If your drive could support unlimited rpm for the same power you would expect the ratio between the two speeds be the same as the ratio in density.
Corrected for the higher friction at the higher speeds.
Shop vacs spin pretty fast (~20,000 RPM), and, there’s a remarkable amount of viscous dissipation. A couple of years ago I stuck a thermometer in my shop vac’s exhaust, as far up into the scroll housing as I could get it without bumping into the impeller. In a 65F basement, at full flow the exhaust air was about 78 degrees. Then I completely blocked the intake hose; in two and a half minutes, the temperature of the air in the scroll had risen to 150F. Note that this is not due to any kind of heating from the motor cooling air; that air has its own intake and exhaust, and the hot air coming off of the motor is never in contact with the scroll housing at all. That 150F temperature was purely due to the churn of the air inside the scroll housing by the impeller.
So glad I’m not the only one familiar with the series, it’s a real treasure. I’d say it’s about time for Technology Connections to do some videos on the vacuum cleaner now.