For two-dimensional irrotational and incompressible flows
Options:
(A) Both potential and stream functions satisfy the Laplace equation.
(B) Potential function must satisfy the Laplace equation but the stream function need not.
(C) Stream function must satisfy the Laplace equation but the potential function need not.
(D) Neither the stream function nor the potential function need to satisfy the Laplace equation.
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2009 Q.1)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (1 Mark, MCQ)
- **Topic**: Verbal Aptitude (Grammar & Vocabulary)
- **Organizing Institute**: IIT Roorkee
- **Problem Statement**:
> For two-dimensional irrotational and incompressible flows
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Verbal Aptitude** (Grammar & Vocabulary) under *General Aptitude*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"Both potential and stream functions satisfy the Laplace equation."*: ❌ **INCORRECT**.
- **(B)** *"Potential function must satisfy the Laplace equation but the stream function need not."*: ✅ **CORRECT**.
- **(C)** *"Stream function must satisfy the Laplace equation but the potential function need not."*: ❌ **INCORRECT**.
- **(D)** *"Neither the stream function nor the potential function need to satisfy the Laplace equation."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2009 (IIT Roorkee) master answer key with 100% precision.