Question $1(5$ points$)$

Water flows through the piping system shown above $($D $=200$ mm$,$ L$1=9$ m$,$ L$2=3\mathrm{.}0$ m$,$ and L$3=1\mathrm{.}5$ m$)$ at a volumetric flow rate of $0\mathrm{.}202$ m$3/$s$.$ It enters the system inside the pipe at A and exits to the atmosphere at C$.$The gage pressure at$$A$$has dipped to only$3700$ Pa$,$ meaning a pump had to be installed as shown to help push the flow through the system and out at C$.$

The gate valve at$$B is fully open, and the elbows are all regular$90$ 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 kW$.$ 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 $0\mathrm{.}5\%,$ so make sure to carry plenty of decimals in your calculations.