$(5$ marks$)$ A village with a need for a simple irrigation system proposes to have a collection pool for rain water and then a simple human$-$powered pump mounted to a stationary bicycle frame to deliver the water to crops during dry times. If the required lift is $2\mathrm{.}5m$ as shown in the sketch and the total loss in the line is $1\mathrm{.}8m,$ determine what flow rate, in liters per minute, is possible with a person producing $125W$ by pedaling, assuming the pumping station to be $65$ percent efficient.