GATE 2024 BT – Question 56

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

Ethanol is produced in a 10,000 L stirred bioreactor using an impeller of diameter 1 m. The density and viscosity of fermentation broth are 1000 kg m$^{-3}$ and 1 cp, respectively. The data relating the Power number and Impeller Reynolds number is given below:

Reynolds number	1-5	5-500	> 10^5
Power number	70	10	5

Using the above data, the power required for the stirrer to operate at 300 rpm is ________ kW (Answer in integer).

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Correct answer: 625

Explanation

$N = 5$ rps, so $N_{Re} = \frac{1000 \times 5 \times 1^2}{0.001} = 5\times10^6 > 10^5$ and $N_P = 5$. $P = N_P\rho N^3D^5 = 5 \times 1000 \times 125 \times 1 = 625{,}000$ W = 625 kW.