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GATE2019: 55

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The dimensions and operating condition of a lab-scale fermentor are as follows:

Volume = $1\:L$

Diameter = $20$ cm

Agitator speed = $600$ rpm

Ratio of impeller diameter to fermentor diameter = $0.3$

This fermentor needs to be scaled up to $8,000\:L$ for a large scale industrial application. If the scale-up is based on constant impeller tip speed, the speed of the agitator in the larger reactor is ___________ rpm. Assume that the scale-up factor is the cube root of the ratio of fermentor volumes.
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