GATE AE 2023 • Q46 MSQ • 2 Marks

Aerodynamics & Fluid Mechanics

Airfoil & Wing Theory

Subtopic: High-Lift Devices & Flaps

Question Statement:

For an airfoil, which of the relations given about the critical Mach number crM and drag divergence Mach number ddM is/are correct?

Options:

  • (A) cr ddMM 
  • (B) 1.0crM 
  • (C) 1.0ddM 
  • (D) 1.0crM 

Official Answer Key:

A, B, C

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2023 Q.46)** **1. Intuitive Physical Setup & Given Parameters**: **Scenario Context**: This question tests core mastery of **Airfoil & Wing Theory** (High-Lift Devices & Flaps) within the *Aerodynamics & Fluid Mechanics* curriculum (2 Mark, MSQ). **Problem Statement**: > For an airfoil, which of the relations given about the critical Mach number crM and drag divergence Mach number ddM is/are correct? **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, B, C`**. **3. Comprehensive Options & Distractor Analysis**: - **(A)** *"cr ddMM "*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws. - **(B)** *"1.0crM "*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws. - **(C)** *"1.0ddM "*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws. - **(D)** *"1.0crM "*: ❌ **INCORRECT**. Contradicts governing physical laws. *Full credit (+2 Marks, 0 Negative Marks) requires selecting all verified choices **`A, B, C`**.* **4. Official Master Key & Exam Takeaway**: - **Official Answer Key**: **A, B, C** - **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2023 (IIT Kanpur) key.

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