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| {{Redirect|Mach 2|the film|Mach 2 (film)}}
| | <br><br>If Americans love anything, it's devices. Unfortunately, that is really a large belief that our landfills are as full simply because they are. [http://www.ractiv.com/ Gadgets] break or become obsolete, and batteries die. Fortunately, gadget makers are finally learning by way of the solar-powered calculator and moving into more eco-friendly offerings.<br><br>A bug is very device that transmits audio or a plan of video and audio to individual that you can put device within your home or business. Once upon a time, most bugs needed to be by telephones or walls purely because they had being hardwired in the electrical system of your house. With wireless technology, a bug can literally be anywhere in your place. The reasons for carrying out this can be many a lot of of options are not legal. Are you involved from a divorce? It could be your spouse or an intrigued party to make the soon-to-be-ex is bugging your premises to get something in order to or just eavesdrop in order to find out what your plans are. Sometimes business partners are bugging you, or it become someone (usually an ex that can't let go) with an obsession about you.<br><br>Judge and select some a lot more. You judge a service by comparing it to competing or similar products. You can also work benchmark the item against on their own.<br><br>Next, search the professional and business media for information. In order to reporters who write because of the organization. You'll quickly identify the trends, and you'll develop questions to ask procedures.<br><br>Know which team you make your outbound calls to: Whoever your call reaches is often a person, just another phone number. Check their names and look them through to Facebook, Linkedin, Twitter and Google +. You'll find valuable information that supply good insights on the best way to to approach them.<br><br>You can have long gatherings. you will have temporary defeat. and you may definitely be laughed at by household members on your beginning of the building.<br><br>There isn't any need for huge financial investment appear for young and delightful all that is needed from you is to come to my care experience. If you'll like the results, you can purchase yourself when you to nurture and preserve the associated with facial skin and process. |
| {{Refimprove|date=August 2011}}
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| [[Image:FA-18 Hornet breaking sound barrier (7 July 1999).jpg|300px|right|thumb|An [[F/A-18 Hornet]] creating a [[vapor cone]] at [[transonic speed]] just before reaching the speed of sound]]
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| In [[fluid mechanics]], '''Mach number''' ('''M''' or '''Ma''') {{IPAc-en|ˈ|m|ɑː|x}} is a [[dimensionless quantity]] representing the ratio of speed of an object moving through a [[fluid]] and the local [[speed of sound]].<ref name="Young_et_al">{{cite book|last=Young|first=Donald F.|title=A Brief Introduction to Fluid Mechanics|year=2010|publisher=John Wiley & Sons|isbn=978-0-470-59679-1|edition=5|coauthors=Bruce R. Munson, Theodore H. Okiishi, Wade W. Huebsch |page=95}}</ref><ref name="Graebel">{{cite book|last=Graebel|first=W.P.|title=Engineering Fluid Mechanics|year=2001|publisher=Taylor & Francis|isbn=978-1-56032-733-2 |page=16}}</ref>
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| :<math>\mathrm{M} = \frac {{v}}{{v_\text{sound}}}</math>
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| where
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| : M is the Mach number,
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| : ''v'' is the velocity of the source relative to the medium, and
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| : ''v''<sub>sound</sub> is the speed of sound in the medium.
