Question

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

Hint:

In mixing problems, a Reynolds number above 10,000 indicates fully turbulent flow.

Answer 1

Correct Answer: 20000

The Reynolds number for an impeller is given by:
\[ Re = \frac{\rho N D^{2}}{\mu} \]
Given data:
\[ \rho = 1000\; \text{kg m}^{-3},\quad N = 2\; \text{s}^{-1},\quad D = 0.1\; \text{m},\quad \mu = 10^{-3}\; \text{kg m}^{-1}\text{s}^{-1} \]
Substitute values:
\[ Re = \frac{1000 \times 2 \times (0.1)^2}{10^{-3}} \]
\[ Re = \frac{1000 \times 2 \times 0.01}{10^{-3}} \]
\[ Re = \frac{20}{10^{-3}} = 20\,000 \]
Thus, the impeller Reynolds number is:
\[ \boxed{20000} \]