Q.59 A bioreactor is scaled up based on equal impeller tip speed.
Consider the following parameters for small and large bioreactors:
| Parameters | Small Bioreactor | Large Bioreactor |
|---|---|---|
| Impeller speed | N1 | N2 |
| Diameter of impeller | D1 | D2 |
| Power consumption | P1 | P2 |
Assuming geometrical similarity and the bioreactors are operated in turbulent regime,
what will be P2/P1?
(A) (D1/D2)2
(B) (D2/D1)2
(C) (D1/D2)5
(D) (D2/D1)5
Given
A bioreactor is scaled up based on equal impeller tip speed.
| Parameter | Small Bioreactor | Large Bioreactor |
|---|---|---|
| Impeller speed | N1 | N2 |
| Impeller diameter | D1 | D2 |
| Power consumption | P1 | P2 |
Assumptions
- Geometrical similarity
- Turbulent flow regime
Step-by-Step Solution
Step 1: Equal Impeller Tip Speed Condition
Impeller tip speed (v) is given by:
v = πND
For equal tip speed:
N1D1 = N2D2
Therefore:
N2/N1 = D1/D2
Step 2: Power Equation in Turbulent Regime
For geometrically similar bioreactors operating in turbulence:
P ∝ N3D5
Hence:
P2/P1 = (N2/N1)3 (D2/D1)5
Step 3: Substitute Tip Speed Relation
Substituting N2/N1 = D1/D2:
P2/P1 =(D1/D2)3 (D2/D1)5
Step 4: Simplification
P2/P1 = (D2/D1)2
Final Answer
P2/P1 = (D2/D1)2
✔ Correct Option: (B)
Explanation of Other Options
- Option (A): (D1/D2)2
Inverse of the correct relationship; implies power decreases on scale-up - Option (C): (D1/D2)5
Ignores equal tip speed constraint; assumes constant impeller speed - Option (D): (D2/D1)5
Valid only for constant speed scaling, not equal tip speed
Why This Question Is Important
- Frequently asked in bioreactor scale-up MCQs
- Tests dimensional analysis concepts
- Critical for industrial bioprocess design
- Prevents over- or under-powering during scale-up
Exam Tip
If impeller tip speed is constant, always replace
N using
ND = constant before applying the power law.
Conclusion
In bioreactor scale-up under equal impeller tip speed and turbulent conditions,
the power consumption ratio depends only on the square of the impeller diameter ratio.
Correct application of this principle ensures energy-efficient and reliable scale-up
in industrial biotechnology.
