Example $12\mathrm{.}4.$ Water is flowing in a pipe with a varying

cross$-$sectional area, and at all points the water

completely fills the pipe. At point $1$ the cross$-$sectional

area of the pipe is $0\mathrm{.}070$ m$2,$ and the magnitude of the

fluid velocity is $3\mathrm{.}50$ m$/$s$.$

$($a$)$ What is the fluid speed at points in the pipe where

the cross$-$sectional area is $0\mathrm{.}105$ m$2$

$($b$)0\mathrm{.}047$ m$2?$

$($c$)$ Calculate the volume of water discharged from the

open end of the pipe in $1$ hr$.$