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| Mach number varies by the composition of the surrounding medium and also by local conditions, especially temperature and pressure. The Mach number can be used to determine if a flow can be treated as an [[incompressible flow]]. If M < 0.2–0.3 and the flow is [[steady flow|(quasi) steady]] and [[isothermal flow|isothermal]], compressibility effects will be small and a simplified incompressible flow model can be used.<ref name="Young_et_al"/><ref name="Graebel"/>
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| The Mach number is named after [[Austria]]n physicist and philosopher [[Ernst Mach]], a designation proposed by aeronautical engineer [[Jakob Ackeret]]. Because the Mach number is often viewed as a [[dimensionless quantity]] rather than a unit of measure, with Mach, the number comes ''after'' the unit; the second Mach number is "Mach 2" instead of "2 Mach" (or Machs). This is somewhat reminiscent of the early modern ocean sounding unit "mark" (a synonym for [[fathom]]), which was also unit-first, and may have influenced the use of the term Mach. In the decade preceding [[Sound barrier#Attempts to break the sound barrier|faster-than-sound human flight]], aeronautical engineers referred to the speed of sound as ''Mach's number'', never "Mach 1."<ref>Bodie, Warren M., ''The Lockheed P-38 Lightning'', Widewing Publications ISBN 0-9629359-0-5</ref>
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| In French, the Mach number is sometimes called the "nombre de Sarrau" ("Sarrau number") after [[Émile Sarrau]] who researched explosions in the 1870s and 1880s.<ref>{{Cite book | publisher = University of California Press | isbn = 978-0-520-01849-5 | last = Blackmore | first = John T. | title = Ernst Mach: His Life, Work, and Influence | year = 1972 | page = 112 }}</ref>
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| == Overview ==
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| The Mach number is commonly used both with objects traveling at high speed in a fluid, and with high-speed fluid flows inside channels such as [[nozzle]]s, [[diffuser]]s or [[wind tunnel]]s. As it is defined as a ratio of two speeds, it is a [[dimensionless number]]. At [[International Standard Atmosphere|Standard Sea Level]] conditions (corresponding to a [[temperature]] of 15 degrees [[Celsius]]), the speed of sound is 340.3 [[Meter per second|m/s]]<ref>Clancy, L.J. (1975), Aerodynamics, Table 1, Pitman Publishing London, ISBN 0-273-01120-0</ref> (1225 km/h, or 761.2 mph, or 661.5 [[Knot (unit)|knots]], or 1116 [[Feet per second|ft/s]]) in the [[Earth's atmosphere]]. The speed represented by Mach 1 is not a constant; for example, it is mostly dependent on temperature and atmospheric composition and largely independent of pressure.
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| Since the speed of sound increases as the temperature increases, the actual speed of an object traveling at Mach 1 will depend on the fluid temperature around it. Mach number is useful because the fluid behaves in a similar way at the same Mach number. So, an aircraft traveling at Mach 1 at 20°C or 68°F, at sea level, will experience shock waves in much the same manner as when it is traveling at Mach 1 at 11,000 m (36,000 [[foot (length)|ft]]) at −50°C or −58F, even though it is traveling at only 86% of its speed at higher temperature like 20°C or 68°F.<ref name=NASA>([http://www.grc.nasa.gov/WWW/k-12/airplane/mach.html]). National Aeronautics and Space Administration website page "Mach Number", NASA.</ref>
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| == Classification of Mach regimes ==
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| <!-- This seems to be a copy of: http://en.wikipedia.org/w/index.php?title=Hypersonic_speed&oldid=511832073; inserted here in this diff: http://en.wikipedia.org/w/index.php?title=Mach_number&oldid=517664045 -->
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| While the terms "subsonic" and "supersonic" in the purest verbal sense refer to speeds below and above the local speed of sound respectively, aerodynamicists often use the same terms to talk about particular ranges of Mach values. This occurs because of the presence of a "transonic regime" around M = 1 where approximations of the [[Navier-Stokes equations]] used for subsonic design actually no longer apply, the simplest of many reasons being that the flow locally begins to exceed M = 1 even when the freestream Mach number is below this value.
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| Meanwhile, the "supersonic regime" is usually used to talk about the set of Mach numbers for which linearised theory may be used, where for example the ([[air]]) flow is not chemically reacting, and where heat-transfer between air and vehicle may be reasonably neglected in calculations.
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| In the following table, the "regimes" or "ranges of Mach values" are referred to, and not the "pure" meanings of the words "subsonic" and "supersonic".
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| Generally, [[NASA]] defines "high" hypersonic as any Mach number from 10 to 25, and re-entry speeds as anything greater than Mach 25. Aircraft operating in this regime include the [[Space Shuttle]] and various space planes in development.
