Surface tension of water at \(20^{0}C\) is \(0.072\frac{N}{m}\). What is the capillary rise of water in a tube of diameter \(1\,mm\). Given: angle of contact \(=8^{o}\), density of water \(=1\frac{g}{cm^{3}}\).
Ans: \(h=2.91\,cm\).
A liquid has surface tension of \(0.064\frac{N}{m}\) at a given temperature. If the liquid rises to \(6\,mm\) above the liquid surface in the capillary tube of diameter \(3\,mm\). Calculate: the angle of contact. density of the liquid is \(900\frac{kg}{m^{-3}}\).
Ans: \(\theta=51.40^{o}\).
A capillary tube with an inside diameter of [latex0.25\,mm][/latex] can support a \(20\,cm\) column of a liquid of density \(0.93\frac{g}{cm^{3}}\). The angle of contact of liquid with the walls of capillary tube is \(15^{o}\). Find: the surface tension of the liquid.
Ans: \(\sigma=0.12\frac{N}{m}\).
A mercury barometer tube is of \(0.25\,cm\) internal radius. What error is introduced in the observed reading of height recorded because of surface tension ? Given: Surface Tension of mercury \(=0.540\frac{N}{m}\), density of mercury \(=13600\frac{kg}{m^{3}}\), Angle of contact \(=135^{o}\) and \(g=9.8\frac{m}{s^{2}}\). How can be the error be corrected?
Ans: \(h=-2.29\,cm\).
Water rises to a height of \(10\,cm\) in a capillary tube and mercury falls to a depth of \(3.5\,cm\) in the same capillary tube. If, densities of mercury and water are \(13.6\frac{g}{cm^{3}}\) and \(1\frac{g}{cm^{3}}\) respectively, and their angles of contact are \(135^{o}\) and \(0^{o}\) respectively. Find: The ration of surface tension of water to that of mercury.
One end of the capillary tube is dipped in the water. The tube is held vertical. If the radius of the capillary tube is \(\frac{1}{28}\,cm\). Find: the height to which the water rises. If, the tube is tilted at an angle \(60^{o}\) with the vertical. Find: the length up to which water rises in the capillary tube. Given: Surface tension of water \(=70\frac{dyne}{cm}\), Density of water \(=1\frac{g}{cm^{3}}\) and \(g=980\frac{cm}{s^{2}}\). consider; the angle of contact as \(0^{o}\).
Ans: \(h=4\,cm\) and \(l=8\,cm\).
One limb of the U-tube manometer has a diameter of \(10\,mm\) whereas the other limb has a diameter of \(2\,mm\). Water is poured into the tube and both limbs are kept open to atmosphere. What is the difference in water level in the two limbs? Given: Surface tension of water \(=\left(7\times10^{-2}\right)\frac{N}{m}\), density of water \(=1000\frac{kg}{m^{3}}\), Angle of contact \(\theta=0^{o}\) and \(g=9.8\frac{m}{s^{2}}\).
