Question

Two narrow bores of diameters 3-0 mm and 6.0 mm are joined together to form a U-tube open at both the ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube? (Surface tension of water at the temperature of the experiment is 72 dyne/cm. Take angle of contact to be zero and density of water to be 1.0 g/cc.)

Solution

We know water rises in the capillary tube.
Height to which water rises in the capillary tube is,

straight h equals fraction numerator 2 straight T space cos space straight theta over denominator rpg end fraction

Therefore the height h₁of the water that rises in the limb of diameter 3 mm is given by,

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The height h₂of the water that will rise in the limb of diameter 6 mm is given by,

straight h subscript 2 equals fraction numerator 2 cross times 72 cross times 1 over denominator 0.3 cross times 1 cross times 980 end fraction equals 0.49 mm

Hence difference in the levels of two limbs is,

Δh equals straight h subscript 1 minus straight h subscript 2 equals 0.98 minus 0.49 equals 0.49 mm

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