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GATE2016-49

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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 $P_2/ P_1$

  1. $(D_1/D_2)^2$
  2. $(D_2/D_1)^2$
  3. $(D_1/D_2)^5$
  4. $(D_2/D_1)^5$

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