Parallel Pipelines

Two water mains take separate routes from a common off$-$take on a major water trunk line $($location A$)$ through to a single connection point for a new network of sub$-$mains $($location B$)$ as shown in the figure below.$$ Details of the pipelines are provided in the table below.

Details of the two pipelines in the parallel system

Pipe $1$

Length $($m$)=1190$

Material $=$ HDPE

Diameter $($mm$)=312\mathrm{.}1$

sigma K $=4\mathrm{.}2$

Pipe $2$

Length $($m$)=440$

Material $=$ HDPE

Diameter $($mm$)=219\mathrm{.}95$

sigma K $=6$

For a discharge of $253$ l$/$s$,$ determine:

$$the head loss between the common off$-$take and the single connection point using the Moody diagram and the Darcy$-$Weisbach equation; and

$$ determine the discharges in each of the pipes.

$$

Complete two iterations of the solution process and identify the final continuity error. $$Provide a justification of whether or not further iterations are required to close on a solution.

Enter your calculated head loss with $3$ significant figures and units of metres