Question $4($Marks $\backslash (30=20+10\backslash ))$

The $11\mathrm{.}25-$in impeller option of the Taco Model $4013$ FI Series centrifugal pump is used to pump water at $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ from a reservoir whose surface is $4\mathrm{.}0$ ft above the centerline of the pump inlet. The piping system from the reservoir to the pump consists of $10\mathrm{.}5$ ft of cast iron pipe with an ID of $4\mathrm{.}0$ in and an average inner roughness height of $0\mathrm{.}02$ in $.$ There are several minor losses: a sharp$-$edged inlet $(\backslash ($ K$\_\{$L$\}=0\mathrm{.}5\backslash )),$ three flanged smooth $\backslash (90^\{\backslash$circ$\}\backslash )$ regular elbows $(\backslash ($ K$\_\{$L$\}=0\mathrm{.}3\backslash )$ each$),$ and a fully open flanged globe valve $(\backslash ($ K$\_\{$L$\}=6\mathrm{.}0\backslash )).$

a$)$ Estimate the maximum volume flow rate $($in units of gpm$)$ that can be pumped without cavitation.

b$)$ If the water were warmer, would this maximum flow rate increase or decrease? Why?