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Question

Water is flowing through a horizontal tube of non-uniform cross section. At a place, the radius of the tube is 2 cm and velocity is 6 m/s. What will be the velocity of water where the radius of pipe is 4 cm?

A
6 m/s
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B
1.5 m/s
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C
3 m/s
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D
2 m/s
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Solution

The correct option is B 1.5 m/s

Let A1,V1 and A2,V2 be the area of cross section, velocity of water at inlet and outlet respectively.
Using equation of continuity.
A1V1=A2V2 ----(1)
Given,
Radius of tube at inlet (r1)=2 cm
Radius of tube at outlet (r2)=4 cm
Velocity of water at inlet (V1)=6 m/s
Area at inlet, A1=πr21
Area of cross-section at outlet, A2=πr22
From equation (1), we get
(πr21)(V1)=(πr22)(V2)
V2=r21r22×V1=(24)2×6=64 m/s=1.5 m/s

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