GATE AE 2022 • Q17 MCQ • 1 Mark

Aerodynamics & Fluid Mechanics

Airfoil & Wing Theory

Subtopic: Kutta-Joukowski Theorem & Thin Airfoil Theory

Question Statement:

Consider the velocity distribution, u(y) shown in the figure. For two adjacent fluid layers L1 and L2, the viscous force exerted by L1 on L2 is

Options:

  • (A) to the right
  • (B) to the left
  • (C) vertically upwards
  • (D) vertically downwards

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2022 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**: > Consider the velocity distribution, u(y) shown in the figure. For two adjacent fluid layers L1 and L2, the viscous force exerted by L1 on L2 is **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 **`B`**. **3. Comprehensive Options & Distractor Analysis**: - **(A)** *"to the right"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. - **(B)** *"to the left"*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions. - **(C)** *"vertically upwards"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. - **(D)** *"vertically downwards"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws. **4. Official Master Key & Exam Takeaway**: - **Official Answer Key**: **B** - **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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