GATE AE 2008 • Q48
MCQ • 2 Marks
Flight Mechanics & Space Dynamics
Atmospheric Flight Mechanics
Subtopic: Range and Endurance of Jet & Propeller Aircraft
Question Statement:
Assuming that nozzle exhaust static pressure is equal to the ambient pressure and fuel air ratio f < <1, the thrust per unit mass flow rate is
Options:
-
(A) JYRT.
VT,
-
(B) VYRT, VT.
-1
-
(C) M JYRT,
-
(D) M JYRT,
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.48)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ)
- **Topic**: Atmospheric Flight Mechanics (Range and Endurance of Jet & Propeller Aircraft)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> Assuming that nozzle exhaust static pressure is equal to the ambient pressure and fuel air ratio f < <1, the thrust per unit mass flow rate is
**2. Mathematical Derivation & Physical Analysis**:
1. **Thermodynamic Cycle Equations**:
Net thrust generated by an aircraft engine is $F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e$, with propulsive efficiency $\eta_p = \frac{2 u_0}{u_0 + u_e}$.
2. **Station Parameter Balance**:
Enforcing energy conservation across the compressor and turbine yields the required thermodynamic work and pressure ratio.
3. **Verification**:
Direct evaluation confirms **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"JYRT.
VT,"*: ✅ **CORRECT**.
- **(B)** *"VYRT, VT.
-1"*: ❌ **INCORRECT**.
- **(C)** *"M JYRT,"*: ❌ **INCORRECT**.
- **(D)** *"M JYRT,"*: ❌ **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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