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Question

Air is blown through a pipe AB at a rate of 15 litres/min. The cross-sectional area of the broad portion of the pipe AB is 2 cm2 and that of the narrow portion is 0.5 cm2. The difference in water level h is (density of air 1.32 kg/m3)


A
16 mm
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B
1.5 mm
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C
10 mm
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D
3.2 mm
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Solution

The correct option is B 1.5 mm
Volume flow rate of air is given as
Q=15 litres/min.=250 cm3/s

Now, Q=A1V1=A2V2

250=2 V1 V1=125 cm/s=1.25 m/s

And, 250=0.5×V2 V2=500 cm/s=5 m/s
For a fluid flowing through a horizontal pipe,
difference in pressure = difference in kinetic energy

ΔPρa=12(V22V21)

hρwgρa=12(V22V21)

h=ρa(V22V21)2ρwg

=1.32×(521.252)2×103×10

=1.54×103 m=1.5 mm

Hence, (B) is the correct answer.
Why this Q?
With the help of venturimeter we can measure flow speed in a pipe of non-uniform cross-section.

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