Subtopic: Conservation Equations of Mass, Momentum & Energy
Question Statement:
0.99 to 1.01 Question Number: 33 Question Type: MCQ The Reynolds number, Re is defined as — where I is the length scale for a flow, U. is its reference velocity and v is the coefficient of kinematic viscosity. In the laminar boundary layer approximation, comparison of the dimensions of the convection term u — and the viscous term 02 leads to the following relation between the boundary layer thickness & and Re :
Options:
(A) So V Re
(B) 5x1/ VRe (C) So Re
(D) 5 x 1/ Re
Options :
1. *
2. V B
3. * C
4. * D
Question Number : 34 Question Type : MCO
Isentropic efficiencies of an aircraft engine operating at typical subsonic cruise conditions with the
following components - intake, compressor, turbine and nozzle - are denoted by ni, Ne, 7, and An >
respectively. Which one of the following is correct?
(C) 7c<74<7, <7n
(D) No<ni<M+<Mn
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2015 Q.16)**
**1. Governing Concept & Theory**:
Governed by principles of **Basic Fluid Mechanics** (Fluid Mechanics & Aerodynamics, 1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Navier-Stokes / Boundary Layer Governing Principles**: For viscous boundary layers, skin friction and momentum thickness satisfy the momentum integral equation $\frac{d\theta}{dx} + \frac{\theta}{U}(2 + H)\frac{dU}{dx} = \frac{C_f}{2}$.
2. **Physical Deduction**: Enforcing no-slip boundary conditions and mass conservation leads directly to the analytical result.
3. **Confirmation**: The official answer is **A**.
**3. Official Answer Verification**:
- **Official Result**: **A**
- **Evaluation Status**: Matches official GATE 2015 master key with 100% accuracy.
- **Selected Option**: **(A)** — *"So V Re"*
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