Question $4$

$($a$)$ A pipeline $400$ mm in diameter and $2,000m$ long connects two reservoirs whose

difference in water level is $6$ m $.$ By ignoring all losses except pipe friction determine the

discharge in the pipe if the friction factor, $f,$ is $0\mathrm{.}0075.$

$[5$ marks$]$

$($b$)$ If the lowest point in the pipeline is $10$ m below the level of the upstream reservoir and

$150$ m from it then calculate the pressure at this point.

$[5$ marks$]$

$($c$)$ In order to increase the flow in the pipeline it is decided to replace the downstream

$150$ m of the pipe with a new pipe of $550$ mm in diameter and to connect the two pipes

with a sudden expansion. Assuming that the friction factor for the larger diameter pipe

is the same as for the existing smaller one then determine the flow in the new pipeline.

Your analysis should include the loss of energy, $h_L,$ in the pipe expansion, this can be

determined using the following expression:$-$

$h_L=\frac{(u_1-u_2{)}^2}{2(g)}$

where $u_1,$ velocity in the upstream pipe

$u_2,$ velocity in the downstream pipe

$[7$ marks$]$

$($d$)$ By comparing the magnitudes of the loss of energy due to pipe friction with the loss in

the expansion indicate with reasons whether it is worth going to the expense of

designing a tapered expansion.