Question

Water rises in a glass capillary tube to a height of 17 cm. What is the diameter of the capillary tube?

Short answer

The diameter of the capillary tube \({\rm{r = 9}}{\rm{.5 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{\;m}}{\rm{.}}\)

Step-by-step solution

Definition of surface tension

Surface tension is the propensity of liquid surfaces to shrink to the smallest feasible surface area while they are at rest.

Find the diameter of the capillary tube

Liquid will rise to a height of 17 cm:-

Calculate the height of the water as shown:

\({\rm{h = }}\frac{{{\rm{2Tcos\theta }}}}{{{\rm{\rho rg}}}},\)where T is surface tension of the liquid, \({\rm{\rho }}\) is the density of the liquid and \({\rm{\theta }}\) is the angle made by water on the capillary tube.

Given, \({\rm{h = 0}}{\rm{.17\;m,}}\)we need to find r.

\(\begin{aligned}{}{\rm{0}}{\rm{.17\;m = }}\frac{{{\rm{2}}\left( {{\rm{0}}{\rm{.0799\;kg/}}{{\rm{s}}^{\rm{2}}}} \right)}}{{{\rm{(r)}}\left( {{\rm{1000\;kg/}}{{\rm{m}}^{\rm{3}}}} \right)\left( {{\rm{9}}{\rm{.8\;m/}}{{\rm{s}}^{\rm{2}}}} \right)}}\\{\rm{ r = 9}}{\rm{.5 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{\;m}}{\rm{.}}\end{aligned}\)

Hence, the diameter of the capillary tube is \({\rm{r = 9}}{\rm{.5 \times 1}}{{\rm{0}}^{{\rm{ - 5}}}}{\rm{\;m}}{\rm{.}}\)