Using primary dimensions, verify that the Archimedes number (Table 7–5) is indeed dimensionless.

Data from Table 7-5

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TABLE 7-5 Some common established nondimensional parameters or II's encountered in fluid mechanics and heat transfer* Name Definition Archimedes number Aspect ratio Biot number Bond number Cavitation number Darcy friction factor Drag coefficient Eckert number Euler number Ar = AR = Bi = Bo = f= CD Ec P.8L³ Ca (sometimes σ) sometimes = hL k || 8T pV² Eu = -(P, - p) 8(P; - p.)I² σ₂ or V² C₂T D FD pV²A ΔΡ PV2 = PP pV² 2(PP) pV2 sometimes ΔΡ pV², Ratio of Significance Gravitational force Viscous force Length Length Width Diameter or Surface thermal resistance Internal thermal resistance Gravitational force Surface tension force Pressure - Vapor pressure Inertial pressure Wall friction force Inertial force Drag force Dynamic force Kinetic energy Enthalpy Pressure difference Dynamic pressure