The Latin word capilla means hair. A tube of very fine (hair-like) bore is called a capillary tube.
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When a capillary tube of glass open at both ends is dipped in liquid which wets its walls (e.g., water, alcohol), the liquid rises in the tube. But when the capillary tube is dipped in a liquid which does not wet its walls (e.g., mercury), the level of liquid is depressed in the tube.
The phenomenon of rise or fall of a liquid in a capillary tube in comparison to the surrounding is called capillarity.
Some examples of capillarity from daily life:
(i) A blotting paper soaks ink by capillary action. The pores of blotting paper act as capillaries.
(ii) Oil rises in the long narrow spaces between the threads of a wick, the narrow spaces act as capillary tubes.
Numerical Problems Based on Capillarity and Ascent Formula
Q.1. A capillary tube of inner diameter 0.5 mm is dipped in a liquid of specific gravity 13.6, surface tension 545 dyne cm-1 and angle of contact 130°. Find the depression or elevation in the tube.
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Answer: – 2.1cmQ.2. A tube of 1 mm bore is dipped into a vessel containing a liquid of density p= 800 kg/m3 and of surface tension, σ = 49×10-3N/m and angle of contact, θ = 0°. The tube is held inclined to the vertical at an angle of 60°, find the height to which the liquid can rise and the length which the liquid will occupy in the tube.
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Answer: 5 cmQ.3. Calculate the diameter of a capillary tube in which mercury is depressed by 1.21 cm. Given surface tension for mercury is 540 × 10-3 Nm-1, the angle of contact with glass is 140° and density of mercury is 13.6 × 103 kg m-3.
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Answer: 1.026 × 10-3mQ.4. The radius of a capillary tube is 0.025 mm. It is held vertically in a liquid whose density is 0.8 × 103kg m-3, surface tension is 3.0 × 10-2 Nm-1 and for which the cosine of the angle of contact is 0.3. Determine the height up to which the liquid will rise in the tube. Given g = 10 ms-2.
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Answer: 9 cmQ.5. The tube of mercury barometer is 5 mm in diameter. How much error does the surface tension cause in the reading? S.T. of mercury = 540 × 10-3 Nm-1. Angle of contact = 135°.
