Mechanical Properties of Fluids

Question : 30

Total: 31

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 7.3×10–2Nm–1. Take the angle of contact to be zero and density of water to be 1.0×103kgm–3(g=9.8ms–2).

Solution:

Here, T=7.3×10−2 N m−1;
ρ=1.0×103 kg m−3;θ=0°
For narrow tube 2r1=3.00‌mm=3×10−3m or r1=1.5×10−3m
For wider tube, 2r2=6.00‌mm=6×10−3m or r2=3×10−3m
Let h1,h2 be the heights to which water rises in narrow tube and wider tube respectively
Then, h1=

2T‌cos‌θ

r1ρg

and h2=

2T‌cos‌θ

r2ρg

∴ Difference in levels of water in two limbs of U tube is,
h1−h2=

2T‌cos‌θ

ρg

[

−

]

2×7.3×10−2×cos‌0°

103×9.8

×[

1.5×10−3

−

3×10−3

]

=4.97×10−3m.

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