Question

If a glass tube is lowered into a dish of mercury, one finds that inside the tube the level of mercury is depressed below that in the dish. What is the level difference if the diameter of the glass tube is 0.80mm ?

Answer 1

According to the Jurin's law, the liquid height inside a glass tube is given by the expression:

$$h = \dfrac{2\gamma\cos\theta}{\rho g r}$$

where $\gamma = 0.47 N/m$ is the surface tension of mercury, $\rho = 13540\space kg/m^3$ is the density of mercury, $g = 9.81 \space m/s^2$ , $r = \dfrac{0.8}{2}\times10^{-3}m = 0.4\times10^{-3}m$ is the tube radius and $\theta\approx 135\degree$.Thus, obtain:

$$h = \dfrac{2\cdot 0.47\cos135\degree}{13540\cdot 9.81\cdot 0.4\times 10^{-3}} \approx-12.51\times 10^{-3}m$$

Answer. The level difference is 12.51 mm.