Design a pump and check its performance for the system below. The pumping system shown below is supposed to deliver at least $140$ GPM of water to the tank on the top of the hill. $3-$inch commercial steel pipe is used for the entire system. Both tanks are open to atmospheric pressure $(14\mathrm{.}7$ psia$),$ and water temperature is $70F.$

$($a$)$ Determine total dynamic head $($TDH$)$ operating against the pump for the design flow rate. Minor losses can be neglected for this step

$($b$)$ Use TDH and design flowrate to select an appropriate pump from the attached choices. Report the appropriate Impeller Diameter as well

$($c$)$ Determine the pump operating point, and report the following parameters for this point: capacity, TDH$,$ efficiency, power required by pump, and NPSHR

$($d$)$ Check pump conditions in terms of cavitation. For this step, use operating capacity $($found in Step c$)$ and include minor losses.