First slide

Surface tension and surface energy

Question

A bowl whose bottom has round holes of diameter 1 mm is filled with water. Assuming that surface tension acts only at holes, find the maximum height (in cm) up to which water can be filled in the vessel without leakage. (Given, surface tension of water = 75 x 10^-3 Nm-l , g=10 ms^-2 and density of water = 1 g/cm³.

Moderate

Solution

The vertical force due to surface at the hole
$\begin{array}{l} = T \cos θ \times L = T \cos θ \times 2 π r \\ This will balance weight m g (= π r^{2} h ρ g) \\ ∴ T \cos θ \times 2 π r = π r^{2} h ρ g \end{array}$
$\begin{array}{l} \Rightarrow h = \frac{2 T \cos θ}{r ρ g} \\ h is maximum, when \cos θ = 1 \\ ∴ h_{max} = \frac{2 T}{r ρ g} = \frac{2 \times 0.075}{0.0005 \times 1000 \times 10} = 0.03 m = 3 cm \end{array}$

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