Applied Hydraulics #$3\mathrm{.}12\mathrm{.}6.$

Pipes $AB$ and $CF$ in the Figure $P3\mathrm{.}12\mathrm{.}6$ have a diameter of $3m$ and Darcy$-$Weisbach friction factor of $0\mathrm{.}02.$ The length of $AB$ is $1,000m$ and that of $CF$ is $900m.$ The discharge in pipe $AB$ is $60\frac{m^3}{s}.$ Branch $1$ is $1,000m$ long, has a diameter of $2m,$ and a friction factor of $0\mathrm{.}018.$ Branch $2$ has a length of $800m,$ a diameter of $3m,$ and a friction factor of $0\mathrm{.}02.$ A discharge of $20\frac{m^3}{s}$ is added to the flow at point $B$ and $10\frac{m^3}{s}$ is taken out at point $C$ as shown in the figure. $($a$)$ Determine the total head loss due to friction between section A and $F$ and $($b$)$ determine the discharge in each of branches $1$ and $2.$