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| {| class="wikitable"
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| |-
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| ! Regime
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| ! Mach
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| ! mph
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| ! km/h
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| ! m/s
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| ! General plane characteristics
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| |-
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| ! style="background-color: #FFFFFF;" | [[Speed of sound|Subsonic]]
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| | <0.8
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| | <610
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| | <980
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| | <270
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| | Most often propeller-driven and commercial [[turbofan]] aircraft with high aspect-ratio (slender) wings, and rounded features like the nose and leading edges.
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| |-
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| ! style="background-color: #FFC0C0;" | [[Transonic]]
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| | 0.8-1.2
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| | 610-915
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| | 980-1,470
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| | 270-410
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| | Transonic aircraft nearly always have [[swept wing]]s, delaying drag-divergence, and often feature design adhering to the principles of the Whitcomb [[Area rule]].
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| |-
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| ! style="background-color: #FF8181;" | [[Supersonic]]
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| | 1.2–5.0
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| | 915-3,840
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| | 1,470–6,150
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| | 410–1,710
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| | Aircraft designed to fly at supersonic speeds show large differences in their aerodynamic design because of the radical differences in the behaviour of flows above Mach 1. Sharp edges, thin [[aerofoil]]-sections, and all-moving [[tailplane]]/[[canards]] are common. Modern [[combat aircraft]] must compromise in order to maintain low-speed handling; "true" supersonic designs include the [[F-104 Starfighter]] and BAC/Aérospatiale [[Concorde]].
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| |-
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| ! style="background-color: #FF4242;" | [[Hypersonic]]
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| | 5.0–10.0
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| | 3,840–7,680
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| | 6,150–12,300
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| | 1,710–3,415
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| | Cooled [[nickel]]-[[titanium]] skin; highly integrated (due to domination of interference effects: non-linear behaviour means that [[Superposition principle|superposition]] of results for separate components is invalid), small wings, see [[Boeing X-51|X-51A Waverider]]
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| |-
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| ! style="background-color: #FF0303;" | High-hypersonic
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| | 10.0–25.0
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| | 7,680–16,250
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| | 12,300–30,740
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| | 3,415–8,465
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| | Thermal control becomes a dominant design consideration. Structure must either be designed to operate hot, or be protected by special silicate tiles or similar. Chemically reacting flow can also cause corrosion of the vehicle's skin, with free-atomic [[oxygen]] featuring in very high-speed flows. Hypersonic designs are often forced into [[Atmospheric_reentry#Blunt_body_entry_vehicles|blunt configurations]] because of the aerodynamic heating rising with a reduced [[Radius of curvature (mathematics)|radius of curvature]].
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| |-
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| ! style="background-color: #C00000;" | [[Re-entry]] speeds
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| | >25.0
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| | >16,250
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| | >30,740
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| | >8,465
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| | Ablative heat shield; small or no wings; blunt shape
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| |}
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| == High-speed flow around objects ==
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| Flight can be roughly classified in six categories:
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| {| class="wikitable" width=60%
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| ! Regime
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| ! [[Speed of sound|Subsonic]]
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| ! [[Transonic]]
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| ! [[Speed of sound|Sonic]]
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| ! [[Supersonic]]
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| ! [[Hypersonic]]
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| ! [[Hypersonic#Classification|High-hypersonic]]
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| |-
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| ! Mach
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| |align=center| <0.8
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| |align=center| 0.8–1.2
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| |align=center| 1.0
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| |align=center| 1.2–5.0
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| |align=center| 5.0–10.0
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| |align=center| >10.0
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| |}
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| For comparison: the required speed for [[low Earth orbit]] is approximately 7.5 km/s = Mach 25.4 in air at high altitudes. The [[speed of light]] in a vacuum corresponds to a Mach number of approximately 881,000 (relative to air at sea level).
