$(35$ pts $)$ The pipe diameters below are $D=0\mathrm{.}1m$ and $d=0\mathrm{.}08m$ and the friction head loss along the entire length of the pipe is $h_{f2}=3m.$ The specific weight of water is ${}_{\text{m}\text{e}\text{s}}=9\mathrm{.}81k\frac{N}{m^3}.$

$($a$)$ Determine the flow rate through the pipe

$($b$)$ Determine the velocity in the $d=0\mathrm{.}08m$ pipe

$($c$)$ Determine the friction head loss, $h_{f1}.$

Exira Credit $(6$pts$)$: Sketch the velocity profiles for $($a$)$ laminar flow, $($b$)$ inviscid flow and $($s$)$ plus thour in :

pipe