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# MCQs on Physical Aspects of Supersonic Flow over Cones

For a given cone angle and freestream Mach number, how many oblique shock(s) is/are present?

a) 1

b) 2

c) 4

d) Infinity

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b

Explanation: For a conical flow placed in a freestream Mach number M∞ with a particular cone angle θc, there exists two oblique shock waves which is a result of one weak and one strong solution. It is similar to the case of wedge where using θ – β – M graph we obtain two shock waves.

Under which condition do we get the detached shock wave on a cone?

a) θc = θcmax

b) θc > θcmax

c) θc = 0

d) θc = infinty

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b

Explanation: For a given freestream Mach number M∞, there exists a maximum cone angle for which if we go beyond that value, the shock wave originating at the cone’s vertex gets detached. Thus, the condition for detached shock wave is θc > θcmax.

The shock wave present on the cone is weaker than the one on the wedge for a particular angle.

a) True

b) False

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a

Explanation: For a particular cone angle, the shock wave formed at the cone’s vertex is usually weaker in strength compared to the shock wave formation on a wedge. This phenomenon is due to the three – dimensional relieving effect.

What is the relation between maximum allowed cone angle and wedge angle for attached shock wave?

a) (θmax)wedge = (θmax)cone

b) (θmax)wedge > (θmax)cone

c) (θmax)wedge < (θmax)cone

d) (θmax)wedge ≈ (θmax)cone

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b

Explanation: Due to the three-dimensional relieving effect, for a particular freestream Mach number, the maximum cone angle allowed is larger than the maximum wedge angle before the shock wave becomes detached.

How are the streamlines for a conical flow behind a shock wave?

a) Parallel throughout

b) Curved at the beginning, parallel as surface tends to infinity

c) Curved till surface tends to infinity

d) Conical

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b

Explanation: For a conical flow at a given Mach number, the shock formation occurs at the vertex of the cone. The streamlines behind the shock wave are initially curved due to 3 – dimensional space unlike streamlines behind the shockwave on a wedge which is parallel. These streamlines eventually become parallel at the cone’s surface tends to infinity.

The flow is parallel behind the shock wave in a cone.

a) True

b) False

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b

Explanation: When the incoming flow passes through an oblique shock in a two – dimensional wedge, the streamline becomes parallel to the surface of the wedge. But, in case of a cone, the streamlines between the shock wave and the cone are not parallel.

Where does the flow remain supersonic in a conical surface?

a) Between the oblique shock and the sonic line

b) Between the oblique shock and the conical surface

c) Between the sonic line and the conical surface

d) Flow is not supersonic beyond the oblique shock

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a

Explanation: The incoming flow over a cone is mostly supersonic between the surface of the cone and the oblique shock wave. Except in some cases when the half cone angle is large, flow sometimes becomes subsonic and one of the rays originating the cone’s vertex acts at the sonic line. The flow between the sonic line and the oblique shock thus remains supersonic.

What happens to the shock wave when the cone angle is less than the maximum cone angle?

a) Oblique shock formation does not occur

b) Shock wave becomes detached

c) Shock wave is attached to the cone

d) There is formation of normal shock wave

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c

Explanation: For the oblique shock wave to be attached to the vertex of the cone, the half cone angle θc must be less than the maximum cone angle θcmax. As soon as θc exceeds θcmax, the oblique shock wave gets detached from the cone.