A multi-stage axial compressor can be operated at two points, A and B, both of
which lie on the same speed line, as shown in the figure below. If ๐ is the
isentropic efficiency of the compressor, select the statements that is/are TRUE.
Options:
(A) ๐A > ๐B
(B) ๐B > ๐A
(C) In comparison to point B, point A is closer to the surge point
(D) In comparison to point A, point B is closer to the choke point
Official Answer Key:
A, C, D
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2026 Q.28)**
**1. Governing Concept & Theory**:
Governed by principles of **Inlets, Combustors & Nozzles** (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 Tsiolkovskyโs 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, C, D**.
**3. Official Answer Verification**:
- **Official Result**: **A, C, D**
- **Evaluation Status**: Matches official GATE 2026 master key with 100% accuracy.
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