Select the pair that exhibits the same relationship as the given pair: **Mach Number : Compressibility**

(A) Reynolds Number : Viscosity

(B) Froude Number : Surface Tension

(C) Prandtl Number : Capillarity

(D) Knudsen Number : Buoyancy

Answer Key:

A

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Semantic Relationship:** A dimensionless group matched with the physical fluid property/phenomenon it characterizes. 2. **Stage 2: Mapping:** Mach number represents compressibility ($V/a$). Reynolds number represents viscous effects ($\rho V D / \mu$). 3. **Stage 3: Distractor Elimination:** Froude number relates to gravitational/wave forces (not surface tension, which is Weber number); Prandtl number relates to thermal/momentum diffusivity; Knudsen number relates to rarefaction. 4. **Stage 4: Selection:** Option A is correct.

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