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| At transonic speeds, the flow field around the object includes both sub- and supersonic parts. The transonic period begins when first zones of M > 1 flow appear around the object. In case of an airfoil (such as an aircraft's wing), this typically happens above the wing. Supersonic flow can decelerate back to subsonic only in a normal shock; this typically happens before the trailing edge. (Fig.1a)
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| As the speed increases, the zone of M > 1 flow increases towards both leading and trailing edges. As M = 1 is reached and passed, the normal shock reaches the trailing edge and becomes a weak oblique shock: the flow decelerates over the shock, but remains supersonic. A normal shock is created ahead of the object, and the only subsonic zone in the flow field is a small area around the object's leading edge. (Fig.1b)
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| {| border="0"
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| | [[File:Transsonic flow over airfoil 1.svg|300px]]
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| | [[File:Transsonic flow over airfoil 2.svg|300px]]
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| |-
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| | (a)
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| | (b)
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| |}
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| '''Fig. 1.''' ''Mach number in transonic airflow around an airfoil; M < 1 (a) and M > 1 (b).''
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| When an aircraft exceeds Mach 1 (i.e. the [[sound barrier]]) a large pressure difference is created just in front of the [[aircraft]]. This abrupt pressure difference, called a [[shock wave]], spreads backward and outward from the aircraft in a cone shape (a so-called Mach cone). It is this shock wave that causes the [[sonic boom]] heard as a fast moving aircraft travels overhead. A person inside the aircraft will not hear this. The higher the speed, the more narrow the cone; at just over M = 1 it is hardly a cone at all, but closer to a slightly concave plane.
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| At fully supersonic speed, the shock wave starts to take its cone shape and flow is either completely supersonic, or (in case of a blunt object), only a very small subsonic flow area remains between the object's nose and the shock wave it creates ahead of itself. (In the case of a sharp object, there is no air between the nose and the shock wave: the shock wave starts from the nose.)
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| As the Mach number increases, so does the strength of the [[shock wave]] and the Mach cone becomes increasingly narrow. As the fluid flow crosses the shock wave, its speed is reduced and temperature, pressure, and density increase. The stronger the shock, the greater the changes. At high enough Mach numbers the temperature increases so much over the shock that ionization and dissociation of gas molecules behind the shock wave begin. Such flows are called hypersonic.
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| It is clear that any object traveling at hypersonic speeds will likewise be exposed to the same extreme temperatures as the gas behind the nose shock wave, and hence choice of heat-resistant materials becomes important.
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| == High-speed flow in a channel ==
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| As a flow in a channel becomes supersonic, one significant change takes place. The conservation of [[mass flow rate]] leads one to expect that contracting the flow channel would increase the flow speed (i.e. making the channel narrower results in faster air flow) and at subsonic speeds this holds true. However, once the flow becomes supersonic, the relationship of flow area and speed is reversed: expanding the channel actually increases the speed.
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| The obvious result is that in order to accelerate a flow to supersonic, one needs a convergent-divergent nozzle, where the converging section accelerates the flow to sonic speeds, and the diverging section continues the acceleration. Such nozzles are called [[de Laval nozzle]]s and in extreme cases they are able to reach [[hypersonic]] speeds ({{convert|13|Mach}} at 20°C).
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| An aircraft [[Machmeter]] or electronic flight information system ([[EFIS]]) can display Mach number derived from stagnation pressure ([[pitot tube]]) and static pressure.
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| ==Calculation==
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| The Mach number at which an aircraft is flying can be calculated by
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| :<math>
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| \mathrm{M} = \frac{v}{v_\text{sound}}
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| </math> | |
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| where:
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| : M is the Mach number
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| : ''v'' is [[velocity]] of the moving aircraft and
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| :''v''<sub>sound</sub> is the [[speed of sound]] at the given altitude
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| Note that the dynamic pressure can be found as:
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| :<math>q = \frac{\gamma}{2} p\, \mathrm{M}^2</math>
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| Assuming air to be an [[ideal gas]], the formula to compute Mach number in a subsonic compressible flow is derived from [[Bernoulli's principle|Bernoulli's equation]] for M < 1:<ref name="Olson">Olson, Wayne M. (2002). "AFFTC-TIH-99-02, ''Aircraft Performance Flight Testing''." ([http://www.aviation.org.uk/pdf/Aircraft_Performance_Flight_Testing.pdf PDF]). Air Force Flight Test Center, Edwards AFB, CA, United States Air Force.</ref>
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| :<math>
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| \mathrm{M}=\sqrt{\frac{2}{\gamma-1}\left[\left(\frac{q_c}{p}+1\right)^\frac{\gamma-1}{\gamma}-1\right]}\,
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| </math>
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| where:
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| : ''q<sub>c</sub>'' is [[impact pressure]] (dynamic pressure) and
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| : ''p'' is [[static pressure]]
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| :<math>\ \gamma\,</math> is the [[Heat capacity ratio|ratio of specific heat]] of a gas at a constant pressure to heat at a constant volume (1.4 for air).
