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Question

A fluid while flowing through a tube as shown passes through points A and B. Find the velocity of the fluid at point B.


A
415 m/s
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B
115 m/s
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C
215 m/s
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D
815 m/s
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Solution

The correct option is D 815 m/s
According to question

On applying equation of continuity at point 1 and 2,
A1v1=A2v2
v1=A2v2A1=2×v24
v1=v22.........(1)
On applying bernoulli's equation at point 1 and 2,
P1+ρgh1+12ρv21=P2+ρgh2+12ρv22
Since height is same at both the points.
P1P2=12ρ(v22v21)
P1P2=12ρ(v22v224) [ from (1) ]
P1P2=38ρv22............(2)
Also, P1P2=ρgho
[ Pressure difference in column ]
P1P2=ρg×0.02 [ho=2 cm=0.02 m]
P1P2=15ρ..........(3)
From (2) and (3),
38ρv22=15ρ
v2=815 m/s
Speed of water at point B is 815 m/s

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