$5\mathrm{.}1\mathrm{.}2.$ A pump is needed to drain water from a small pond before the earthen dam collapses. The water must be pumped over the top of the dam, which is about $2$ m above the water surface. The only pump available is an old $10$ cm diameter fan pump. The power requirement for the motor is $1000$ W$,$ and the pump and motor combination has a low efficiency of $50$ percent. How many cm will the lake drop in the initial $24$ hours if the lake surface area is $5000$ m$2?($Note: Poly friction losses and minor losses are insignificant when compared to the height of the position that the pump must overcome.$)$