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| The formula to compute Mach number in a supersonic compressible flow is derived from the [[Rayleigh number|Rayleigh]] Supersonic Pitot equation:
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|
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| :<math> \frac{q_c}{p} = \left[\frac{\gamma+1}{2}\mathrm{M}^2\right]^\left(\frac{\gamma}{\gamma-1}\right)\cdot \left[ \frac{\gamma+1}{\left(1-\gamma+2 \gamma\, \mathrm{M}^2\right)} \right]^\left(\frac{1}{ \gamma-1 }\right) </math>
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| ===Calculating Mach Number from Pitot Tube Pressure===
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| At altitude, for reasons explained, Mach number is a function of temperature.
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| Aircraft [[flight instruments]], however, operate using pressure differential to compute Mach number, not temperature. The assumption is that a particular pressure represents a particular altitude and, therefore, a standard temperature. Aircraft flight instruments need to operate this way because the stagnation pressure sensed by a [[Pitot tube]] is dependent on altitude as well as speed.
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| Assuming air to be an [[ideal gas]], the formula to compute Mach number in a subsonic compressible flow is found from Bernoulli's equation for M < 1 (above):<ref name="Olson" />
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| :<math>
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| \mathrm{M} = \sqrt{5\left[\left(\frac{q_c}{p}+1\right)^\frac{2}{7}-1\right]}\,
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| </math>
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| The formula to compute Mach number in a supersonic compressible flow can be found from the Rayleigh Supersonic Pitot equation (above) using parameters for air:
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| :<math>\mathrm{M} = 0.88128485 \sqrt{\left(\frac{q_c}{p} + 1\right)\left(1 - \frac{1}{7\,\mathrm{M}^2}\right)^{2.5}}</math>
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| where:
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| :''q<sub>c</sub>'' is dynamic pressure measured behind a normal shock
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| As can be seen, M appears on both sides of the equation. The easiest method to solve the supersonic M calculation is to enter both the subsonic and supersonic equations into a computer spreadsheet such as [[Microsoft Excel]], [[Openoffice Calc|OpenOffice.org Calc]], or some equivalent program. First determine if M is indeed greater than 1.0 by calculating M from the subsonic equation. If M is greater than 1.0 at that point, then use the value of M from the subsonic equation as the initial condition in the supersonic equation. Then perform a simple iteration of the supersonic equation, each time using the last computed value of M, until M converges to a value—usually in just a few iterations.<ref name=Olson/>
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| == See also ==
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| *[[Critical Mach number]]
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| *[[Machmeter]]
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| *[[Ramjet]]
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| *[[Scramjet]]
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| *[[Speed of sound]]
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| *[[True airspeed]]
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| == Notes ==
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| {{Reflist}}
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| == External links ==
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| *[http://web.ics.purdue.edu/~alexeenk/GDT/index.html Gas Dynamics Toolbox] Calculate Mach number and normal shock wave parameters for mixtures of perfect and imperfect gases.
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| *[http://www.grc.nasa.gov/WWW/K-12/airplane/mach.html NASA's page on Mach Number] Interactive calculator for Mach number.
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| *[http://www.newbyte.co.il/calc.html NewByte standard atmosphere calculator and speed converter]
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| *[http://www.youtube.com/watch?v=d0WiiGIOPNU FDTD simualtion of MACH-CONE within a pixel space] FDTD with no units.
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| {{NonDimFluMech}}
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| [[Category:Aerodynamics]]
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| [[Category:Airspeed]]
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| [[Category:Dimensionless numbers of fluid mechanics]]
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| [[Category:Fluid dynamics]]
| |
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