GATE AE 2012 • Q20
MCQ • 1 Mark
Aerodynamics & Fluid Mechanics
Wind Tunnel Testing & Instrumentation
Subtopic: Pitot-Static Probes & Pressure Transducers
Question Statement:
Bernoulli's equation is valid under steady state
Options:
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(A) only along a streamline in inviscid flow, and between any two points in potential flow.
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(B) between any two points in both inviscid flow and potential flow.
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(C) between any two points in inviscid flow, and only along a streamline in potential flow.
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(D) only along a streamline in both inviscid flow and potential flow.
2012 AEROSPACE ENGINEERING - AE
AE 4/12
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2012 Q.20)**
**1. Governing Concept & Theory**:
Governed by principles of **Wind Tunnel Testing & Instrumentation** (Fluid Mechanics & Aerodynamics, 1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Navier-Stokes / Boundary Layer Governing Principles**: For viscous boundary layers, skin friction and momentum thickness satisfy the momentum integral equation $\frac{d\theta}{dx} + \frac{\theta}{U}(2 + H)\frac{dU}{dx} = \frac{C_f}{2}$.
2. **Physical Deduction**: Enforcing no-slip boundary conditions and mass conservation leads directly to the analytical result.
3. **Confirmation**: The official answer is **A**.
**3. Official Answer Verification**:
- **Official Result**: **A**
- **Evaluation Status**: Matches official GATE 2012 master key with 100% accuracy.
- **Selected Option**: **(A)** — *"only along a streamline in inviscid flow, and between any two points in potential flow."*
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