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A fermentation broth of density $1000 \; \text{kg m}^{-3}$ and viscosity $10^{-3} \; \text{kg m}^{-1} \text{s}^{-1}$ is mixed in a $100\;\text{L}$ fermenter using a $0.1 \; \text{m}$ diameter impeller, rotating at a speed of $2 \; \text{s}^{-1}.$ The impeller Reynolds number is _________.
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