Question

For a specific bioreactor configuration, the power requirement for a Rushton-turbine impeller agitating an unaerated Newtonian fluid in the turbulent regime will be

• A. proportional to the stirring speed of the impeller
• B. proportional to the square of the stirring speed of the impeller
• C. proportional to the cube of the stirring speed of the impeller
• D. inversely proportional to the stirring speed of the impeller

Hint:

In the turbulent regime, the power requirement for a Rushton turbine is proportional to the cube of the stirring speed, which is important for understanding the energy demand in bioreactor operations.

Answer 1

The Correct Option is C

Step 1: Understand the power requirement in turbulent flow.

For an impeller agitating a fluid in a bioreactor, the power required to agitate the fluid in the turbulent regime is generally proportional to the cube of the stirring speed of the impeller. This is derived from the relationship for power consumption in the turbulent flow regime for a Rushton-turbine impeller.

Step 2: Relationship between power and stirring speed.

The power requirement \( P \) in the turbulent regime is given by:
\[ P \propto N^3, \]
where \( N \) is the stirring speed (or impeller speed). This means that the power requirement increases with the cube of the impeller speed.

Step 3: Conclusion.

The correct answer is \( \boxed{(C)} \), as the power requirement is proportional to the cube of the stirring speed of the impeller.