In a convergent-divergent nozzle operating at design conditions, the Mach number at the throat is:
Options:
(A) less than 1
(B) equal to 1
(C) greater than 1
(D) zero
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2011 Q.43)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (2 Mark, MCQ)
- **Topic**: Airfoil & Wing Theory (Finite Wing Theory & Induced Drag)
- **Organizing Institute**: IIT Madras
- **Problem Statement**:
>
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Airfoil & Wing Theory** (Finite Wing Theory & Induced Drag) under *Aerodynamics & Fluid Mechanics*. 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)** *"-0.05 0.02i"*: ❌ **INCORRECT**.
- **(B)** *"-0.5 0.2i"*: ❌ **INCORRECT**.
- **(C)** *"-0.028 1.26i"*: ✅ **CORRECT**.
- **(D)** *"0.028 1.26i
Consider the inviscid, adiabatic flow of air at free stream conditions, M
1 = 2, p 1 = 1 atm and T 1 =
288 K around a sharp expansion corner ( θ = 20°) as shown below. The Prandtl-Meyer function, ν,
is given as a function of Mach number, M, as 1 M tan ) 1 M (1
1tan1
1) M ( 2 121
Assume air to be calorically perfect with = 1.4. The Mach number, M 2, downstream of the
expansion corner is approximately"*: ❌ **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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