question_answer

    Water is flowing through a pipe of constant cross-section. At some point the pipe becomes narrow and the cross-section is halved. The speed of water is

A)  reduced to zero

B)  decreased by a factor of 2

C)  increased by a factor of 2

D)  unchanged

Correct Answer: C

Solution :

                From the equation of continuity, the amount of mass that flows past any cross-section of a pipe has to be the same as the amount of mass that flows past any other cross-section. i.e.,        \[{{m}_{1}}={{m}_{2}}\]    \[\Rightarrow \]               \[{{\rho }_{1}}{{A}_{1}}{{v}_{1}}={{\rho }_{2}}{{A}_{2}}{{v}_{2}}\] Given,   \[{{\rho }_{1}}={{\rho }_{2}},{{A}_{2}}=\frac{{{A}_{1}}}{2}\] \[\therefore \]  \[{{A}_{1}}{{v}_{1}}=\frac{{{A}_{1}}}{2}{{v}_{2}}\] \[\Rightarrow \]               \[{{v}_{2}}=2{{v}_{1}}\]