The shadowgraph flow visualization technique depends on
Options:
(A) the variation of the value of density in the flow.
(B) the first derivative of density with respect to spatial coordinate.
(C) the second derivative of density with respect to spatial coordinate.
(D) the third derivative of density with respect to spatial coordinate.
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2012 Q.7)**
**1. Governing Concept & Theory**:
This problem evaluates **Quantitative 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 **(C)** (`the second derivative of density with respect to spatial coordinate.`) 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 **(C)** is the unique correct answer.
**3. Official Answer Verification**:
- **Official Result**: **C**
- **Evaluation Status**: Matches official GATE 2012 master key with 100% accuracy.
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