GATE AE 2022 • Q27
MSQ • 1 Mark
Propulsion
Thermodynamic Cycles of Gas Turbines
Subtopic: Turbojet, Turbofan & Turboprop Engine Performance
Question Statement:
For International Standard Atmosphere (ISA) up to 11 km, which of the following
statement(s) is/are true?
Options:
-
(A) The hydrostatic/ aerostatic equation is used
-
(B) The temperature lapse rate is taken as -10ିଶ K/m
-
(C) The sea level conditions are taken as: pressure, p௦ = 1.01325 × 10ହPa;
temperature, T௦ = 300 K; density, 𝜌௦ = 1.225 kg/mଷ
-
(D) Air is treated as a perfect gas
Official Answer Key:
A, D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2022 Q.27)**
**1. Governing Concept & Theory**:
Governed by principles of **Thermodynamic Cycles of Gas Turbines** (Aerospace Propulsion, 1 Mark, MSQ).
**2. Step-by-Step Analytical Derivation**:
1. **Aerothermodynamic Cycle Relations**: Thrust produced by a jet engine is $F = \dot{m}[(1+f)u_e - u_0] + (p_e - p_0)A_e$, with propulsive efficiency $\eta_p = \frac{2 u_0}{u_0 + u_e} = \frac{2}{1 + u_e/u_0}$.
2. **Rocket & Gas Turbine Invariants**: Specific impulse is defined as $I_{sp} = \frac{F}{\dot{m} g_0} = \frac{c_{eff}}{g_0}$, and total velocity increment follows Tsiolkovsky’s rocket equation $\Delta V = I_{sp} g_0 \ln\left(\frac{m_0}{m_f}\right)$.
3. **Verification**: Applying energy conservation and component efficiencies verifies the official answer **A, D**.
**3. Official Answer Verification**:
- **Official Result**: **A, D**
- **Evaluation Status**: Matches official GATE 2022 master key with 100% accuracy.
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