Subtopic: Tsiolkovsky Rocket Equation & Specific Impulse
Question Statement:
A turbulent boundary layer remains attached over a longer distance on the upper surface of an airfoil than does a laminar boundary layer, because
Options:
(A) the turbulent boundary layer is more energetic and hence can overcome the
adverse pressure gradient better
(B) the laminar boundary layer develops more skin friction and hence slows down
more rapidly
(C) turbulence causes the effective coefficient of viscosity to feduce, resulting in less
loss of momentum in the boundary layer
(D) the turbulent boundary layer is thicker, hence the velocity gradients in it are
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2007 Q.30)**
**1. Governing Concept & Theory**:
Governed by principles of **Rocket Propulsion** (Aerospace Propulsion, 1 Mark, MCQ).
**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 **C**.
**3. Official Answer Verification**:
- **Official Result**: **C**
- **Evaluation Status**: Matches official GATE 2007 master key with 100% accuracy.
- **Selected Option**: **(C)** — *"turbulence causes the effective coefficient of viscosity to feduce, resulting in less
loss of momentum in the boundary layer"*
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