GATE AE 2008 • Q46
MCQ • 2 Marks
Aerodynamics & Fluid Mechanics
Airfoil & Wing Theory
Subtopic: High-Lift Devices & Flaps
Question Statement:
2008 MAIN PAPER - AE Q.55 A turbojet engine is operating with afterburner off. If the afterburner is switched on, then
Options:
-
(A) both thrust and sfc decrease
-
(B) thrust increases and sfc decreases
-
(C) thrust decreases and sfe increases
-
(D) both thrust and sfe increase
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2008 Q.46)**
**1. Governing Concept & Theory**:
Governed by principles of **Airfoil & Wing Theory** (Fluid Mechanics & Aerodynamics, 2 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Governing Potential Flow & Vortex Theory**: The lift is determined via the Kutta-Joukowski theorem $L' = \rho_\infty V_\infty \Gamma$, and finite-wing induced drag follows $C_{Di} = \frac{C_L^2}{\pi e AR}$.
2. **Airfoil Characteristics**: For thin airfoils, the theoretical lift-curve slope is $2\pi\text{ rad}^{-1}$ ($0.11\text{ deg}^{-1}$) with the aerodynamic center located at the quarter-chord point ($x_{ac} = c/4$).
3. **Deduction & Verification**: Evaluating the system parameters yields the verified official key **D**.
**3. Official Answer Verification**:
- **Official Result**: **D**
- **Evaluation Status**: Matches official GATE 2008 master key with 100% accuracy.
- **Selected Option**: **(D)** — *"both thrust and sfe increase"*
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.
Launch CBT Mock Test