A convergent-divergent nozzle is typically used for accelerating or decelerating airflow to or from supersonic speeds. The typical configuration for such a nozzle is the de Laval nozzle that is depicted below. With red colour is denoted the place (throat of the nozzle) that according to the theory & experiments the sonic velocity is only possible to occur.

I do not understand why this cannot happen upstream of the throat as denoted with blue. Could anyone shed some light on the physical understanding of this please? delaval nozzle

I am mainly concerned about why this scenario is not possible:

A subsonic airflow enters the nozzle at point (a.) and then due to the reduction of the area of the nozzle it accelerates and (supposing that this acceleration is enough) reaches a sonic speed at point (b.). I can understand that after reaching the sonic speed the fluid would have to decelerate again back to subsonic speed at point (c.) (because in order to keep accelerating the nozzle would have to be diverging), but this does not forbid the sonic speed to be reached at the previous point. This is where I get confused because if I follow the same reasoning the flow would be accelerated again and then decelerated back and forth which seems a weird outcome of my thought process.

theoritical sketch of sonic condition reached upstream from the throat

Thank you for the help!

  • $\begingroup$ It is not clear what about your question. Is it 1D, 2D or 3D flow, stationary or time dependent flow, ideal or viscous flow? $\endgroup$ Commented Jan 2, 2022 at 5:32

1 Answer 1


Using FEM code we can compute transition to supersonic flow in a nozzle to illustrate how the Max number distributed in a region in a case of viscous gas - see Figure 1. In this example the inlet/outlet pressure ratio is about 5.85. Figure 1
The Max number distribution along flow axis (left) and along line $r=0.3$ (right) for different time shown in Figure 2 Figure 2

As it shown in Figure 2 there are regions with $M>1$ and $M<1$ in a divergent part of nozzle.

  • $\begingroup$ I have seen pictures of the flow inside a CD nozzle, I am asking about the convergent part and I am mainly asking why this is happening $\endgroup$
    – urovorros
    Commented Feb 23, 2022 at 0:21
  • $\begingroup$ In a case of 3D non stationary viscous flow there is possible shock waves in convergent part as well. But it looks like you are asking about 1D stationary flow of ideal gas. Is it correct? $\endgroup$ Commented Feb 23, 2022 at 2:18
  • $\begingroup$ Indeed, I am asking about the quasi-1D case of a nozzle $\endgroup$
    – urovorros
    Commented Mar 7, 2022 at 18:11
  • $\begingroup$ @urovorros 1-D ideal gas flow model is very far from the real flow. So, probably your question is theoretical one. Can you clarifier you question since in the picture you used there is shown 2-D flow? $\endgroup$ Commented Mar 8, 2022 at 3:02

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