two glass capillary tubes of inside diameters of 20 and 13 microns are used to test the capillary rise by inserting them into a large water tank. The smaller tube is inserted in the bigger one so an a

a) The height of capillary rise in an annular space can be described by the following equation: h = (2 * ? * cos?) / (? * g * (r2^2 - r1^2)) where h is the height of capillary rise, ? is the surface tension between air and water, ? is the contact angle between water and the glass surface, ? is the density of water, g is the acceleration due to gravity, r2 is the outer radius of the bigger capillary tube, and r1 is the inner radius of the smaller capillary tube. b) When the outside diameter of the inner capillary tube becomes zero, r1 becomes zero and the annular space disappears. Therefore, the limit of the equation is h = 0. c) The rise of the water in the inner capillary can be calculated using the same equation as part a) with r2 = 10 microns (half the diameter of the bigger capillary tube) and r1 = 6.5 microns (half the diameter of the smaller capillary tube plus half the thickness of the wall). Plugging in the given values for ?, ?, ?, and g, we get: h_inner = (2 * 71.97 * cos?) / (1000 * 9.81 * (10^2 - 6.5^2)) ? 0.038 mm The rise of water in the annular space can also be calculated using the same equation with r2 = 10 microns and r1 = 13 microns (half the diameter of the smaller capillary tube plus half the thickness of the wall). Thus: h_annular = (2 * 71.97 * cos?) / (1000 * 9.81 * (10^2 - 13^2)) ? 0.025 mm d) The capillary pressure for the inner capillary tube can be calculated using the equation: P = 2? cos? / r1 where P is the capillary pressure. Plugging in the given values, we get: P_inner = (2 * 71.97 * cos?) / 6.5 ? 22.13 atm Similarly, the capillary pressure for the annular space can be calculated using the equation: P = 2? cos? / (r2 - r1) Plugging in the values, we get: P_annular = (2 * 71.97 * cos?) / 6.5 ? 7.38 atm