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Question

An open capillary tube contains a drop of water. When the tube is in its vertical position, the drop forms a column with a length of 2cm. The internal diameter of the capillary tube is 1mm. Determine the radii of curvature of the upper and lower meniscus in each case. Consider the wetting to be complete. Surface tension of water =0.0075N/m
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Solution

When capillary is in vertical position, thge upper meniscus is concave and pressure due to surface tension

Ps=2TR1

is directed vertically upward, R1 being radius of curvature of upper
meniscus. When wetting is complete

P1=2Tr

r being radius of the capillary tube =D2=12mm

R1=r=0.5mm in each case.

We have P1=2Tr=2×75×1030.5×103=300N/m2

The hydrostatic pressure P2=hρg is always directed downwards.

At h=2cm

P2=hρg=2×102×10×103=200N/m2

Clearly P1>P2. That is resulting pressure is directed upward. For
equilibrium, the pressure due to lower meniscus should be downward. This
makes the lower meniscus concave downwards. Then,

P1P2=2TR2

300200=2×75×103R2

R2=2×75×103100=1.50×103m=1.50mm

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