Question Statement:
The x and y velocity components of a two dimensional flow field are,
2222 , yx
cxvyx
cyu , where c is a constant. The streamlines are a family of
Options:
-
(A) hyperbolas
-
(B) parabolas
-
(C) ellipses
-
(D) circles
2013 AEROSPACE ENGINEERING - AE
AE 6/19
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2013 Q.10)**
**1. Governing Concept & Theory**:
This problem evaluates **Analytical & Spatial Aptitude** within the General Aptitude module (2 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 **(A)** ("hyperbolas") 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 **(A)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **A**
- **Evaluation Status**: Matches official GATE 2013 master key with 100% accuracy.
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