$2.$ A piping system connecting two large open water tanks is shown below. The pipeline characteristics and friction coefficients are provided in the following table. Determine $($a$)$ the flow rate in each pipe of the piping system $(\backslash (\backslash$mathrm$\{$Q$\}\_\{\backslash$mathrm$\{$A$\}\},\backslash$mathrm$\{$Q$\}\_\{\backslash$mathrm$\{$B$\}\}\backslash ),$ and $\backslash (\backslash$mathrm$\{$Q$\}\_\{\backslash$mathrm$\{$C$\}\}\backslash )),($b$)$ the head loss in pipe A $,$ and $($c$)$ the pressure at the junction J$.($Neglect minor head losses.$)$

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|$l$|\}$

$\backslash$hline Pipe & $\backslash$begin$\{$tabular$\}\{$l$\}$

Diameter $\backslash \backslash$

$\backslash ((\backslash$mathrm$\{$ft$\})\backslash )$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Length $\backslash \backslash$

$\backslash ((\backslash$mathrm$\{$ft$\})\backslash )$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Area $\backslash \backslash$

$\backslash (\backslash$left$(\backslash$mathrm$\{$ft$\}^\{2\}\backslash$right$)\backslash )$

$\backslash$end$\{$tabular$\}$ & f $\backslash \backslash$

$\backslash$hline A & $0\mathrm{.}833$ & $1200$ & $0\mathrm{.}541$ & $0\mathrm{.}022\backslash \backslash$

$\backslash$hline B & $0\mathrm{.}667$ & $1500$ & $0\mathrm{.}353$ & $0\mathrm{.}028\backslash \backslash$

$\backslash$hline C & $1$ & $1000$ & $0\mathrm{.}785$ & $0\mathrm{.}025\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$