# Calculate the mach number after an oblique shockwave

• JD88
In summary, when the angle of the shockwave exceeds the maximum allowable theta, the shockwave becomes detached and the downstream Mach number is equal to the upstream Mach number.
JD88
I am trying to calculate the mach number after an oblique shockwave. The freestream mach number is 2.0 and the angle theta is 25 deg. But on the Theta-Beta-Mach Diagram the line Theta=25deg does not intersect the Mach=2 line. So this means that the angle has exceeded the maximum allowable theta and the shockwave has come detached, right? If it were not detached I would just look up Beta off of the diagram and use it to calculate the normal mach number normal to the shockwave and go from there.

So how would I go about determining the mach number after the oblique shockwave when the angle has exceed the max and the wave is detached?

When an oblique shockwave is detached, the downstream Mach number will be the same as the upstream mach number. In this case, the downstream Mach number after the detached shockwave is 2.0.

## 1. What is a mach number and why is it important to calculate after an oblique shockwave?

A mach number is the ratio of an object's speed to the speed of sound in the surrounding medium. It is important to calculate after an oblique shockwave because it helps determine the level of compression and heating that occurs during the shockwave, which can have significant impacts on the object and its surroundings.

## 2. How is the mach number calculated after an oblique shockwave?

The mach number after an oblique shockwave can be calculated using the equation M2 = [(M1^2 * sin^2θ) + 2] / [(2 * M1^2 * sin^2θ) - (M1^2 - 1)], where M1 is the mach number before the shockwave and θ is the angle of the shockwave relative to the object.

## 3. What factors can affect the mach number after an oblique shockwave?

The mach number after an oblique shockwave can be affected by the angle of the shockwave relative to the object, the mach number before the shockwave, and the properties of the surrounding medium such as temperature and density.

## 4. Can the mach number after an oblique shockwave be greater than the mach number before the shockwave?

Yes, it is possible for the mach number after an oblique shockwave to be greater than the mach number before the shockwave. This occurs when the shockwave is at a shallow angle and the object is traveling at a high mach number, resulting in an increase in the mach number after the shockwave.

## 5. How is the mach number after an oblique shockwave used in real-world applications?

The mach number after an oblique shockwave is used in aerospace engineering to design and analyze the behavior of supersonic and hypersonic vehicles. It is also used in the study of high-speed aerodynamics and in understanding the effects of shockwaves on structures and materials.

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