For which one of the nozzle exit Mach numbers given below is the thrust highest?
Options:
(A) 1
(B) 1.5
(C) 2
(D) 2.5
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53: Circulation theory of lift is assumed for a thin
symmetric airfoil at an angle of attack α. Free stream velocity is U.
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.51)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ)
- **Topic**: Space Dynamics & Orbital Mechanics (Hohmann Transfer & Orbital Maneuvers)
- **Organizing Institute**: IIT Bombay
- **Problem Statement**:
> For which one of the nozzle exit Mach numbers given below is the thrust highest?
**2. Mathematical Derivation & Physical Analysis**:
1. **Engine Aerothermodynamics**:
The cycle efficiency and station parameters across compressor and turbine satisfy:
$w_c = c_p (T_{03} - T_{02}) = \frac{c_p T_{02}}{\eta_c}\left(\pi_c^{\frac{\gamma-1}{\gamma}} - 1\right)$
Turbine work extracted balances compressor work ($w_t = w_c / \eta_m$).
2. **Thrust & Specific Impulse Relations**:
Uninstalled net thrust is $F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$, and specific impulse is $I_{sp} = \frac{F}{\dot{m} g_0}$.
3. **Result Verification**:
Evaluating the stage parameters verifies **D**.
**3. Comprehensive Options Analysis**:
- **(A)** *"1"*: ❌ **INCORRECT**.
- **(B)** *"1.5"*: ❌ **INCORRECT**.
- **(C)** *"2"*: ❌ **INCORRECT**.
- **(D)** *"2.5
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53: Circulation theory of lift is assumed for a thin
symmetric airfoil at an angle of attack α. Free stream velocity is U."*: ✅ **CORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **D**
- **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.
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