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Turbocharger turbine A/R Radius value

Turbocharger turbine A/R Radius value

Turbocharger turbine A/R Radius value

(OP)
In terms of turbocharger turbine section, A/R is the ratio of Area at the begining of the volute to the Radius which is the radial distance from center shaft to the center of the aformentioned area.  For a given mass flow rate,  If A/R is large, shaft speed is lower but backpressure is less.  If A/R is small, then the opposite is true.  Here is my question.
Why does increasing R increase shaft speed with the wheel size and all other things constant?

Thanks

RE: Turbocharger turbine A/R Radius value

increasing R doesn't increase shaft speed it increases the torque the shaft is able to develop

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