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Question: Water is flowing through a tube of non-uniform cross-section ratio of the radius at entry and exit e...

Water is flowing through a tube of non-uniform cross-section ratio of the radius at entry and exit end of the pipe is 3 : 2. Then the ratio of velocities at entry and exit of liquid is

A

4 : 9

B

9 : 4

C

8 : 27

D

1 : 1

Answer

4 : 9

Explanation

Solution

If velocities of water at entry and exit points are v1 and v2, then according to equation of continuity,

v1v2=A2A1=(r2r1)2=(23)2=49\frac { v _ { 1 } } { v _ { 2 } } = \frac { A _ { 2 } } { A _ { 1 } } = \left( \frac { r _ { 2 } } { r _ { 1 } } \right) ^ { 2 } = \left( \frac { 2 } { 3 } \right) ^ { 2 } = \frac { 4 } { 9 }