GATE AE 2008 • Q16 MCQ • 1 Mark

Aerodynamics & Fluid Mechanics

Basic Fluid Mechanics

Subtopic: Conservation Equations of Mass, Momentum & Energy

Question Statement:

3 (B) 5 (C) 9 Q.19 The compatibility conditions in theory of elasticity ensure that

Options:

  • (A) there is compatibility between various direct and shear stresses
  • (B) relationships between stresses and strains are consistent with constitutive relations
  • (C) displacements are single-valued and continuous
  • (D) stresses satisfy bi-harmonic equation

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Official Solution & Step-by-Step Derivation (GATE AE 2008 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 2008 master key with 100% accuracy. - **Selected Option**: **(A)** — *"there is compatibility between various direct and shear stresses"*

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