Question $2(10$ points$)$

Water flows through the piping system shown above $(\backslash ($ D$=200\backslash$mathrm$\{$~mm$\},$ L$\_\{1\}=9\backslash$mathrm$\{$~m$\},$ L$\_\{2\}=\backslash )3\mathrm{.}1$ m $,$ and $\backslash (\backslash$left$.$L$\_\{3\}=1\mathrm{.}5\backslash$mathrm$\{$~m$\}\backslash$right$)\backslash )$ at a volumetric flow rate of $\backslash (0\mathrm{.}230\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$ It enters the system inside the pipe at $\backslash ($ A $\backslash )$ and exits to the atmosphere at $\backslash ($ C $\backslash ).$ The gage pressure at $\backslash ($ A $\backslash )$ has dipped to only $4500$ Pa $,$ meaning a pump had to be installed as shown to help push the flow through the system and out at $\backslash ($ C $\backslash ).$

The gate valve at $\backslash ($ B $\backslash )$ is fully open, and the elbows are all regular $\backslash (90^\{\backslash$circ$\}\backslash )$ elbows. All fittings are flanged, there are no entrance or exit effects for the system, and the diameter can be treated as $8$ inches for the purposes of reading the minor losses chart $($for your other calculations, use $200$ mm $).$

Based on this information and that provided in the diagram, determine the power the pump puts into the system in $\backslash ($ k W $\backslash ).$ Use the friction factor equation given since coding a value into ilearn prohibited the use of approximate values from reading the Moody Chart $($you will still need to read the Moody Chart on exams$).$

The tolerance on this problem is only $\backslash (0\mathrm{.}5\backslash \%\backslash ),$ so make sure to carry plenty of decimals in your calculations.