Machzahl

Machzahl, or Mach number, is the dimensionless quantity used in aerodynamics and gas dynamics to compare an object's velocity with the local speed of sound. It is defined as M = v / a, where v is the flow velocity and a is the local speed of sound.

The speed of sound a in an ideal gas depends on temperature and composition: a = sqrt(gamma * R * T), with gamma the ratio of specific heats, R the specific gas constant, and T the absolute temperature. For air near sea level, gamma ≈ 1.4 and a ≈ 340 m/s at 15 °C.

In compressible, isentropic flow, the stagnation-to-static pressure relation links Mach number to pressures: p0/p = (1 + (gamma - 1)/2 M^2)^{gamma/(gamma - 1)}. Equivalently, M = sqrt( (2/(gamma - 1)) [ (p0/p)^{(gamma - 1)/gamma} - 1 ] ). Mach can be measured with Pitot-static probes, comparing total and static pressures to infer velocity and thus M.

Machzahl is used to classify flow regimes. Subsonic flows have M < 1, transonic flows occur near M ≈ 1 (often 0.8–1.2, where both subsonic and sonic regions coexist), supersonic flows have M > 1, and hypersonic flows are typically M > 5. The Mach number governs compressibility effects, the formation of shock waves, drag characteristics, and aerodynamic heating, and it is central to the design of aircraft, rockets, and turbomachinery.

The term derives from Ernst Mach, the Austrian physicist who studied shock waves and gas dynamics in the 19th century.