GATE 2022 BT – Question 34
A broth has density $1000\ \mathrm{kg/m^3}$ and viscosity $10^{-3}\ \mathrm{kg\ m^{-1}s^{-1}}$. A 100 L fermenter uses a 0.1 m impeller at $2\ \mathrm{s^{-1}}$. The impeller Reynolds number is ___________.
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Correct answer: 20000
Explanation
The **impeller Reynolds number** is
$$Re=\frac{\rho N D^2}{\mu},$$
where $N$ is the impeller speed in rev/s and $D$ the impeller diameter.
**Numbers.** $\rho=1000$ kg/m³, $N=2$ s⁻¹, $D=0.1$ m, $\mu=10^{-3}$ kg m⁻¹ s⁻¹:
$$Re=\frac{1000\times2\times(0.1)^2}{10^{-3}}=\frac{20}{10^{-3}}=\mathbf{20\,000}.$$
(This is above about 10 000, so the flow in the vessel is fully turbulent.)