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
### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.7)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (2 Mark, MCQ)
- **Topic**: Quantitative Aptitude (Data Interpretation)
- **Organizing Institute**: IIT Delhi
- **Problem Statement**:
> The shadowgraph flow visualization technique depends on
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Quantitative Aptitude** (Data Interpretation) 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 **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"the variation of the value of density in the flow."*: ❌ **INCORRECT**.
- **(B)** *"the first derivative of density with respect to spatial coordinate."*: ❌ **INCORRECT**.
- **(C)** *"the second derivative of density with respect to spatial coordinate."*: ✅ **CORRECT**.
- **(D)** *"the third derivative of density with respect to spatial coordinate."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.