I. Consider the hydraulic system carrying $\backslash (1\mathrm{.}5\backslash$mathrm$\{$l$\}/\backslash$mathrm$\{$s$\}\backslash )$ of hot oil with a pump as shown opposite. Pipes are $\backslash (1^\{13/2\}\backslash )$ commercial steel $($schedule $40).$ Between $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash ),$ the pipe total length is of $50$ m and the elevation variation is of $25$ m $.$ The circuit consists of pipes, a swing check valve, two $\backslash (90^\{\backslash$circ$\}\backslash )$ bends of short radius, a gate valve and a discharge tank. All valves are fully open. The oil specific gravity SG is of $0\mathrm{.}863$ and the dynamic viscosity $\backslash (\backslash$mu$\_\{\backslash$mathrm$\{$c$\}\}\backslash )$ is of $46\mathrm{.}4$ cP $.$ Pipe dimensions and the fittings characteristics are given in appendix.

$1.$ What is the regime of the flow in this circuit?

$2.$ Determine all the head losses and give the results as indicated in the following table. Justify your results.

$3.$ Determine in bar the value of the gauge pressure at $\backslash ($ A P$\_\{$L$\}\backslash )$ :

$4.$ Calculate the required power on the pump shaft. Assume a pump efficiency of $\backslash (65\backslash \%\backslash ).$

$5.$ Calculate the annual energy consumption for $24$ h operation.