Editing Mach number (section)

{{Short description|Dimensionless quantity in fluid dynamics}}
{{Use British English|date=January 2020}}
{{Redirect|Mach}}

[[File:FA-18 Hornet breaking sound barrier (7 July 1999).jpg|right|thumb|An [[F/A-18 Hornet]] creating a [[vapor cone]] at [[transonic speed]] just before reaching the [[speed of sound]].]]

The '''Mach number''' ('''M''' or '''Ma'''), often only '''Mach''', ({{IPAc-en|m|ɑː|k}}; {{IPA|de|max|lang}}) is a [[dimensionless quantity]] in [[fluid dynamics]] representing the ratio of [[flow velocity]] past a [[Boundary (thermodynamic)|boundary]] to the local [[speed of sound]].<ref name="Young_et_al">{{cite book|last=Young|first=Donald F.|title=A Brief Introduction to Fluid Mechanics|date=2010-12-21|publisher=John Wiley & Sons|isbn=978-0-470-59679-1|edition=5th|first2=Bruce R. | last2 =  Munson |first3=Theodore H. | last3 = Okiishi | author-link3 = Theodore H. Okiishi |first4 = Wade W. | last4 = Huebsch  |page=95 | ol = OL24479108M | oclc = 667210577 | lccn = 2010038482 | df = dmy-all}}</ref><ref name="Graebel">{{cite book|last=Graebel|first=William P.|title=Engineering Fluid Mechanics|date = 2001-01-19 |publisher=[[CRC Press]] | edition = 1st |isbn=978-1-56032-733-2 |page=16|ol = OL9794889M | oclc = 1034989004 | df = dmy-all }}</ref>
It is named after the  [[Austria]]n physicist and philosopher [[Ernst Mach]].

<math display="block">\mathrm{M} = \frac{u}{c},</math>

where:
* {{serif|M}} is the local Mach number,
* {{mvar|u}} 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
* {{mvar|c}} is the speed of sound in the medium, which in air varies with the square root of the [[thermodynamic temperature]].

By definition, at Mach{{nbsp}}1, the local flow velocity {{mvar|u}} is equal to the speed of sound. At Mach{{nbsp}}0.65, {{mvar|u}} is 65% of the speed of sound (subsonic), and, at Mach{{nbsp}}1.35, {{mvar|u}} is 35% faster than the speed of sound (supersonic).

The local speed of sound, and hence the Mach number, depends on the temperature of the surrounding gas. The Mach number is primarily used to determine the approximation with which a flow can be treated as an [[incompressible flow]]. The medium can be a gas or a liquid. The boundary can be travelling in the medium, or it can be stationary while the medium flows along it, or they can both be moving, with different [[velocity|velocities]]: what matters is their relative velocity with respect to each other. The boundary can be the boundary of an object immersed in the medium, or of a channel such as a [[nozzle]], [[jet engine#Air intake|diffuser]] or [[wind tunnel]] channelling the medium. As the Mach number is defined as the ratio of two speeds, it is a dimensionless quantity. If {{serif|M}}&nbsp;<&nbsp;0.2–0.3 and the flow is [[steady flow|quasi-steady]] and [[isothermal flow|isothermal]], compressibility effects will be small and simplified incompressible flow equations can be used.<ref name="Young_et_al" /><ref name="Graebel" />