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Question: Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line. The velocity of ...

Two water pipes of diameters 2 cm and 4 cm are connected with the main supply line. The velocity of flow of water in the pipe of 2 cm diameter is

A

4 times that in the other pipe

B

14\frac { 1 } { 4 }times that in the other pipe

C

2 times that in the other pipe

D

12\frac { 1 } { 2 }times that in the other pipe

Answer

4 times that in the other pipe

Explanation

Solution

dA=2 cmd _ { A } = 2 \mathrm {~cm} and dB=4 cmd _ { B } = 4 \mathrm {~cm}

rB=2 cmr _ { B } = 2 \mathrm {~cm}

From equation of continuity av = constant

∴ vAvB=aBaA=π(rB)2π(rA)2=(21)2⇒vA=4vB\frac { v _ { A } } { v _ { B } } = \frac { a _ { B } } { a _ { A } } = \frac { \pi \left( r _ { B } \right) ^ { 2 } } { \pi \left( r _ { A } \right) ^ { 2 } } = \left( \frac { 2 } { 1 } \right) ^ { 2 } \Rightarrow v _ { A } = 4 v _ { B }