Using the Newton method and appropriate computer software, analyze the pipe network in Figure

P$4\mathrm{.}4\mathrm{.}13$ if $H_A=190ft,H_E=160ft,H_G=200ft,Q_B=6\mathrm{.}0cfs,Q_C=6\mathrm{.}0cfs,Q_D=6cfs,$

and $Q_F=12\mathrm{.}0cfs.$ Suppose the $K=1\mathrm{.}0s\frac{e{c}^2}{f{t}^5}$ for pipes $1\mathrm{.}7,$ and $8$ and $3\mathrm{.}0s\frac{e{c}^2}{f{t}^5}$ for the

other pipes. Use initial estimates of $Q_1=10cfs,Q_2=1\mathrm{.}0cfs,Q_3=2\mathrm{.}0cfs,Q_4=1\mathrm{.}0cfs,$

$Q_5=10cfs,Q_6=4\mathrm{.}0cfs,Q_7=10\mathrm{.}0cfs,$ and $Q_8=10\mathrm{.}0cfs.$