Heavy machine oil $(($:$sg=0\mathrm{.}89,=3\mathrm{.}80{10}^{-2}(Pa)*s\}$ is circulated through a system repeatedly to test its stability.

The $8-$inch Schedule steel pipe on the suction side of the pump has a square entrance and a length of $6\mathrm{.}25m^{-}$and the $3\mathrm{.}5-$inch Schedule steel pipe on the discharge side of the pump has a length of $18\mathrm{.}0m.$

$($Note that the $3\mathrm{.}5-$inch discharges into the atmosphere above the tank so there is no exit loss in this question!$)$ All elbows are long radius. The flow rate through the system is $13\mathrm{.}5\frac{L}{s}.$

Determine the head added by the pump.