Question

Power number is expressed as

• A. \( P/N^3 D_i^5 \rho \)
• B. \( P/N^2 D_i^2 \rho \)
• C. \( P/N^3 D_i^3 \rho \)
• D. \( P/N^2 D_i^3 \rho \)

Hint:

The power requirement increases with the cube of the speed and the fifth power of the impeller diameter!

Answer 1

The Correct Option is A

Concept: In bioprocess engineering, dimensionless numbers are used to characterize mixing and power requirements in stirred tanks.
• The Power Number (\(N_p\)) is analogous to the friction factor in pipe flow.
• It relates the power input to the impeller speed, diameter, and fluid density.

Step 1: Variables involved in Power Calculation.
The power consumed (\(P\)) by an impeller depends on the fluid density (\(\rho\)), the impeller rotational speed (\(N\)), and the impeller diameter (\(D_i\)). Through dimensional analysis, these variables are grouped to form the Power Number.

Step 2: Mathematical Expression.
The standard formula for the Power Number is: \[ N_p = \frac{P}{\rho N^3 D_i^5} \] This number remains constant in the fully turbulent regime for a specific impeller geometry. Final Answer: The expression for the Power Number is \( P/N^3 D_i^5 \rho \).