Problem #$1(50$ point$)$:

In Figure below, the pipe entrance is sharp$-$edged having $K_1=0\mathrm{.}5,$ and for the open globe valve assume $K_2=6\mathrm{.}0.$ The flow rate of water is $0\mathrm{.}016\frac{m^3}{s}.$

$($a$)$ Calculate the velocity and Reynolds number of flow in pipe.

$($b$)$ Find the head loss due to friction, $h_f($in m $).$

$($c$)$ Calculate the Turbine head $($in m $)$ and Power generated $($in Watt$).$

Given: Density of water, ${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=1000k\frac{g}{m^3}$; Viscosity of water, $=0\mathrm{.}001k\frac{g}{m}.s$; Friction factor from Moody Chart, $f=0\mathrm{.}024.$

Draw sketch and show all calculations.