Explanation

(c) 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.
$ie,\ \ \ m_{1} = m_{2}$
$\Longrightarrow \ \ \ \rho_{1}A_{1}v_{1} = \rho_{2}A_{2}v_{2}$
[image:10_image84.emf]
$Given\ \ \rho_{1} = \rho_{2}\ \ A_{2} = \frac{A_{1}}{2}$
$\therefore\ \ \ A_{1}v_{1} = \frac{A_{1}}{2}v_{2}$
$\Longrightarrow \ \ \ v_{2} = 2v_{1}$