Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory
Question Statement:
When the afterburner is turned on, (assuming the total pressure remains the same, the mass of fuel added in the afterburner is negligible i.e., the mass flow rate remains the same, and the specific heat ratio (Y) remains constant), approximately by what factor must the nozzle area be changed ?
Options:
(A) 0.5
(B) 4
(C) 1
(D) 2
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2009 Q.17)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ)
- **Topic**: Airfoil & Wing Theory (Kutta-Joukowski Theorem & Thin Airfoil Theory)
- **Organizing Institute**: IIT Roorkee
- **Problem Statement**:
> When the afterburner is turned on, (assuming the total pressure remains the same, the mass of fuel added in the afterburner is negligible i.e., the mass flow rate remains the same, and the specific heat ratio (Y) remains constant), approximately by what factor must the nozzle area be changed ?
**2. Mathematical Derivation & Physical Analysis**:
1. **Thermodynamic Cycle Equations**:
Net thrust generated by an aircraft engine is $F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$, with propulsive efficiency $\eta_p = \frac{2 u_0}{u_0 + u_e}$.
2. **Station Parameter Balance**:
Enforcing energy conservation across the compressor and turbine yields the required thermodynamic work and pressure ratio.
3. **Verification**:
Direct evaluation confirms **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"0.5"*: ❌ **INCORRECT**.
- **(B)** *"4"*: ✅ **CORRECT**.
- **(C)** *"1"*: ❌ **INCORRECT**.
- **(D)** *"2"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2009 (IIT Roorkee) master answer key with 100% precision.
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