Factory real problem $01-$ Re$-$do

As the project engineer in a concrete block plant, you must determine the performance of a centrifugal pump for installation in a factory section. The system into which the pump will be installed consists of suction and discharge pipes of length $21$ m and $42$ m $,$ respectively; and diameters $300$ mm and $240$ mm$,$ respectively. The pump rums at $1800$ revimin and provides a total vertical lift of $12$ m $,$ and losses due to strainers and pipe bends may be neglected. The friction factor is $0\mathrm{.}009.$ The pump manufacturer supplies the following performance data:

$\backslash$table$[[Q(m^{\text{'}}sec),0,00,0,10,0,15,0,20,0,25,0,30],[H_{rcq}(m),40,37,34,29,5,24,5,17,5],[,0,68,77,76,66,45],[H_{gr}(m),12,14,07,16,66,20,29,24,95,30,65]]$

$$ Determine the system head equation for the factory:

Ting the erraph prosided, determina the potver required to ron the above pump.