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.