A self$-$priming centrifugal pump is used to pump water at $)=7\mathrm{.}9910-4(Pa).s,P_v=(3\mathrm{.}17$kPa from a reservoir whose surface is $2\mathrm{.}2m$ above the centerline of the pump inlet. The pipe is made of PVC with an internal diameter $($ID$)$ of $24\mathrm{.}0mm$ with smooth surface roughness. The pipe length from the reservoir to the pump inlet is $2\mathrm{.}8m.$ There are only two minor losses in the piping system from the reservoir to the pump inlet which are a sharp$-$edged reentrant inlet $)=(0\mathrm{.}85$ and a flanged smooth $90$ regular elbow $)=(0\mathrm{.}3.$ The pump's required net positive suction head is provided by the manufacturer as a curve fit:

$NPS{H}_R=2\mathrm{.}2m+(0\mathrm{.}0013\frac{m}{L}p{m}^2)Q^2$

where the volumetric flow rate is measured in Lpm $($liter per minute$)$

$($Hint: construct both NPSH curves $-$ H vs Q$)$ using excel$)$

Estimate the maximum volume flow rate $($in Lpm $-$ liter per minute$)$ that can be pumped without cavitation.