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Is there a way to compute the location of an compression shock inside de laval nozzles as a function of either the the pressure ratio or the area ratio in the divergent part of the nozzle?

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Is there a way to compute the location of an compression shock inside de laval nozzles as a function of either the the pressure ratio or the area ratio in the divergent part of the nozzle?

A de Laval nozzle is quite well documented online.

As for calculating the various thermodynamic parameters vs location within the nozzle, you can find the relevant relations in this answer.

Location of Compression shock wave in de laval nozzles

Why do you assume a shock wave forms within the nozzle? The flow can be supersonic but form no shock unless it is incident on something that is not supersonic (e.g., an obstacle or the ambient air outside the nozzle). A shock forming inside the nozzle is not a good thing as it causes mechanical stresses (due to flow separation from nozzle walls) and inefficiency, as explained in rocket engine articles online.

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