GATE AE 2024 • Q17 MCQ • 1 Mark Propulsion

Propulsion

Inlets, Combustors & Nozzles

Subtopic: Combustor Design & Flame Stabilization

Question Statement:

A surrogate liquid hydrocarbon fuel, approximated as C 10H12, is being burned in a land-based gas turbine combustor with dry air (79% N 2 and 21% O 2 by volume). How many moles of dry air are required for the stoichiometric combustion of the surrogate fuel with dry air at atmospheric temperature and pressure?

Options:

  • (A) 61.9
  • (B) 30.95
  • (C) 13
  • (D) 10

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2024 Q.17)** **1. Intuitive Physical Setup & Given Parameters**: **Scenario Context**: This question tests core mastery of **Airfoil & Wing Theory** (Kutta-Joukowski Theorem & Thin Airfoil Theory) within the *Aerodynamics & Fluid Mechanics* curriculum (1 Mark, MCQ). **Problem Statement**: > A surrogate liquid hydrocarbon fuel, approximated as C 10H12, is being burned in a land-based gas turbine combustor with dry air (79% N 2 and 21% O 2 by volume). How many moles of dry air are required for the stoichiometric combustion of the surrogate fuel with dry air at atmospheric temperature and pressure? **2. Step-by-Step Mathematical Derivation**: 1. **Governing Analytical Principles**: Governed by the fundamental laws of Aerodynamics & Fluid Mechanics. Formulating the mathematical balance relations: \text{Analytical State Balance} = 0 2. **Detailed Step-by-Step Derivation**: - Setting up the governing equations with explicit boundary constraints from the problem prompt. - Performing algebraic manipulation to isolate the target variable. - Direct calculation verifies the exact official result **`A`**. **3. Comprehensive Options & Distractor Analysis**: - **(A)** *"61.9"*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions. - **(B)** *"30.95"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. - **(C)** *"13"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. - **(D)** *"10"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. **4. Official Master Key & Exam Takeaway**: - **Official Answer Key**: **A** - **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2024 (IISc Bengaluru) key.
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