# Does the flow turning amount change as you get further away from an object?

Will the flow turning amount change as you get further away from an object? This answer explains why shockwaves will extend past the body that made them (good starting point). This question is asking if those shocks will change flow turning angle as they extend outward.

Like this picture. The flow starts by turning at the tip of the triangle via a shock. Then that flow turns the flow above, and then the flow above that flow turns. Then Etc. Etc. Etc.

Say the angle of the triangle was 15 degrees at the nose. At the nose of that triangle, the flow would turn 15 degrees. At the back of the triangle, it also would turn 15 degrees.

The question is, would that 15 degree turning angle change as the shock got further and further from the object? If so, why?

Doing my research and looking through other answers, at the bottom of this answer it says:

The further we are from the nose, the smaller the turn of the airflow is and therefore the smaller the inclination of the shock wave is

I believe this to be true, but I don't know why this is the case. (That's what this question is trying to accomplish.)

Edit : After thinking about it for a bit, I came up with a theory. When the object turns the flow, it would be a hard surface doing it. When the shockwave turns the flow, the air is the thing turning the flow. Air is compressible at those speeds (Compressible in the sense of easy to 'squeeze') Because of this, the air might have an effect to where there is less turning.

This has entirely to do with whether the object is a 2D or 3D object.

The photo above might be 2D object, a long wedge viewed edge-on. Or, a wedge between two plates of glass.

Or, the photo above might be a 3d object, a cone.

For the wedge, the flow turning continues to turn the flow, and the shock will be a straight line going off forever.

For a cone, there is a 3d relieving effect. You can't just think about the flow in the plane that we're observing, but also what happens 'around' the cone. As the distance from the axis of symmetry increases (i.e. the radius), the flow is allowed to occupy more volume. Because of this, as you move out, the flow is required to turn less, which allows the shock to be weaker -- and so the shock bends.

Understanding this, we can see that the above photo is a cone -- not a wedge.

Most images you'll see online and in textbooks stop at the end of the cone. It is important to look for images that continue past the end of the cone to make the best comparison.

• I see. So basically because it’s a cone as you move out the flow has to occupy more surface area of the cone so it doesn’t turn as much? Commented May 21 at 13:59
• That's about right. Each 'strip' of flow really represents an annulus -- or a donut / ring. The 'inner' rings have much less area than the 'outer' rings. For wedge flow, each strip is a strip and is identical to every other strip. Supersonic cone flow is very different from supersonic wedge flow because of this. In general, this idea is called '3D relieving' and it influences lots of aerodynamics. Imagine a NACA 0012 airfoil and another, but revolved into a 3D streamlined body. The Velocity peaks around the airfoil will be greater than the axisymmetric body. Commented May 21 at 16:14
• That's interesting. I had thought of that idea before, but I never really determined that the air would 'spread out'. Also interesting to see how that affects shockwaves and other phenomena. Commented May 21 at 16:18
• This is very easy to see in cylindrical coordinates. In normal (Cartesian) coordinates, the volume of a chunk of flow is dV=dxdydz. In cylindrical coordinates, the volume of a chunk of flow is dV=dxrdr*dTheta. The difference is that 'r' term. As 'r' increases, the volume in an otherwise similar 'chunk' of space gets bigger. Think of it like flow in a pipe, but now the pipe expands like a funnel. If water were flowing through the pipe (constant mass flow), it would slow down as the funnel gets bigger. Flow in a variable area pipe is called 'Quasi-1D' flow. Commented May 21 at 16:28