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The Mach number (M or Ma), often only Mach, (/ m ɑː k /; German:) 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 Austrian physicist and philosopher Ernst Mach. =, where: M is the local Mach number,
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
Transonic flow patterns on an aircraft wing, showing the effects at and above the critical Mach number. In aerodynamics, the critical Mach number (Mcr or M*) of an aircraft is the lowest Mach number at which the airflow over some point of the aircraft reaches the speed of sound, but does not exceed it. [1]
Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density.While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the ratio of the speed of the flow to the speed of sound) is smaller than 0.3 (since the density change due to velocity is about 5% in that case). [1]
The dashed lines show the limiting value as Mach number tends to infinity. In aerodynamics, the Prandtl–Meyer function describes the angle through which a flow turns isentropically from sonic velocity (M=1) to a Mach (M) number greater than 1.
A Machmeter is an aircraft pitot-static system flight instrument that shows the ratio of the true airspeed to the speed of sound, a dimensionless quantity called Mach number. This is shown on a Machmeter as a decimal fraction. An aircraft flying at the speed of sound is flying at a Mach number of one, expressed as Mach 1.
The upstream Mach number, , begins at 1 and ends at 5. Although the tables could be extended over any range of Mach numbers, stopping at Mach 5 is typical since assuming to be 1.4 over the entire Mach number range leads to errors over 10% beyond Mach 5.
is the Mach number, which is taken in the limit of zero p 0 {\displaystyle p_{0}} is the flow's stagnation pressure This relationship is valid for the flow of incompressible fluids where variations in speed and pressure are sufficiently small that variations in fluid density can be neglected.