In fluid mechanics, the Reynolds number $Re = \frac{\rho v D}{\mu}$ represents the ratio of which two physical forces?

(A) Inertia forces to Viscous forces

(B) Gravity forces to Inertia forces

(C) Pressure forces to Surface tension forces

(D) Viscous forces to Buoyancy forces

Answer Key:

A

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Governing Concept & Domain Context:** * This question evaluates **Conservation Equations of Mass, Momentum & Energy** under *Basic Fluid Mechanics* in GATE AE. 2. **Stage 2: Mathematical Derivation:** * By dimensional analysis: Inertial force $\sim \rho v^2 L^2$, Viscous force $\sim \mu v L$. Ratio $= \frac{\rho v L}{\mu} = Re$. 3. **Stage 3: Distractor Elimination Forensics:** * The evaluated correct answer is derived using standard physical equations. * Distractor values correspond to typical unit conversion omissions or inverted formulas. 4. **Stage 4: Common Student Trap:** * *Trap:* Confusing Reynolds number with Froude number (inertia to gravity). *Reference: John D. Anderson Jr., Fundamentals of Aerodynamics (McGraw-Hill).*

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