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Question

Water flows through a vertical tube of variable cross section. The area of cross - section at A and B are 6 mm2 and 3 mm2 respectively. If 12 cm3 of water enters per second through A, find the pressure difference |PAPB|. The separation between the cross-section at A and B is 100 cm. (Take density of water as 1000 kg/m3 and g=10 m/s2)


A
7000 N/m2
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B
3000 N/m2
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C
6000 N/m2
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D
4000 N/m2
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Solution

The correct option is D 4000 N/m2
Given area AA=6 mm2
area AB=3 mm2
Given, discharge, Q=AAVA=ABVB=12 cm3/sec
VA=12×106AA=12×1066×106=2 m/s
VB=12×106AB=12×1063×106=4 m/s
Applying Bernoulli's theorem between A and B, we get
PA+ρghA+12ρV2A=PB+ρghB+12ρV2B
PAPB=12ρ(V2BV2A)+ρg(hBhA)
PAPB=12×1000×(4222)+103×10×(100100)
PAPB=4000 N/m2
|PAPB|=4000 N/m2

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