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Question

Water flows through a horizontal tube as shown in figure. If the difference in heights of the water columns in the vertical tubes is 4 cm, and the cross-sectional area A1 and A2 are 6 cm2 and 3 cm2 respectively, find the rate of flow of water across any section.


A
306.72 cm3/s
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B
204.2 cm3/s
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C
102.48 cm3/s
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D
372.6 cm3/s
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Solution

The correct option is A 306.72 cm3/s
Rate of flow of water is the discharge Q given as,
Q=Av
From continuity equation,
A1v1=A2v2
Q=A1v1=A2v2=constant
For the given venturimeter set-up, the velocity v1 is
v1=   2gh(A1A2)21
Here, h=4 cm is the difference in heights of the water columns.
Flow rate through the tube is,
Q=A1v1
=A1×   2gh(A1A2)21
Here, g=9.8×100=980 cm/s2, and A1A2=63=2
Q=6×2×980×4221
Q=306.72 cm3/s

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