Question $2$: Pipe Network Analysis and Water Supply Case Study $($Total $30$ marks$)$

a$.$ Calculate the head losses and the corrected flows in the various pipes of a water reticulation

system as shown below, where head loss is given by $h_L$ or $h_f=r{Q}^n.$ The diameter and the lengths

of the pipes used are given against each pipe. Compute the corrected flows using Hardy$-$Cross

method. Use Darcy$-$Weisbach formula to determine the head loss per unit flow and assume $n=2$

and $f=0\mathrm{.}02.$ Initial assumed flows $(\frac{L}{s})$ are $AB=45,AD=35,BC=23,CD=20,CF=28,EF=$

$4,$ and $DE=5.$

Note: Go up to $2$ iterations and draw the pipe flow diagrams $($for $2$ iterations$)$ with corrected flows

directions & quantities.