GATE AE 2022 • Q19 MCQ • 1 Mark

Aerodynamics & Fluid Mechanics

Compressible Flow & Shocks

Subtopic: 1D Isentropic Flow & Area-Mach Relations

Question Statement:

Regarding the horizontal tail of a conventional airplane, which one of the following statements is true?

Options:

  • (A) It contributes to C௠ഀ < 0
  • (B) It makes C௠ഀ = 0
  • (C) It makes C௠ഀ > 0
  • (D) It makes C௠଴ > 0 and C௠ഀ > 0

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2022 Q.19)** **1. Intuitive Physical Setup & Given Parameters**: **Scenario Context**: This question tests core mastery of **Compressible Flow & Shocks** (1D Isentropic Flow & Area-Mach Relations) within the *Aerodynamics & Fluid Mechanics* curriculum (1 Mark, MCQ). **Problem Statement**: > Regarding the horizontal tail of a conventional airplane, which one of the following statements is true? **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)** *"It contributes to C௠ഀ < 0"*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions. - **(B)** *"It makes C௠ഀ = 0"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. - **(C)** *"It makes C௠ഀ > 0"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. - **(D)** *"It makes C௠଴ > 0 and C௠ഀ > 0"*: ❌ **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 2022 (IIT Kharagpur) key.

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