When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to the surface tension of water. To calculate h just before water starts flowing, model the shape of the water above the rim as a disc o

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When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to the surface tension of water. To calculate h just before water starts flowing, model the shape of the water above the rim as a disc of thickness h having semicircular edges, as shown schematically in the figure. When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surfac

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Pressure at the bottom of disc (= ) pressure due to surface tension ( aligned & g h=T ( 1 R ₁ + 1 R ₂ ) & R ₁ > R ₂ & So 1 R ₁ < 1 R ₂ and R ₂= h / 2 & gh = T [ 1 R ₁ + 1 R ₂ ]= T [0+ 1 ~h / 2 ] & h ^2= 2 ~T g & h = 2 ~T g = 2 0.07 10^3 10 = 14 100 10^4 100 & ~h = 14 ~mm =3.741 aligned )

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