$($b$)$ A pump is installed in a $15-$em diameier, $300m$ long delivery pipeline to pamp $0\mathrm{.}060m^3/$ of water at $20$ having $f=0\mathrm{.}0219.$ The elevation difference between the lower reservoir $($sump$)$ and the upper rectiving reservoir is $2\mathrm{.}5m.$ The suction pipe has a diameter of $18cm,$ and the total head lass $($friction plus minor lasses$)$ on the suction side of the punp is $1\mathrm{.}3m.$ The pump bas Thoma cavitation parameter of of $0\mathrm{.}12.$ Detennine the maximum allowable distance between the pump inlet and the water surface elevation in the sump $($lower reservoir$).$

$(12$ Marks$)$