GATE2016-49

Question

A bioreactor is scaled up based on equal impeller tip speed. Consider the following parameters for small and large bioreactors: $$\begin{array}{|l|l|l|l|} \hline  \textbf{Parameters} & \textbf{Small bioreactor} & \textbf{Large bioreactor} \\ \hline \text{Impeller speed} & N_1 & N_2 \\ \hline \text{Diameter of impeller} & D_1 & D_2 \\ \hline \text{Power consumption} & P_1 & P_2 \\ \hline \end{array}$$ Assuming geometrical similarity and the bioreactors are operated in turbulent regime, what will be $P_2/ P_1$

• A. $(D_1/D_2)^2$
• B. $(D_2/D_1)^2$
• C. $(D_1/D_2)^5$
• D. $(D_2/D_1)^5$