Q$2)($a$)$ A $7$ inch impeller centrifugal pump has the performance characteristics shown in Fig $12\mathrm{.}12,$ shown below. The pump is used to pump water at $100$ F $,$ and its inlet is $10$ ft above the open water surface. When the flowrate is $160$ gpm the head loss between the water surface and the pump inlet is $5\mathrm{.}5$ ft of water. Would you expect cavitation in the pump to be a problem? Explain how you arrived at your answer. Assume standard atmospheric pressure.

Eigure $12\mathrm{.}12$ Performance curves for a two$-$stage centrifugal pump operating at $3500$ rpm $.$ Data given for three different impeller diameters.

$($b$)(0)$ For the pump in part $($a$)$ above, what is the head $($in ft$),$ the efficiency, the bhp $($use a standard size up$).$

$($ii$)$ If the rotational speed is reduced by $25\%,$ determine the new flowrate, head, and power?

$($ii$)$ At the reduced rotational speed, determine the new flowrate, head, and power, if the impeller diameter is reduced to $6\mathrm{.}5$ in$??$