Question 2.6: The Capillary Rise of Water in a Tube A 0.6-mm-diameter gla...
The Capillary Rise of Water in a Tube
A 0.6-mm-diameter glass tube is inserted into water at 20°C in a cup. Determine the capillary rise of water in the tube (Fig. 2–39).
The rise of water in a slender tube as a result of the capillary effect is to be determined.
Assumptions 1 There are no impurities in the water and no contamination on the surfaces of the glass tube. 2 The experiment is conducted in atmospheric air.
Properties The surface tension of water at 20°C is 0.073 N/m (Table 2–4). The contact angle of water with glass is approximately 0° (from preceding text). We take the density of liquid water to be 1000 kg/m³.
Analysis The capillary rise is determined directly from Eq. 2–42 by substituting the given values, yielding
h = \frac{2\sigma _s}{\rho gR}\cos \phi = \frac{2(0.073 N/m)}{(1000 kg/m^3)(9.81 m/s^2)(0.3 \times 10^{-3} m)} (\cos 0°)\left(\frac{1 kg.m/s^2}{1 N} \right)
= 0.050 m = 5.0 cm
Therefore, water rises in the tube 5 cm above the liquid level in the cup.
Discussion Note that if the tube diameter were 1 cm, the capillary rise would be 0.3 mm, which is hardly noticeable to the eye. Actually, the capillary rise in a large- diameter tube occurs only at the rim. The center does not rise at all. Therefore, the capillary effect can be ignored for large-diameter tubes.
TABLE 2–4
Surface tension of some fluids in air at 1 atm and 20°C (unless otherwise stated)
| Fluid | Surface Tension \sigma _s, N/m |
| †Water: | |
| 0°C | 0.076 |
| 20°C | 0.073 |
| 100°C | 0.059 |
| 300°C | 0.014 |
| Glycerin | 0.063 |
| SAE 30 oil | 0.035 |
| Mercury | 0.440 |
| Ethyl alcohol | 0.023 |
| Blood, 37°C | 0.058 |
| Gasoline | 0.022 |
| Ammonia | 0.021 |
| Soap solution | 0.025 |
| Kerosene | 0.028 |
† See Appendices for more precise data for water.