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# Turbocharger choke line?

I was wondering, what would happen, how would I estimate the power increase if we land outside the choke line on the compressor map?

So for example at maximum turbo shaft RPM our airflow is 10kg/min at 2 atm absolute pressure (if we go higher on boost then that same turbo shaft RPM will obviously get us less volume of air) but for our engine we would need 12kg/min of airflow at 2 atm absolute pressure, the only way for us to get that maximum 10kg/min is to drop the pressure ratio by ~20%, meaning we have roughly 1.6 atm absolute pressure at 10kg/min, BUT, our compressor map shows that 1.6 atm is below the choke point. So I was wondering what would happen in this case, how would I estimate power output?

I know that typically a rough rule of thumb used is take the absolute pressure and multiply by current torque at a certain engine RPM (but that works if we are assuming we have an intercooler and whatnot in place) but I just don't know exactly what to do in this case, where we can not get back inside the compressor map as the engine is too big and requires too much volume vs not enough pressure (and yes, I know that we shouldn't choose such turbochargers that choke up the engine, but this question out of pure curiosity, WHAT IF).

And yes, I do have somewhat of an idea why the choke line exists (though it's nowhere near as easy to grasp as the surge line). The lower the pressure, the higher the air flow velocity, add into the equation the RPM of the turbo shaft and we get

-more airflow as the RPM increases, once the air velocity reaches the speed of sound it can not speed up anymore and causes a limit to be placed upon our turbocharger.

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