Question

Two narrow bores of diameters 3.0 mm and 6.0 mm are joined together to form a U-tube open at both 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 7.3 × 10–2 N m–1. Take the angle of contact to be zero and density of water to be 1.0 × 103 kg m–3 (g = 9.8 m s–2).

Answer 1

Here,
Surface tension (S) = 7.3 × 10^-2 N/m
Density of water ( d) = 10³ kg/m³
Acceleration due to gravity (g) = 9.8m/s²
radius of one side ( r1) = 3× 10^-3/2 = 1.5 × 10^-3m
Radius of other side ( r2) = 6× 10^-3/2 = 3 × 10^-3 m

Height of water column rises in first tube ( h1) = 2Scos∅/r1dg
Height of water column rises in 2nd tube ( h2) = 2Scos∅/r2dg

Difference in level of water rises in both tubes = h1 - h2
∆h = 2Scos∅/r1dg - 2Scos∅/r2dg
= 2Scos∅/dg { 1/r1 - 1/r2}
= 2 × 7.3 × 10^-2 × cos0°/10³×9.8 { 1/1.5 × 10^-3 - 1/3 × 10^-3 }
= 14.6/9.8 × 10^-2 [ 2/3 - 1/3 ]
= 14.6 × 10^-2/9.8 × 3
= 4.965 × 10^-3 or 4.965 mm

Answer 2

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