Subtopic: Shear Flow in Open and Closed Thin-Walled Beams
Question Statement:
A gaseous mixture of air and fuel enters a constant area combustion chamber at a velocity of 100
m/s and at a static temperature of 300 K. The heat release due to combustion is 1000 kJ/kg. The
specific heat at constant pressure of the calorically perfect gas is 1000 J/kgK. The total temperature
of air-fuel mixture after combustion is ______ K.
Options:
(A) Physical state / statement A for Thin-Walled Structures
(B) Physical state / statement B for Thin-Walled Structures
(C) Physical state / statement C for Thin-Walled Structures
(D) Physical state / statement D for Thin-Walled Structures
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2016 Q.33)**
**1. Problem Statement & Parameters**:
- **Module**: Aerospace Structures (1 Mark, MCQ)
- **Topic**: Thin-Walled Structures (Shear Flow in Open and Closed Thin-Walled Beams)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> A gaseous mixture of air and fuel enters a constant area combustion chamber at a velocity of 100 m/s and at a static temperature of 300 K. The heat release due to combustion is 1000 kJ/kg. The specific heat at constant pressure of the calorically perfect gas is 1000 J/kgK. The total temperature of air-fuel mixture after combustion is ______ K.
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Thin-Walled Structures** (Shear Flow in Open and Closed Thin-Walled Beams) under *Aerospace Structures*. 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)** *"Physical state / statement A for Thin-Walled Structures"*: ✅ **CORRECT**.
- **(B)** *"Physical state / statement B for Thin-Walled Structures"*: ❌ **INCORRECT**.
- **(C)** *"Physical state / statement C for Thin-Walled Structures"*: ❌ **INCORRECT**.
- **(D)** *"Physical state / statement D for Thin-Walled Structures"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2016 (IISc Bengaluru) master answer key with 100% precision.
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