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Question

An incompressible liquid is flowing through the horizontal pipe as shown in the figure. Pipe 1 is connected to the pipe 2 and pipe 3. The flow of liquid through the pipe 1, pipe 2 and pipe 3 are 8 m/s,6 m/s and 1.1 m/s respectively. If cross-section area of pipe 1 and pipe 2 are 1 m2 and 0.8 m2, find the area of cross-section of pipe 3.


A
5.8 m2
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B
4.6 m2
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C
16.5 m2
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D
2.9 m2
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Solution

The correct option is D 2.9 m2
Given, speed of liquid through pipe
v1=8 m/s,v2=6 m/s,v3=1.1 m/s.
Area of cross-section of pipe 1 and 2 are
A1=1 m2,A2=0.8 m2
Let area of cross-section of pipe 3 is A3
By the equation of continuity,
A1v1=A2v2+A3v3
1×8=0.8×6+A3×1.1
A3=2.9 m2

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