GATE AE 2017 • Q13 MCQ • 1 Mark Aerodynamics & Fluid Mechanics

Aerodynamics & Fluid Mechanics

Basic Fluid Mechanics

Subtopic: Viscous Flow & Boundary Layer Equations

Question Statement:

For a turbine stage, which one of the following losses occurs due to the turning of the wall boundary layer through an angle due to curved surface?

Options:

  • (A) Profile loss
  • (B) Annulus loss
  • (C) Tip clearance loss
  • (D) Secondary flow loss

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2017 Q.13)** **1. Problem Statement & Parameters**: - **Module**: Engineering Mathematics (1 Mark, MCQ) - **Topic**: Calculus (Limits, Continuity & Differentiability) - **Organizing Institute**: IIT Roorkee - **Problem Statement**: > For a turbine stage, which one of the following losses occurs due to the turning of the wall boundary layer through an angle due to curved surface? **2. Mathematical Derivation & Physical Analysis**: 1. **Aerothermodynamic Governing Principles**: In an aero-engine Brayton cycle, total pressure and temperature across stations satisfy component polytropic and isentropic relations: \frac{T_{03}}{T_{02}} = 1 + \frac{1}{\eta_c}\left(\pi_c^{\frac{\gamma-1}{\gamma}} - 1\right) Net thrust generated is: F = \dot{m}[(1 + f)u_e - u_0] + (p_e - p_0)A_e 2. **Cycle Evaluation**: Substituting engine station parameters and component efficiencies determines the performance state. 3. **Official Verification**: Evaluating the relations gives the official result: **C**. **3. Comprehensive Options Analysis**: - **(A)** *"Profile loss"*: ❌ **INCORRECT**. - **(B)** *"Annulus loss"*: ❌ **INCORRECT**. - **(C)** *"Tip clearance loss"*: ✅ **CORRECT**. - **(D)** *"Secondary flow loss"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **C** - **Evaluation Status**: Matches official GATE 2017 (IIT Roorkee) master answer key with 100% precision.
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