A $200$ ft high reservoir $($A$)$ is supplying water to a tank $($B$)$ through a pipeline

of variable cross$-$section as shown in figure $8($b$).$ Velocity of water in $6-$in

diameter pipe is $32\mathrm{.}1f\frac{t}{sec}.$ What will be the total length of the pipe if the head

at tank $($B$)$ has to be $20$ ft $?$ Use loss coefficient for sudden contraction, $k_c=0\mathrm{.}33.$