Consider a potential flow with free stream velocity V_inf, over a spinning circular cylinder of radius R and circulation Gamma. The lift per unit span is given by Kutta-Joukowski theorem as:
Options:
(A) rho * V_inf * Gamma
(B) 0.5 * rho * V_inf^2 * Gamma
(C) 2 * pi * R * rho * V_inf
(D) rho * Gamma^2 / (2 * pi * R)
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2011 Q.21)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (1 Mark, MCQ)
- **Topic**: Atmospheric Flight Mechanics (Standard Atmosphere Properties)
- **Organizing Institute**: IIT Madras
- **Problem Statement**:
>
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Atmospheric Flight Mechanics** (Standard Atmosphere Properties) under *Flight Mechanics & Space Dynamics*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"R
r
r
Rr V ln21 sin2
2
"*: ❌ **INCORRECT**.
- **(B)** *"R
r
r
Rr V ln21 sin2
2
A main objective of by-pass in a turbo-fan engine is to increase"*: ❌ **INCORRECT**.
- **(C)** *"mass flow rate through engine inlet"*: ✅ **CORRECT**.
- **(D)** *"turbine inlet temperature"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2011 (IIT Madras) master answer key with 100% precision.
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