Why is it important to have a Mach number=1 at the throat of Convergence-Divergence nozzle? What if the Mach number at the throat is less than 1? Is a modification in the nozzle design required then?
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Related: https://physics.stackexchange.com/a/524215/59023 and https://physics.stackexchange.com/a/137842/59023 and https://physics.stackexchange.com/a/415810/59023 – honeste_vivere Feb 16 '20 at 21:06
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Supersonic flow expands when accelerating while subsonic flow contracts. This is due to the increasing influence of density changes: While subsonic flow shows litte change in density over speed, in supersonic flow the density changes become dominant.
If the speed at the throat is still subsonic, it will drop further as the nozzle expands again. Only when it has reached Mach 1 in the throat, the flow will be able to accelerate further once the cross section expands downstream.

Peter Kämpf
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Thank you so much for your response! if the mach number is not equal to 1 at the throat, does that imply that a change in the nozzle design is required? if yes, what can be the most important parameters to modify to end up with mach number=1 at the throat?How about in real nozzles in the industries, is the Mach number at the throat always=1? – Z090 Feb 17 '20 at 08:56