Two clean vertical glass plates are separated by 0.75 mm and dipped in perfectly wetting water of surface tension 0.075 N/m. Take ρ = 1000 kg/m³ and g = 10 m/s². If the capillary rise between the plates is N cm, find N.
Physics · Properties of solid and fluid · properties of fluid and surface tension
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Question

Two clean vertical glass plates are separated by 0.75 mm and dipped in perfectly wetting water of surface tension 0.075 N/m. Take ρ = 1000 kg/m³ and g = 10 m/s². If the capillary rise between the plates is N cm, find N.

Physics · Properties of solid and fluid · properties of fluid and surface tension

G1 Physics · Accepted Answer

Let the plate separation be d. For two vertical parallel plates, the upward surface-tension force on a liquid strip of breadth b is F(up) = 2Sb for complete wetting. The weight of the risen liquid column is W = ρg(db)h. At equilibrium, 2Sb = ρgdbh. Cancel b: h = 2S/[ρgd]. Substitute S = 0.075, ρ = 1000, g = 10, d = 0.75 mm = 7.5×10⁻⁴ m. Therefore, h = 0.15/ [1000×10×7.5×10⁻⁴] = 0.02 m = 2 cm. Hence, N = 2.