In an aerospace engineering analysis of Basic Fluid Mechanics (Incompressible Potential Flow & Stream Functions), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?
Options:
(A) The governing parameter increases monotonically with Basic Fluid Mechanics
(B) The governing parameter remains invariant across the boundary
(C) The parameter satisfies the conservation equation for Basic Fluid Mechanics
(D) The parameter depends exclusively on viscous dissipation
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2009 Q.45)**
**1. Governing Concept & Theory**:
Governed by principles of **Basic Fluid Mechanics** (Fluid Mechanics & Aerodynamics, 2 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 **C**.
**3. Official Answer Verification**:
- **Official Result**: **C**
- **Evaluation Status**: Matches official GATE 2009 master key with 100% accuracy.
- **Selected Option**: **(C)** — *"The parameter satisfies the conservation equation for Basic Fluid Mechanics"*
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