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 $=75 \times 10^{-3} Nm ^{-1}, g=10\, ms ^{-2}$ and density of water $=1\, g / cm ^{3}$.

Answer 1

The vertical force due to surface at the hole

$=T \cos \theta \times L=T \cos \theta \times 2 \pi r$
This will balance weight $m g\left(=\pi r^{2} h \rho g\right)$
$\therefore T \cos \theta \times 2 \pi r=\pi r^{2} h \rho g$
$\Rightarrow h=\frac{2 T \cos \theta}{r \rho g}$
$h$ is maximum, when $\cos \theta=1$
$\therefore h_{\max }=\frac{2 T}{r \rho g}=\frac{2 \times 0.075}{0.0005 \times 1000 \times 10}$
$=0.03\, m =3\, cm$