Answer to Question #126105 in Classical Mechanics for Mirza Adnan Baig

Question

A fermentation broth is required to be mixed turbulently using an impeller. The density & viscosity of broth is found to be 850 kg/m³ and 22 Pas. What must be the minimum diameter of the impeller to achieve Reynolds number of 5600, if impeller is required to rotate at 100 revolution per minute?

Answer 1

The stirrer speed is

$$\omega=\frac{100}{60}=1.67\text{ s}^{-1}.$$

The expression for Reynolds number:

$$R=\frac{\rho\omega D^2}{\mu},$$

the diameter is

$$D=\sqrt{\frac{\mu R}{\rho\omega}}=\sqrt{\frac{22 \cdot5600}{850\cdot1.67}}=9.3\text{ m}.$$