I know that in case of wedge we have a 2D behavior which creates a discontinuity across the shock, but I am unable to understand why this discontinuity is not present in the case of a conical surface. I have a vague idea that the continuity equation ensures this as, due to increase in the flow area, the velocity must increase.

But still it would be great help if I could get a proper explanation, I couldn't find one in books and net.

I would also like to know which 2D constraints are actually relieved which causes the 3D relaxation effect.

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EDIT:- I think i need to reiterate the question, I wanted to ask why does the supersonic flow bend toward the surface in case of being obstructed by a cone unlike in case of wedge, and as per its reasoning i have also read that the flow is more free in case of cone, due to presence of 3 dimensions, commonly known as 3D relaxation, so it would be nice if someone could comment upon it too.

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  • $\begingroup$ Really vague and unclear question. Could you edit it to explain all the context? Without the comments it could even be asking about hammering a spike into wood/concrete. $\endgroup$
    – jhabbott
    Commented Apr 5, 2015 at 21:03
  • $\begingroup$ With your edit, what do you mean by "bend toward the surface"? Both the wedge and the cone are "bending" in a very similar way at the shock front. Are you asking why one is drawn as straight lines (wedge) and one has some curves (cone)? $\endgroup$
    – hazzey
    Commented Apr 6, 2015 at 14:00
  • $\begingroup$ yes exactly, thats what i want to know, why parallel in one case and not in other. $\endgroup$
    – Manish
    Commented Apr 6, 2015 at 16:27
  • $\begingroup$ I think the best way to get a "heuristic" understanding is to jump over to [Nasa] (grc.nasa.gov/WWW/k-12/airplane/shock.html). They have a nice simulator which solves the equations for you and does not only draw stream lines but also rays (which are the answer to your question). $\endgroup$
    – rul30
    Commented Apr 18, 2015 at 17:36

1 Answer 1


The answer to this question is complicated since the flow is fundamentally different.

When supersonic flow hits a wedge it is abruptly turned by one oblique shock. After this all streamlines are parallel since in this 2D-flow-scenario the geometry/flow-area does not change anymore.

When supersonic flow (think of a stream tube/cylinder) hits a cone a differential volume element of the stream tube will constantly increase in size while it follows the cone surface. This changes the pressure and is called relaxation. Due to this volume increase of the stream tube the cone flow has two features/regimes which the wedge flow cannot have:

  1. The stream lines after the shock are curved (bent) so that they align with the cone geometry.

  2. Certain flow-settings will result in a sonic-line within the flow downstream of the shock. This means that the supersonic flow after the oblique shock is decelerated until it is subsonic see figure below taken from Naca Report 1242.

    Naca Report 1242


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