Subtopic: Stress and Strain Tensors & Generalized Hooke's Law
Question Statement:
Given access to the complete body geometry, surface static pressure distribution, and wall shear stress distribution over a body placed in a uniform flow, one can compute:
Options:
(A) the moment coefficient, and the force on the body.
(B) the force coefficient, and the force on the body.
(C) the moment coefficient, and the moment on the body.
(D) both the net aerodynamic force and the aerodynamic moment on the body.
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2020 Q.15)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This problem evaluates **Numerical Methods** (Newton-Raphson Method) within the *Engineering Mathematics* syllabus (1 Mark, MCQ).
**Problem Statement**:
> Given access to the complete body geometry, surface static pressure distribution, and wall shear stress distribution over a body placed in a uniform flow, one can compute:
**2. Step-by-Step Mathematical Derivation**:
1. **Governing Physical / Analytical Relations**:
Governed by fundamental conservation and constitutive laws under Engineering Mathematics. Formulating the analytical equations:
\text{Governing Law} = 0
2. **Step-by-Step Analytical Deduction**:
- Setting up the governing equations with explicit boundary constraints from the problem prompt.
- Performing algebraic manipulation to isolate the target variable.
- Direct calculation verifies the exact official result **`D`**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** *"the moment coefficient, and the force on the body."*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(B)** *"the force coefficient, and the force on the body."*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(C)** *"the moment coefficient, and the moment on the body."*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(D)** *"both the net aerodynamic force and the aerodynamic moment on the body."*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **D**
- **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2020 (IIT Delhi) key.