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A batch bioreactor is to be scaled up from $\text{10 to 10,000}$ liters. The diameter of the large bioreactor is $10$ times that of the small bioreactor. The agitator speed in the small bioreactor is $\text{450 rpm}$. Determine the agitator speed (rpm) of the large bioreactor with same impeller tip speed as that of the small bioreactor. ____________
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