Basic Fluid Mechanics

### **Official Solution & Step-by-Step Derivation (GATE AE 2025 Q.41)** **1. Governing Concept & Theory**: Governed by principles of **Basic Fluid Mechanics** (Fluid Mechanics & Aerodynamics, 2 Mark, NAT). **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 **2.0**. **3. Official Answer Verification**: - **Official Result**: **2.0** (Acceptable Range: `[2.0, 2.0]`) - **Evaluation Status**: Matches official GATE 2025 master key with 100% accuracy.