GATE AE 2024 • Q45
MSQ • 2 Marks
Aerodynamics & Fluid Mechanics
Basic Fluid Mechanics
Subtopic: Incompressible Potential Flow & Stream Functions
Question Statement:
Consider the function
f(x) = {x2 for x < 0
x for x ≥ 0
where x is real. Which of the following statements is/are correct?
Options:
-
(A) The function is continuous for all x
-
(B) The derivative of the function is discontinuous at x = 0
-
(C) The derivative of the function is continuous at x = 1
-
(D) The function is discontinuous at x = 0
Official Answer Key:
A, B, C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2024 Q.45)**
**1. Governing Concept & Theory**:
Governed by principles of **Basic Fluid Mechanics** (Fluid Mechanics & Aerodynamics, 2 Mark, MSQ).
**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, B, C**.
**3. Official Answer Verification**:
- **Official Result**: **A, B, C**
- **Evaluation Status**: Matches official GATE 2024 master key with 100% accuracy.
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