Section 4: Bioprocess Engineering and Process Biotechnology
Bioreactor types, scale-up
Subtopic: Fundamentals of Bioreactor types, scale-up
Question Statement:
For a liquid flowing in a circular cross section pipe, the transition from laminar to
turbulent flow will NOT depend on which of the following factor(s)?
Options:
(A) The diameter of the pipe
(B) The length of the pipe
(C) The linear velocity of the liquid
(D) The viscosity of the liquid
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2026 Q.47)**
**1. Governing Concept**:
- **Topic**: Fluid Mechanics & Pipe Flow Regime Transitions
- In fluid flow through a closed circular pipe of internal diameter $D$, the dimensionless Reynolds number is:
$Re = \frac{\rho v D}{\mu}$
where $\rho$ is fluid density, $v$ is mean cross-sectional flow velocity, and $\mu$ is dynamic viscosity.
- Flow regimes for internal circular pipe flow:
- **Laminar Flow**: $Re < 2100$ (viscous forces dominate).
- **Transition Zone**: $2100 \le Re \le 4000$.
- **Turbulent Flow**: $Re > 4000$ (inertial forces dominate).
- The critical transition Reynolds number is widely taken as $Re_{\text{crit}} \approx 2100$.
**2. Option Analysis**:
- **Option (A) is INCORRECT**: Re = 500 is deeply in the laminar flow regime.
- **Option (B) is CORRECT**: The onset of transition from laminar flow begins at a critical Reynolds number of approximately 2100.
- **Option (C) is INCORRECT**: Re = 10,000 represents fully developed turbulent flow.
- **Option (D) is INCORRECT**: Transition does not depend solely on velocity without diameter and viscosity.
**3. Final Answer**:
- **Correct Option**: **B**
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