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Is there any equation for minimum area ratio (Throat area (At)/ Combustion Chamber area (Ac) ) required for choked flow in convergent nozzle (just like equations for minimum Pressure ratio and Temperature ratios)?

While searching online for minimum Area ratio required, most of them are related to CD nozzle. But in my case I'm looking for Convergent nozzle only so that I can get an estimate how wide combustion chamber should be to the exhaust area.

I tried to derive equation from mass flow continuity equation but it is dependent on flow velocity inside combustion chamber which is generally assumed to be near zero. (and I got stuck here.)

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  • $\begingroup$ Mass flow and velocity should help... $\endgroup$
    – Solar Mike
    Commented Apr 5, 2019 at 4:56

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Of course there is, you can find it on the NASA webpage:

https://www.grc.nasa.gov/www/k-12/airplane/astar.html

You can demonstrate the equation with mass flow conservation equation (continuity), ideal gas law and isentropic relations.

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  • $\begingroup$ Thanks for reply but the link you provided , is for CD nozzle. There area ratio is throat area to divergent exhaust area. But I'm looking for just convergent nozzle. Here I need area ratios of combustion chamber and convergent exhaust area. So, basically my question is about how much convergent nozzle needs to be converged just to have choked flow for given pressure and temperature ratios. $\endgroup$
    – SRD
    Commented Apr 15, 2019 at 0:14
  • $\begingroup$ You can use the same formula for the convergent zone by using the inlet Mach. The ration will then be A_inlet/A_throat. $\endgroup$
    – user20096
    Commented Apr 15, 2019 at 9:29
  • $\begingroup$ @SRD If your nozzle is purely convergent with no divergent section, why do you think it has a location that can be identified as the "throat"? $\endgroup$
    – user28774
    Commented May 4, 2021 at 15:54
  • $\begingroup$ Because the shock wave forms at a velocity, not some arbitrary human description of geometry. Everything that happens after the shockwave is irrelevant to its formation (roughly) $\endgroup$
    – Greg Locock
    Commented Dec 20, 2023 at 4:20

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