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GATE 2024 BT – Question 61

Fundamentals of Biological Engineering · Bioreaction Engineering: Batch, fed-batch and continuous processes, microbial and enzyme reactors, optimization and scale up · 2 marks · Numerical answer

Consider scale-up of fungal fermentation from a 20 L model-type to 20,000 L prototype stirred tank reactor. The model-type and prototype have the same aspect ratio during scale-up. The impeller speed in the model-type is 500 rpm and the scale-up criterion is constant shear.

The impeller speed in the prototype reactor will be ________ rpm (Answer in integer).

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Correct answer: 50

Explanation

Constant shear means a constant impeller tip speed, $ND$ = constant. With the same aspect ratio the diameter scales as the cube root of the volume, $\frac{D_2}{D_1} = 1000^{1/3} = 10$, so $N_2 = \frac{500}{10} = 50$ rpm.