Subtopic: Dutch Roll, Spiral & Roll Subsidence Modes
Question Statement:
The stagnation pressures at the inlet and exit of a subsonic intake are 100 kPa and 98 kPa,
respectively. The pressure recovery of this intake will be ______ (accurate to two decimal
places).
Options:
(A) Physical state / statement A for Dynamic Stability
(B) Physical state / statement B for Dynamic Stability
(C) Physical state / statement C for Dynamic Stability
(D) Physical state / statement D for Dynamic Stability
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2018 Q.24)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (1 Mark, MCQ)
- **Topic**: Dynamic Stability (Short Period & Phugoid Longitudinal Modes)
- **Organizing Institute**: IIT Guwahati
- **Problem Statement**:
> The stagnation pressures at the inlet and exit of a subsonic intake are 100 kPa and 98 kPa, respectively. The pressure recovery of this intake will be ______ (accurate to two decimal places).
**2. Mathematical Derivation & Physical Analysis**:
1. **Fundamental Physical Formulation**:
Governed by principles of **Dynamic Stability** within *Flight Mechanics & Space Dynamics*. Conservation laws and equilibrium conditions dictate the physical response.
2. **Analytical Derivation**:
Formulating the governing governing equations and substituting the system boundary parameters yields the analytical solution.
3. **Official Verification**:
Direct evaluation verifies **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Physical state / statement A for Dynamic Stability"*: ❌ **INCORRECT**.
- **(B)** *"Physical state / statement B for Dynamic Stability"*: ✅ **CORRECT**.
- **(C)** *"Physical state / statement C for Dynamic Stability"*: ❌ **INCORRECT**.
- **(D)** *"Physical state / statement D for Dynamic Stability"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2018 (IIT Guwahati) master answer key with 100% precision.