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
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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