GATE AE 2008 • Q16 MCQ • 1 Mark

Aerodynamics & Fluid Mechanics

Basic Fluid Mechanics

Subtopic: Conservation Equations of Mass, Momentum & Energy

Question Statement:

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

### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.16)** **1. Problem Statement & Parameters**: - **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ) - **Topic**: Basic Fluid Mechanics (Conservation Equations of Mass, Momentum & Energy) - **Organizing Institute**: IISc Bengaluru - **Problem Statement**: > The compatibility conditions in theory of elasticity ensure that **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Basic Fluid Mechanics** (Conservation Equations of Mass, Momentum & Energy) under *Aerodynamics & Fluid Mechanics*. 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 **A**. **3. Comprehensive Options Analysis**: - **(A)** *"there is compatibility between various direct and shear stresses"*: ✅ **CORRECT**. - **(B)** *"relationships between stresses and strains are consistent with constitutive relations"*: ❌ **INCORRECT**. - **(C)** *"displacements are single-valued and continuous"*: ❌ **INCORRECT**. - **(D)** *"stresses satisfy bi-harmonic equation"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **A** - **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.

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