Two open tanks $($ A and B $)$ are connected by a $1000$ m pipe with a constant diameter of $0\mathrm{.}2$ m $.$ The pipe flow rate in the pipe is $0\mathrm{.}8\frac{m^3}{s},$ and the pipe material is cast$-$iron $($friction factor $0\mathrm{.}0004$ in $).$ The elevations of the Tank A and Tank B are $32\mathrm{.}2$ m and $51\mathrm{.}5$ m $,$ respectively. Minor head losses are negligible. A pump is installed to deliver water from Tank A to Tank B$.$ What is the equation for the system curve?

$h_p=83\mathrm{.}7+103\mathrm{.}3Q^2$

$h_p=19\mathrm{.}3+103\mathrm{.}3Q^2$

$h_p=19\mathrm{.}3+195\mathrm{.}3Q^2$

$h_p=83\mathrm{.}7+195\mathrm{.}3Q^2$