$8.$ A pipeline transporting the hot$-$water flow of a district heating system at $100\backslash$deg C at a rate of $3\mathrm{.}5$

m $3/$s branches out into two parallel pipes made of commercial steel but reconnects downstream.

Pipe A is $750$ m long and has a diameter of $50$ cm$,$ while Pipe B is $1200$ m long with a diameter

of $50$ cm$.$ Neglecting minor losses and providing appropriate assumptions, determine the

following:

$($a$)$ Flow rates $($in m $3/$s$)$ through pipe A and pipe B$.$

$($b$)$ Head losses $($in m$)$ in pipe A and pipe B