A process pump is used to keep a discharge tank completely full. The relevant parts of the system are shown in the figure. It is estimated that a minimum of $20$ gpm of flow is required to keep the tank full to the overflow discharge line.

Characteristics: $$ The fluid is water at an average temperature of $120$F

$$ The suction tank fluid level may vary approximately $5$ feet from the MIN to MAX fluid height.

$$ The elevation change from the MAX fluid height to the process pump is $35$ feet.

$$ The elevation change from the MAX fluid height to the highest piping point $($labelled $3)$ is $50$ feet.

$$ The elevation change from the discharge point $($labelled $4)$ to the highest piping point is $5$ feet.

$$ The elevation change from the discharge tank fluid level to the discharge point is $3$ feet.

$$ The elevation of the return line exit and the MAX fluid height are the same.

$$ The suction line has a pipe length of $55$ feet and the shown number of elbows

$$ Pipe length of the discharge line is $45$ feet and the shown number of elbows

$$ Pipe length of the return line is $35$ feet and the shown number of elbows

$$ The open$-$air suction and discharge tank volumes are $100,000$ liters and $50,000$ liters, respectively

$$ All pipe entrances and exits are sharp

$$ All pipes are $3-$inch standard schedule $40$ galvanized steel pipe

$$ All elbow K$-$values are considered to be $1\mathrm{.}4$

$$ The performance of process pump at $1750$ rpm used is shown in the figure.

Find: $1.$ Determine the system resistance curve of the pump$/$piping system under steady$-$state conditions.

$2.$ Rewrite the expression in $(1)$ when Q is given in $[$gpm$].$