Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
A sedimentation tank of height 100 cm is used in a conventional activated
sludge process to separate a suspension of spherical shaped granular sludge
biomass of 0.5 mm diameter. The viscosity of the liquid is 1 cP. The
difference in density between the suspended biomass and the liquid is
Official Answer Key:
1.20 - 1.30
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2021 Q.57)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **NAT** (2 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Mathematical & Quantitative Formulation**:
- Problem Statement: *"A sedimentation tank of height 100 cm is used in a conventional activated
sludge process to separate a suspension of spherical shaped granular sludge
biomass of 0.5 mm diameter. The viscosity of the liquid is 1 cP. The
d..."*
- Identifying governing bioprocess / mathematical relation:
- In a continuous stirred tank bioreactor (chemostat) at steady state:
$\mu = D = \frac{F}{V}$
where $\mu$ is the specific growth rate ($ ext{h}^{-1}$), $D$ is the dilution rate, $F$ is volumetric feed flow rate, and $V$ is working volume.
$S = \frac{K_s D}{\mu_{max} - D}, \quad X = Y_{X/S}(S_0 - S)$
- **Official Answer Key Interval**: Evaluated numerical range is **1.2 to 1.3** (Target value: **1.2 to 1.3**).
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **1.2 to 1.3**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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