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Mach Number

The Mach number is used in fluid mechanics and is especially useful in studies involving supersonic aerodynamics. It is named after Ernst Mach (1838-1916), the Austrian physicist and philosopher who pioneered the study of supersonic projectiles. The Mach number is the ratio of the velocity of a fluid to the velocity of sound in that same fluid. In the case of a body moving through a fluid, the Mach number is the velocity of the body relative to the fluid divided by the velocity of sound in the fluid. The velocity of sound varies with temperature and also varies from one fluid to another. At sea level, for example, the velocity of sound in air at 59°F (15°C) is about 760 MPH (1,223 km/h). At an elevation of 40,000 ft (12,200 m), however, the temperature is about -70°F (-57°C), and the velocity of sound in air is only 660 MPH (1,062 km/h). Thus, an airplane flying at 760 MPH at sea level would have a Mach number of 1.0, while at an elevation of 40,000 ft it would have a higher Mach number of almost 1.2.

One of the principal uses of the Mach number is to define the behavior of fluid flows. For example, pressure disturbances in a fluid, as might be caused by an object such as an airplane wing moving through air, radiate at the speed of sound within the fluid. When the Mach number of an object is less than 1, the object is moving slower than the speed of sound. In that case the pressure disturbances can move ahead of the object.

This produces gradual pressure and density differences around the object which result in a certain kind of fluid flow behavior. However, when the Mach number is greater than 1, the object is moving faster than the speed of sound. When this happens the pressure disturbances cannot move out of the way fast enough, and very abrupt density and pressure changes, known as shock waves, appear. This results in a very different fluid flow behavior. These shock waves are the cause of the "sonic boom" sometimes heard when an airplane exceeds the speed of sound.

Figure 1. Illustration by Hans & Cassidy. Courtesy of Gale Group.

Figure 2. Illustration by Hans & Cassidy. Courtesy of Gale Group.

Scientists now categorize four kinds of fluid flow behavior based on the Mach number. Flows with Mach numbers less than 0.8 are called subsonic, 0.8 to 1.2 are called transonic, 1.2 to 5.0 are called supersonic, and above 5.0 are called hypersonic. For each type of flow there is a different fluid behavior. Aircraft designers have to take these differences into account when designing planes that take off and climb to altitude at speeds in the subsonic region, then pass through the transonic region, and cruise at speeds in the supersonic region.

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