Applied Hydraulics #$4\mathrm{.}4\mathrm{.}1.$

The total discharge from $A$ to $B$ in Figure $P4\mathrm{.}4\mathrm{.}1$ is $0\mathrm{.}936\frac{m^3}{s}.$ Pipe $1$ is $100m$ long with a diameter of $40cm,$ and pipe $2$ is $100m$ long with a diameter of $50cm.$ Determine the head loss between A and $B($junctions$)$ and the flow rate in each pipe using $($a$)$ Hardy$-$Cross principles and $($b$)$ the method of equivalent pipes. Assume $e_1=2\mathrm{.}0mm$ and $e_2=1\mathrm{.}25mm$ for the highly tuberculated pipes, $20C$ water, and minor losses are negligible.