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Question

Water flows through the tube shown in figure. The areas of cross section of the wide and the narrow portions of the tube are 5 cm2 and 2 cm2 respectively. The rate of flow of water through the tube is 500 cm3 s-1. Find the difference of mercury levels in the U-tube. Assume this tube lying horizontally on a table.


A

1.93 cm

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B

1.93 m

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C

2.58 cm

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D

2.58 m

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Solution

The correct option is A

1.93 cm


As clear from the sitution,
P1P2=,ρgh
h= difference in height of the mercury column.
Using Bernoulli's equation,
P1+ρgH+12V2=constant
As both the points are at the same horizontal level.
P1+12V21=P2+12V22ρ
P1P2=12[V22V22]ρ
12ρ(V22V21)=,ρgh .....(1)

From equation of continuity,
A1V1=A2V2
5V1=2V2
V2=52V1 ......(2)
also A1V1=A2V2=500cm3s
V1=100cms=1ms......(3)
from (3) &(1)
12ρ{214}=,ρgh
12×1000{214}=13600×10×h
h=0.0193m
h=1.93 cm

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