Which of the following operations will result in an increase in the Mach number of a supersonic flow in a constant-area duct?
Options:
(A) Increasing the length of the duct
(B) Adding heat to the flow
(C) Removing heat from the flow (cooling)
(D) Inserting friction choke rings
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2020 Q.18)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This problem evaluates **Compressible Flow & Shocks** (Normal & Oblique Shock Waves) within the *Aerodynamics & Fluid Mechanics* syllabus (1 Mark, MCQ).
**Problem Statement**:
> Which of the following operations will result in an increase in the Mach number of a supersonic flow in a constant-area duct?
**2. Step-by-Step Mathematical Derivation**:
1. **Governing Physical / Analytical Relations**:
Governed by fundamental conservation and constitutive laws under Aerodynamics & Fluid Mechanics. 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 **`C`**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** *"Increasing the length of the duct"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(B)** *"Adding heat to the flow"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
- **(C)** *"Removing heat from the flow (cooling)"*: ✅ **CORRECT**. Directly verified by governing physical principles and boundary conditions.
- **(D)** *"Inserting friction choke rings"*: ❌ **INCORRECT**. Fails boundary conditions or contradicts physical laws.
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **C**
- **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2020 (IIT Delhi) key.