Problem #$2(50$ point$)$:

Water is to be pumped through $1400$ ft of pipe from the lower to upper reservoir at a rate of $4f\frac{t^3}{s},$ as shown in Figure below. The pipe is cast iron of diameter $8$ inch $.$ The pump is $80\%$ efficient.

$($a$)$ Find the velocity and Reynolds number of flow through pipe.

$($b$)$ Find the head loss due to friction, $h_i$ in ft $.$ Neglect minor losses.

$($c$)$ Compute the pump head, $h_p$ in ft and the pump power needed, $P_{\text{p}\text{u}\text{m}\text{p}}$ in horse power $($hp$).$

Given: Density of water, ${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=1\mathrm{.}94$ slug$/$ft ${?}^3$; Viscosity of water, $=2\mathrm{.}05{10}^{-5}$ slug$/$ft$.$s; Friction factor from Moody Chart, $f=0\mathrm{.}021.$

Draw sketch and show all calculations.