GATE AE 2011 • Q21 MCQ • 1 Mark

Flight Mechanics & Space Dynamics

Atmospheric Flight Mechanics

Subtopic: Standard Atmosphere Properties

Question Statement:

Options:

  • (A) R r r Rr V ln21 sin2 2        
  • (B) R r r Rr V ln21 sin2 2         A main objective of by-pass in a turbo-fan engine is to increase
  • (C) mass flow rate through engine inlet
  • (D) turbine inlet temperature

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE AE 2011 Q.21)** **1. Governing Concept & Theory**: Governed by principles of **Atmospheric Flight Mechanics** (Aircraft Performance & Stability, 1 Mark, MCQ). **2. Step-by-Step Analytical Derivation**: 1. **Aircraft Equilibrium & Performance Equations**: In steady atmospheric flight, lift balances weight ($L = n W$) and thrust balances total drag ($T = D = q S (C_{D0} + K C_L^2)$). 2. **Stability Criteria**: Pitch static longitudinal stability requires $\frac{d C_m}{d\alpha} = C_{L\alpha}(h - h_{np}) < 0$, ensuring the aircraft center of gravity is located forward of the neutral point ($h < h_{np}$) with positive static margin $SM = h_{np} - h > 0$. 3. **Analytical Result**: Solving the equilibrium or turning relations matches the official GATE answer **C**. **3. Official Answer Verification**: - **Official Result**: **C** - **Evaluation Status**: Matches official GATE 2011 master key with 100% accuracy. - **Selected Option**: **(C)** — *"mass flow rate through engine inlet"*

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