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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.
C L is a function of the angle of the body to the flow, its Reynolds number and its Mach number. The section lift coefficient c l refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord. [1] [2]
where a 0 is 1,225 km/h (661.45 kn) (the standard speed of sound at 15 °C), M is the Mach number, P is static pressure, and P 0 is standard sea level pressure (1013.25 hPa). Combining the above with the expression for Mach number gives EAS as a function of impact pressure and static pressure (valid for subsonic flow):
With a given upstream Mach number, the post-shock Mach number can be calculated along with the pressure, density, temperature, and stagnation pressure ratios. Such tables are useful since the equations used to calculate the properties after a normal shock are cumbersome.
Consider a converging nozzle connecting a reservoir with a receiver. If the reservoir pressure is held constant and the receiver pressure reduced, the Mach number at the exit of the nozzle will increase until M e = 1 is reached, indicated by the left curve in figure 2.
This assumption is commonly made in engineering practice when the Mach number is less than about 0.3. C p {\displaystyle C_{p}} of zero indicates the pressure is the same as the freestream pressure. C p {\displaystyle C_{p}} of one corresponds to the stagnation pressure and indicates a stagnation point .
Low Mach-number flow, or pseudo-incompressibility: () =. The low Mach-number constraint can be derived from the compressible Euler equations using scale analysis of non-dimensional quantities. The restraint, like the previous in this section, allows for the removal of acoustic waves, but also allows for large perturbations in density and/or ...