The Hummingbird Feeder Drip · AI Generator #GEN-233BD9C8

Physics · fluid-mechanics

Problem

A hummingbird feeder consists of a vertical glass tube of radius R=2.0  mmR = 2.0\;\text{mm} that extends down into a sugar water reservoir. The tube opening is h=15  cmh = 15\;\text{cm} below the water surface. Due to surface tension, the sugar water forms a meniscus at the bottom of the tube that can support a pressure difference before the first drop falls. Given that the surface tension of sugar water is γ=0.080  N/m\gamma = 0.080\;\text{N/m} and its density is ρ=1200  kg/m3\rho = 1200\;\text{kg/m}^3, determine the minimum height hminh_{\text{min}} below the water surface at which the tube opening must be placed so that the sugar water will drip out. Take g=9.8  m/s2g = 9.8\;\text{m/s}^2.

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