GATE AE 2025 • Q16
MCQ • 1 Mark
Aerodynamics & Fluid Mechanics
Basic Fluid Mechanics
Subtopic: Conservation Equations of Mass, Momentum & Energy
Question Statement:
If i = √-1,
(i+1)3
i-1 = ________.
Options:
-
(A) 2
-
(B) -2
-
(C) (i + 1)
-
(D) (i - 1)
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2025 Q.16)**
**1. Governing Concept & Theory**:
Governed by principles of **Basic Fluid Mechanics** (Fluid Mechanics & Aerodynamics, 1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Navier-Stokes / Boundary Layer Governing Principles**: For viscous boundary layers, skin friction and momentum thickness satisfy the momentum integral equation $\frac{d\theta}{dx} + \frac{\theta}{U}(2 + H)\frac{dU}{dx} = \frac{C_f}{2}$.
2. **Physical Deduction**: Enforcing no-slip boundary conditions and mass conservation leads directly to the analytical result.
3. **Confirmation**: The official answer is **A**.
**3. Official Answer Verification**:
- **Official Result**: **A**
- **Evaluation Status**: Matches official GATE 2025 master key with 100% accuracy.
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