(A) only along a streamline in inviscid flow, and between any two points in potential flow.
(B) between any two points in both inviscid flow and potential flow.
(C) between any two points in inviscid flow, and only along a streamline in potential flow.
(D) only along a streamline in both inviscid flow and potential flow.
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.20)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ)
- **Topic**: Wind Tunnel Testing & Instrumentation (Pitot-Static Probes & Pressure Transducers)
- **Organizing Institute**: IIT Delhi
- **Problem Statement**:
> Bernoulli's equation is valid under steady state
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Wind Tunnel Testing & Instrumentation** (Pitot-Static Probes & Pressure Transducers) under *Aerodynamics & Fluid Mechanics*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"only along a streamline in inviscid flow, and between any two points in potential flow."*: ✅ **CORRECT**.
- **(B)** *"between any two points in both inviscid flow and potential flow."*: ❌ **INCORRECT**.
- **(C)** *"between any two points in inviscid flow, and only along a streamline in potential flow."*: ❌ **INCORRECT**.
- **(D)** *"only along a streamline in both inviscid flow and potential flow.
2012 AEROSPACE ENGINEERING - AE
AE 4/12"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.