To use all functions of this page, please activate cookies in your browser.

my.chemeurope.com

With an accout for my.chemeurope.com you can always see everything at a glance – and you can configure your own website and individual newsletter.

- My watch list
- My saved searches
- My saved topics
- My newsletter

## Mach number
where - is the Mach number
- is the velocity of the object relative to the medium and
- is the velocity of sound in the medium
Mach number is the number of times the speed of sound an object or a duct, or the fluid medium itself, move relative to each other. It is named after Austrian physicist and philosopher Ernst Mach. Unlike most units of measure, with Mach the number comes after the unit, so one says "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 man flying faster than sound, aeronautical engineers referred to the speed of sound as ## Additional recommended knowledge
## OverviewThe Mach number is commonly used both with objects travelling at high speed in a fluid, and with high-speed fluid flows inside channels such as nozzles, diffusers or wind tunnels. As it is defined as a ratio of two speeds, it is a dimensionless number. At a temperature of 15 degrees Celsius and at sea level, Mach 1 is 340.3 m/s (1,225 km/h, 761.2 mph, or 661.7 kn) in the Earth's atmosphere. The speed represented by Mach 1 is not a constant; For example, it is dependent on temperature and atmospheric composition. In the stratosphere it remains constant irrespective of altitude even though the air pressure varies with altitude. Since the speed of sound increases as the temperature increases, the actual speed of an object travelling at Mach 1 will depend on the fluid temperature around it. Mach number is useful because the fluid behaves in a similar way at the same Mach number. So, an aircraft travelling at Mach 1 at sea level (340.3 m/s, 1,225.08 km/h) will experience shock waves in much the same manner as when it is travelling at Mach 1 at 11,000 m (36,000 ft), even though it is travelling at 295 m/s (654.632 mph, 1,062 km/h, 86% of its speed at sea level). It can be shown that the Mach number is also the ratio of inertial forces (also referred to aerodynamic forces) to elastic forces. ## High-speed flow around objectsHigh speed flight can be roughly classified in five categories: **Subsonic:**Ma < 1**Sonic:**Ma=1**Transonic:**0.8 < Ma < 1.2**Supersonic:**1.2 < Ma < 5**Hypersonic:**Ma > 5
(For comparison: the required speed for low Earth orbit is ca. 7.5 km·s At transonic speeds, the flow field around the object includes both sub- and supersonic parts. The transonic period begins when first zones of Ma>1 flow appear around the object. In case of an airfoil (such as an aircraft's wing), this typically happens above the wing. Supersonic flow can decelerate back to subsonic only in a normal shock; this typically happens before the trailing edge. (Fig.1a) As the velocity increases, the zone of
When an aircraft exceeds Mach 1 (i.e. the sound barrier) a large pressure difference is created just in front of the aircraft. This abrupt pressure difference, called a shock wave, spreads backward and outward from the aircraft in a cone shape (a so-called Mach cone). It is this shock wave that causes the sonic boom heard as a fast moving aircraft travels overhead. A person inside the aircraft will not hear this. The higher the speed, the more narrow the cone; at just over At fully supersonic velocity the shock wave starts to take its cone shape, and flow is either completely supersonic, or (in case of a blunt object), only a very small subsonic flow area remains between the object's nose and the shock wave it creates ahead of itself. (In the case of a sharp object, there is no air between the nose and the shock wave: the shock wave starts from the nose.) As the Mach number increases, so does the strength of the shock wave and the Mach cone becomes increasingly narrow. As the fluid flow crosses the shock wave, its speed is reduced and temperature, pressure, and density increase. The stronger the shock, the greater the changes. At high enough Mach numbers the temperature increases so much over the shock that ionization and dissociation of gas molecules behind the shock wave begin. Such flows are called hypersonic. It is clear that any object traveling at hypersonic velocities will likewise be exposed to the same extreme temperatures as the gas behind the nose shock wave, and hence choice of heat-resistant materials becomes important. ## High-speed flow in a channelAs a flow in a channel crosses The obvious result is that in order to accelerate a flow to supersonic, one needs a convergent-divergent nozzle, where the converging section accelerates the flow to An aircraft Machmeter or electronic flight information system (EFIS) can display Mach number derived from stagnation pressure (pitot tube) and static pressure. ## Calculating Mach NumberAssuming air to be an ideal gas, the formula to compute Mach number in a subsonic compressible flow is derived from Bernoulli's equation for where: - is Mach number
- is impact pressure and
- is static pressure.
- is the ratio of specific heats.
The formula to compute Mach number in a supersonic compressible flow is derived from the Rayleigh Supersonic Pitot equation: where: - is now impact pressure measured behind a normal shock
As can be seen, ## See also- Machmeter
- Speed of sound
- True airspeed
## References |
|||||||

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Mach_number". A list of authors is available in Wikipedia. |