on a flat wall parallel to the free s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Science+Business Media
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
McGraw-Hill
McGraw Hill is an American educational publishing company and one of the "big three" educational publishers that publishes educational content, software, and services for pre-K through postgraduate education. The company also publishes reference and trade publications for the medical, business, and engineering professions. McGraw Hill operates in 28 countries, has about 4,000 employees globally, and offers products and services to about 140 countries in about 60 languages. Formerly a division of The McGraw Hill Companies (later renamed McGraw Hill Financial, now S&P Global), McGraw Hill Education was divested and acquired by Apollo Global Management in March 2013 for $2.4 billion in cash. McGraw Hill was sold in 2021 to Platinum Equity for $4.5 billion. Corporate History McGraw Hill was founded in 1888 when James H. McGraw, co-founder of the company, purchased the ''American Journal of Railway Appliances''. He continued to add further publications, eventually establishing The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
