A fermentation broth of density 1000 kg m-3 and viscosity 10-3 kg m-1 s-1 is mixedin a 100 L fermenter using a 0.1 m diameter impeller, rotating at a speed of 2 s-1.The impeller Reynolds number is ___________
Question
A fermentation broth of density 1000 kg m-3 and viscosity 10-3 kg m-1 s-1 is mixedin a 100 L fermenter using a 0.1 m diameter impeller, rotating at a speed of 2 s-1.The impeller Reynolds number is ___________
Solution
The Reynolds number (Re) is a dimensionless quantity that is used to predict flow patterns in different fluid flow situations. It is defined as the ratio of inertial forces to viscous forces and can be calculated using the following formula:
Re = (ρ * D * N) / μ
where: ρ = density of the fluid (kg/m^3) D = diameter of the impeller (m) N = speed of rotation (s^-1) μ = dynamic viscosity of the fluid (kg/m^-1 s^-1)
Substituting the given values into the formula:
Re = (1000 kg/m^3 * 0.1 m * 2 s^-1) / 10^-3 kg/m^-1 s^-1
Re = 200,000
Therefore, the impeller Reynolds number is 200,000.
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