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Such tables are useful since the equations used to calculate the properties after a normal shock are cumbersome. The tables below have been calculated using a heat capacity ratio, , equal to 1.4. The upstream Mach number, , begins at 1 and ends at 5.
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.
is the cross sectional area of the nozzle at the point of interest (m 2) is the cross sectional area of the nozzle at the sonic point, or the point where gas velocity is Mach 1 (m 2). Ideally this will occur at the nozzle throat.
For example, consider that at Mach 1.3 the angle of the Mach cone generated by the nose of the aircraft will be at an angle μ = arcsin(1/M) = 50.3° (where μ is the angle of the Mach cone, also known as Mach angle, and M is the Mach number). In this case the "perfect shape" is biased rearward; therefore, aircraft designed for lower wave drag ...
Figure 2 Common thermodynamic property ratios plotted as a function of Mach number using the Fanno flow model. As was stated earlier, the area and mass flow rate in the duct are held constant for Fanno flow. Additionally, the stagnation temperature remains constant. These relations are shown below with the * symbol representing the throat ...
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 .
where is the Prandtl–Meyer function, is the Mach number of the flow and is the ratio of the specific heat capacities. By convention, the constant of integration is selected such that ν ( 1 ) = 0. {\displaystyle \nu (1)=0.\,}