In fluid mechanics, Mach number (\mathrm{Ma} or M) /ˈmɑːx/ is a dimensionless quantity representing the ratio of speed of an object moving through a fluid and the local speed of sound.[1][2]

\ M = \frac `v``v_{sound}`

where

\ M is the Mach number,

\ v is the velocity of the source relative to the medium, and

\ v_{sound} is the speed of sound in the medium.

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 (quasi) steady and isothermal, compressibility effects will be small and a simplified incompressible flow model can be used.[1][2]

The Mach number is named after Austrian 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 faster-than-sound human flight, aeronautical engineers referred to the speed of sound as Mach's number, never "Mach 1."[3]

In French, the Mach number is sometimes called the "nombre de Sarrau" ("Sarrau number") after Émile Sarrau who researched into explosions in the 1870s and 1880s.[4]