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The first Mach line is at an angle = with respect to the flow direction, and the last Mach line is at an angle = with respect to final flow direction. Since the flow turns in small angles and the changes across each expansion wave are small, the whole process is isentropic. [ 1 ]
The Mach angle is acute, showing that the body exceeds Mach 1. The angle of the Mach wave (~59 degrees) indicates a velocity of about Mach 1.17. In fluid dynamics , a Mach wave , also known as a weak discontinuity , [ 1 ] [ 2 ] is a pressure wave traveling with the speed of sound caused by a slight change of pressure added to a compressible flow .
A sonic boom produced by an aircraft moving at M=2.92, calculated from the cone angle of 20 degrees. Observers hear nothing until the shock wave, on the edges of the cone, crosses their location. Mach cone angle NASA data showing N-wave signature. [1] Conical shockwave with its hyperbola-shaped ground contact zone in yellow
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. The maximum angle through which a sonic ( M = 1) flow can be turned around a convex corner is calculated for M = ∞ {\displaystyle \infty } .
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 ...
The interest in compressibility research emerged after the WWI, when the aircraft propeller tips started to reach M=0.8. Ludwig Prandtl had taught the transformation in his lectures about 1922, however the first rigorous proof was published in 1928 by Hermann Glauert. [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,
For a given Mach number, M 1, and corner angle, θ, the oblique shock angle, β, and the downstream Mach number, M 2, can be calculated. Unlike after a normal shock where M 2 must always be less than 1, in oblique shock M 2 can be supersonic (weak shock wave) or subsonic (strong shock wave).