Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
The power required for agitation of non-aerated medium in fermentation is ________ kW.
Operating conditions are as follows:
Fermentor diameter = 3 m
Number of impellers = 1
Mixing speed = 300 rpm
Diameter of the Rushton turbine = 1 m
Viscosity of the broth = 0.001 Pa.s
Density of the broth = 1000 kg.m-3
Power number = 5
Official Answer Key:
625.0
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2016 Q.30)**
**1. Governing Concept & Definition**:
- **Topic**: Bioprocess Engineering & Impeller Power Consumption
- In the turbulent regime ($N_{Re} > 10^4$), the power consumption ($P$) of an un-aerated Rushton turbine is independent of Reynolds number:
$P = N_p \cdot \rho \cdot N^3 \cdot D_i^5$
where $N_p$ is the power number, $\rho$ is broth density, $N$ is agitation speed, and $D_i$ is impeller diameter.
**2. Detailed Step-by-Step Calculation**:
- Direct substitution of the given geometric and operating parameters:
$P = 625.0\text{ kW}$
**3. Final Answer**:
- **Calculated Value**: **625.0 kW**
- **Official GATE Accepted Range**: **625.0 to 625.0**
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