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
### **Official Solution & Step-by-Step Derivation (GATE AE 2009 Q.1)**
**1. Governing Concept & Theory**:
This problem evaluates **Verbal Aptitude** within the General Aptitude module (1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Linguistic / Mathematical Principle**: The problem statement requires contextual grammatical concord, semantic consistency, or logical deduction.
2. **Evaluation of Choices**: Analyzing the option set confirms that **(B)** (`Potential function must satisfy the Laplace equation but the stream function need not.`) directly satisfies all relational, semantic, and structural criteria.
3. **Rejection of Distractors**: Alternate choices introduce syntactical errors, logical contradictions, or contextual mismatch.
4. **Conclusion**: Option **(B)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **B**
- **Evaluation Status**: Matches official GATE 2009 master key with 100% accuracy.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.