# Super to Subcritical, and Super to Subsonic Flow

• Clausius2
In summary, The conversation discusses the possibility of obtaining subcritical flow downstream of an obstacle in an open channel without the presence of a hydraulic jump. It also explores the concept of a convergent-divergent nozzle decelerating a supersonic flow to a subsonic one without the use of a shock wave. The question is whether this is mathematically and physically possible.
Clausius2
Gold Member
My aim in this thread is to bring light to the physical foundations of the next event.

1) Assume there is a long open channel filled with water. Due to some difference of height between its extremes, there is an steady flow of water. Imagine there is an smooth obstacle of height $$z_o$$ (like a small and smooth hill) in the middle of the channel. Because of open channel flow theory we know that if the flow is subcritical upstream the obstacle and if the obstacle has enough peak height $$z_o$$ then it would be possible (not necessary) to have supercritical flow behind it.

Now assume there is supercritical flow upstream the obstacle (with supercritical flow I mean Froude number is larger than unity $$F_r>1$$ and the contrary for subcritical flow). My question is: would it be possible to obtain subcritical flow just downstream the obstacle without the presence of an hydraulic jump?

Those who don't know nothing about open channel flow could answer to this another similar question. Imagine a convergent-divergent nozzle in which inlet there is supersonic flow. Assuime the inlet flow is free of shock waves. Now the flow enters the nozzle and because of the reduction of section the flow is being slowed down progressively until it reaches the critical section (minimum area) where the flow is sonic. Once it enters the divergent section, the flow could be deccelerated to subsonic flow due to the dynamic diffusing effect. So that we will have a global transition of supersonic to subsonic flow without the presence of a shock wave. Is it possible?.

I have some more questions about physics of open channel flow, but I'll wait for some brave guy who wants to give me some opinion of these.

Regards,

Javier.

I'm not an expert or even somewhat knowledgeable in these matters, but...I thought that if you had a convergent-divergent nozzle and flow reached sonic at the throat, then it would accelerate back up where it diverges (nozzles diverge for sonic,supersonic, diffusers converge, opposite of subsonic)

minger said:
I'm not an expert or even somewhat knowledgeable in these matters, but...I thought that if you had a convergent-divergent nozzle and flow reached sonic at the throat, then it would accelerate back up where it diverges (nozzles diverge for sonic,supersonic, diffusers converge, opposite of subsonic)

This event could be possible too. The fact is when there are critical conditions just at the throat it can be a sudden transition to anyone of the regimes.

My actual question is if a convergent-divergent nozzle could decelerate a supersonic stream to a subsonic one without any shock wave, merely by the same principle of how it accelerates a subsonic stream to a supersonic one. Would it be mathematically and physically possible such a smooth transition?

## 1. What is the difference between supercritical and subcritical flow?

Supercritical flow is when the flow velocity is greater than the critical velocity, which is the minimum velocity required for the flow to remain continuous. Subcritical flow is when the flow velocity is lower than the critical velocity. In supercritical flow, the flow behavior is dominated by compressibility effects, while in subcritical flow, the flow is incompressible.

## 2. How does supercritical flow transition to subcritical flow?

Supercritical flow transitions to subcritical flow when the flow velocity decreases below the critical velocity. This can happen when there is a sudden increase in the flow area or when the flow encounters an obstacle. As the flow velocity decreases, the compressibility effects become less significant and the flow behavior becomes more similar to that of incompressible flow.

## 3. What is the significance of critical velocity in flow?

Critical velocity is an important characteristic of flow as it marks the transition between supercritical and subcritical flow. It is also a key parameter in determining the type of flow behavior and the presence of shock waves in the flow.

## 4. How is supercritical flow different from subsonic flow?

Supercritical flow refers to flow where the flow velocity is greater than the critical velocity, while subsonic flow refers to flow where the flow velocity is lower than the speed of sound. While supercritical flow can occur at both subsonic and supersonic velocities, subsonic flow can only occur at subsonic velocities.

## 5. What are some applications of supercritical and subcritical flow?

Supercritical and subcritical flow have various applications in different fields such as aerospace engineering, hydraulics, and aerodynamics. Some examples include the design of supersonic aircraft, the study of shock waves in fluids, and the design of hydraulic structures such as dams and spillways.

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