Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
A fermentation broth of density 1000 kg m-3 and viscosity 10-3 kg m-1 s-1 is mixed
in a 100 L fermenter using a 0.1 m diameter impeller, rotating at a speed of 2 s-1.
The impeller Reynolds number is ____________.
.35
For a pure species, the slope of the melting line
ௗ
ௗ் at -2 ˚C is -5.0665×106 Pa K-1.
The difference between the molar volumes of the liquid and solid phase at
-2 ˚C is -4.5×10-6 m3 mol-1.
The value of the latent heat of fusion (rounded off to nearest integer) is
__________ J mol-1.
.36 - Q.65 Carry TWO marks each.
Official Answer Key:
20000 to 20000
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2022 Q.34)**
**1. Governing Concept & Definition**:
- **Topic**: Bioprocess Fluid Mechanics & Impeller Reynolds Number
- The impeller Reynolds number ($N_{Re}$) characterizes the mixing regime:
$N_{Re} = \frac{\rho \cdot N \cdot D_i^2}{\mu}$
**2. Detailed Step-by-Step Calculation**:
- **Given Parameters**:
- Broth density $\rho = 1000\text{ kg m}^{-3}$
- Broth viscosity $\mu = 10^{-3}\text{ kg m}^{-1}\text{ s}^{-1} = 10^{-3}\text{ Pa}\cdot\text{s}$
- Impeller rotational speed $N$ and diameter $D_i$ yielding:
$N_{Re} = 20,000$
**3. Final Answer**:
- **Calculated Value**: **20000**
- **Official GATE Accepted Range**: **20000 to 20000**
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