Subtopic: Conservation Equations of Mass, Momentum & Energy
Question Statement:
In a two-dimensional potential flow, the doublet is a limit of the superposition of
Options:
(A) a uniform stream and a source
(B) a source and a sink of equal strength
(C) a uniform stream and a sink
(D) a source and a vortex
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2023 Q.16)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This question tests core mastery of **Basic Fluid Mechanics** (Conservation Equations of Mass, Momentum & Energy) within the *Aerodynamics & Fluid Mechanics* curriculum (1 Mark, MCQ).
**Problem Statement**:
> In a two-dimensional potential flow, the doublet is a limit of the superposition of
**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)** *"a uniform stream and a source"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(B)** *"a source and a sink of equal strength"*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions.
- **(C)** *"a uniform stream and a sink"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(D)** *"a source and a vortex"*: ❌ **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 2023 (IIT Kanpur) key.
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