Question

A capillary tube of radius $0.50mm$ is applied vertically in a pot of water. Find the difference between the pressure of the water in the tube $5.0cm$ below the surface and the atmospheric pressure. Surface tension of water $=0.75N/m^{-1}$

Answer 1

Given radius of capillary tube $r=0.5mm=5\times {10}^{-4}m$

depth (where pressure to be found) $h=5cm=5\times {10}^{-2}m$

Surface tension of water $T=075N/m$

Excess pressure at $5cm$ before the surface

$P=\rho hg=1000\times (5\times {10}^{-2})\times 9.8$

$=490N/m$

$P_0=\frac{2T}{r}=\frac{2\times 0.75}{5\times {10}^{-4}}=300N/m^2$

Difference in pressure $P_0-P=490-300=190N/m^2$