For a specific bioreactor configuration, the power requirement for a
Rushton-turbine impeller agitating an unaerated Newtonian fluid in
the turbulent regime will be
Options:
(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 of the stirring speed of the impeller
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2025 Q.44)**
**1. Governing Concept & Domain**:
This question evaluates **Bioprocess Engineering** under *Section 4: Bioprocess Engineering & Process Biotechnology* (2 Marks, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Bioprocess Engineering.
- Applying governing bioprocess and biochemical equations:
$v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$
- Deductive verification establishes option **(C)** as the correct solution.
**3. Final Answer**:
Correct Option is **(C)**.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.