Mach number

The Mach number (M or Ma), often only Mach, (/mɑːk/; German: [max]) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.^[1]^[2] It is named after the Czech physicist and philosopher Ernst Mach.

\mathrm {M} ={\frac {u}{c}},

where:

M is the local Mach number,

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

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 1, the local flow velocity $u$ is equal to the speed of sound. At Mach 0.65, $u$ is 65% of the speed of sound (subsonic), and, at Mach 1.35, $u$ is 35% faster than the speed of sound (supersonic). Pilots of high-altitude aerospace vehicles use flight Mach number to express a vehicle's true airspeed, but the flow field around a vehicle varies in three dimensions, with corresponding variations in local Mach number.

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 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, 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 M < 0.2–0.3 and the flow is quasi-steady and isothermal, compressibility effects will be small and simplified incompressible flow equations can be used.^[1]^[2]

^ ^a ^b Young, Donald F.; Munson, Bruce R.; Okiishi, Theodore H.; Huebsch, Wade W. (21 December 2010). A Brief Introduction to Fluid Mechanics (5th ed.). John Wiley & Sons. p. 95. ISBN 978-0-470-59679-1. LCCN 2010038482. OCLC 667210577. OL 24479108M.
^ ^a ^b Graebel, William P. (19 January 2001). Engineering Fluid Mechanics (1st ed.). CRC Press. p. 16. ISBN 978-1-56032-733-2. OCLC 1034989004. OL 9794889M.

[Young_et_al-1] Young, Donald F.; Munson, Bruce R.; Okiishi, Theodore H.; Huebsch, Wade W. (21 December 2010). A Brief Introduction to Fluid Mechanics (5th ed.). John Wiley & Sons. p. 95. ISBN 978-0-470-59679-1. LCCN 2010038482. OCLC 667210577. OL 24479108M.

[Graebel-2] Graebel, William P. (19 January 2001). Engineering Fluid Mechanics (1st ed.). CRC Press. p. 16. ISBN 978-1-56032-733-2. OCLC 1034989004. OL 9794889M.

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