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Question

Water flows through a horizontal tube as shown in figure. If the difference of heights of water column in the vertical tubes is 4 cm, and the cross-sectional area A1 and A2 are 4 cm2 and 2 cm2 respectively, find the rate of flow of water across any section.
Take g=9.8 m/s2, 2613.33=51.12 for calculation.


A
122.43 cm3/s
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B
204.48 cm3/s
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C
298.6 cm3/s
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D
302.2 cm3/s
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Solution

The correct option is B 204.48 cm3/s
For a venturimeter, velocity of liquid is given as
v1=   2gh(A1A2)21
Where, h=4 cm is difference in height of liquid columns in the vertical tubes
A1=4 cm2
A2=2 cm2
v1 is the velocity of the liquid through larger cross-section.

Discharge of the liquid is given as
Q=A1v1
Q1=A1×   2gh(A1A2)21
Q1=4×2×980×4221
g=9.8×100=980 cm/s2
Q1=4×2613.33
Q1=4×51.12=204.48 cm3/s
Hence, the rate of flow of water is 204.48 cm3/s

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