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Water can be filled a little above the rim of a glass, reaching a height h above the rim before it overflows, thanks to surface tension. To find h just before flow begins, model the water bulging above the rim as a disc of thickness h with semicircular edges (as shown). When the water pressure at the bottom of this disc exceeds the value that surface tension can hold, the surface ruptures near the rim and water begins to flow. Taking the density of water = 10³ kg/m³, surface tension = 0.07 N/m, and g = 10 m/s², find h in mm.
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Correct answer: 4
Solution
The bulge's edge is a semicircular meniscus of radius h/2. The surface-tension pressure it can support is 2T/(h/2) = 4T/h. The water at the bottom of the disc has gauge pressure rho*g*h. At the breaking point these are equal.
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