In the design of an aerated bioreactor, which dimensionless number is used to determine mixer power?

• A. Aeration Number
• B. Reynolds Number
• C. Power Number
• D. Friction Factor

Answer: (A)

The key idea is that mixer power is predicted using a dimensionless hydraulic power number. This number encapsulates how much power the impeller draws for a given geometry and flow regime, independent of scale. The relationship is P = Np × ρ × N^3 × D^5, where P is the power, ρ is the liquid density, N is the rotation speed, D is the impeller diameter, and Np is the Power Number. Once you know Np for your specific impeller at the operating Reynolds number, you can calculate the required motor power for a desired speed and impeller size. The Reynolds number tells you whether the flow is laminar or turbulent and helps select the appropriate Np curve, but it does not alone give the power. Friction factor applies to pressure losses in piping, not to the impeller power in a mixer, and Aeration Number isn’t a standard parameter for predicting mixer power. In aerated bioreactors, gas hold-up can affect the effective flow and viscosity, but the fundamental tool for sizing power remains the Power Number provided for the chosen impeller geometry and operating conditions.