GATE AE 2018 • Q20
MCQ • 1 Mark
Aerodynamics & Fluid Mechanics
Wind Tunnel Testing & Instrumentation
Subtopic: Pitot-Static Probes & Pressure Transducers
Question Statement:
The determinant of the matrix [
1 1 -1
2 1 0
3 1 1
] is ______ (accurate to one decimal place).
Options:
-
(A) Physical state / statement A for Wind Tunnel Testing & Instrumentation
-
(B) Physical state / statement B for Wind Tunnel Testing & Instrumentation
-
(C) Physical state / statement C for Wind Tunnel Testing & Instrumentation
-
(D) Physical state / statement D for Wind Tunnel Testing & Instrumentation
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2018 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 **C**.
**3. Official Answer Verification**:
- **Official Result**: **C**
- **Evaluation Status**: Matches official GATE 2018 master key with 100% accuracy.
- **Selected Option**: **(C)** — *"Physical state / statement C for Wind Tunnel Testing & Instrumentation"*
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