$($a$)$ From basic principles, show that; friction head loss in pipe flow system

$h_f=(\frac{10\mathrm{.}65L{Q}^{185}}{C_H^{185}{d}^{487}})$

Where;

$L-$ length of the pipe in$($m$)$

Q$-$ discharge in $\frac{m^3}{s}$

d $-$ diameter of the pipe$($m$)$

$($b$)$ Figure I.D shows a two $-$ looped pipe network. On the basis of the Darcy's $-$ Weisbach approach, analyse the network to determine the flow rate in each pipe and the direction of flow upto two trials only. Take $f=0\mathrm{.}005$ for each pipe.