Question

An open capillary tube contains a drop of water. When the tube is in its vertical position, the drop forms a column with a length of $2.98cm$. The internal diameter of the capillary tube is $1mm$. The radii of curvature of the upper meniscus (in mm)is $\frac{x}{4}$. Consider the wetting to be complete. Surface tension of water $=0.0075N/m$. Find the value of x.

Answer 1

When capillary is in vertical position, thge upper meniscus is concave and pressure due to surface tension

$P_s=\frac{2T}{R_1}$

is directed vertically upward, $R_1$ being radius of curvature of upper

meniscus. When wetting is complete

$P_1=\frac{2T}{r}$

$r$ being radius of the capillary tube $=\frac{D}{2}=\frac{1}{2}mm$

$R_1=r=0.5mm$ in each case.

Given, the raidus of curvature of the upper meniscus is $\frac{x}{4}$

Then,

$\frac{x}{4}=0.5mm$

That is,

$x=0.5\times 4=2mm$