Question

A bowl whose bottom has a round hole of diameter $1\text{mm}$ is filled with water. Assuming that surface tension acts only at hole, find the maximum height (in $\text{cm}$) up to which water can be filled in the vessel without leakage. (Given, surface tension of water $=75\times {10}^{-3}{\text{Nm}}^{-1},g=10{\text{ms}}^{-2}$ and density of water $1000{\text{kg/m}}^3$).
cm.

Answer 1

The free body diagram at the hole is

Surface tension force is equal to the weight of the liquid
$T\cos \theta 2\pi r=(\pi r^{2}h\times \rho \times g)$
To have this maximum the value of $\cos \theta =1$ for that the value of $\theta$ must be equal to $0^o$
$2T=rh\rho g$
$h=\frac{2T}{r\rho g}$
$h=\frac{2\times 75\times {10}^{-3}}{0.5\times {10}^{-3}\times 1000\times 10}=\frac{15}{500}m=\frac{1500}{500}cm$
$h=3cm$.