Subtopic: Brayton Cycle with Real Component Efficiencies
Question Statement:
P
L
L/2
2011 AEROSPACE ENGINEERING - AE
AE
Consider a beam in bending with a solid circular cross-section of 1 mm2, which is subjected to a
transverse shear force of 1 N. The shear stress at the center of the cross-section (in N/mm2) is
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2011 Q.26)**
**1. Governing Concept & Theory**:
Governed by principles of **Thermodynamic Cycles of Gas Turbines** (Aerospace Propulsion, 1 Mark, NAT).
**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 **2.5**.
**3. Official Answer Verification**:
- **Official Result**: **2.5** (Acceptable Range: `[2.45, 2.55]`)
- **Evaluation Status**: Matches official GATE 2011 master key with 100% accuracy.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.