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Question

Water flows along a horizontal pipe of non-uniform cross-section. The pressure is 1 cm of Hg where the velocity is 35 cm/s. At a point where the velocity is 65 cm/s, the pressure will be

A
0.89 cm of Hg
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B
0.62 cm of Hg
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C
0.5 cm of Hg
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D
1 cm of Hg
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Solution

The correct option is A 0.89 cm of Hg
Applying the Bernoulli's equation between given points,
p1+12ρv21=p2+12ρv22 ...(i)
p1=ρHggh=13600×1×(10)2×10 N/m2
v1=35×102 m/s
v2=65×102 m/s
Since pipe is horizontal (constant elevation), hence the potential energy terms will cancel out from both sides.

From Eq.(i),
(13.6×103×10×102)+12×103×(0.35)2=p2+12×103×(0.65)2
p2=1210 N/m2
Hence, corresponding reading of mercury column,
h=p2ρHgg
h=121013.6×103×10
h=8.89×103 m
h=0.89 cm of Hg

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