Question

TO what height does a liquid of density 0.4 into 10 raise to power 3 kg m/ cube and surface tension 0.05 N/m rise in a capillary tube of radius 0.2 mm when dipped in (given cos@=0.4 , g=10 m /s square)

Answer 1

TO what height does a liquid of density 0.4 into 10 raise to power $3\,\mathrm{kg}\,\mathrm{m}/\mathrm{cube}$ and surface tension $0.05\,\mathrm{N/m}$ rise in a capillary tube of radius $0.2\,\mathrm{mm}$ when dipped in (given $\cos \gamma = 0.4$, $g=10\,\mathrm{m/s}$ square)

Solution

The capillary force is in equilibrium with the gravitational force:

$$2 \pi r \sigma \cos \gamma = \pi r ^ {2} h g \rho ,$$

where $r$ - radius of tube, $\sigma$ - surface tension, $\gamma$ - contact angle, $h$ - height of liquid, $g$ - acceleration of gravity, $\rho$ - density of liquid.

The height of liquid

$$h = \frac {2 \sigma \cos \gamma}{g \rho r} = \frac {2 * 0 . 0 5 \frac {\mathrm {N}}{\mathrm {m}} * 0 . 4}{1 0 \frac {\mathrm {m}}{\mathrm {s} ^ {2}} * 0 . 4 * 1 0 ^ {3} \frac {k g}{m ^ {3}} * 0 . 2 * 1 0 ^ {- 3} m} = 0. 0 5 m.$$

Answer: 0.05 m.