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Question -

Two narrow bores of diameters 3.0 mm and 6.0 mm are joinedtogether to form a U-tube open at both ends. If the U-tube contains water, whatis the difference in its levels in the two limbs of the tube? Surface tensionof 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 kgm–3 (g = 9.8 m s–2).



Answer -

Diameter of the first bore, d1 = 3.0mm = 3 × 10–3 m

Diameter of the second bore, = 6.0 mm

Surface tension of water, s = 7.3 × 10–2 Nm–1

Angle of contact between the bore surface and water, θ=0

Density of water, ρ =1.0 × 103 kg/m–3

Acceleration due to gravity, g = 9.8 m/s2

Let h1 and hbethe heights to which water rises in the first and second tubes respectively.These heights are given by the relations:

The difference between the levels of water in the two limbs of thetube can be calculated as:

Hence, the difference between levels of water in the two bores is4.97 mm.

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