Water is transported by gravity through a $2-$cm$-$diameter, $800-$m$-$long plastic pipe with an elevation gradient of $0\mathrm{.}01($i$.$e$.$ an elevation drop of $1$ m per $100$ m of pipe length$).$ If both ends of the pipe are open to the atmosphere, determine the flow rate of water through the pipe. If the pipe were horizontal, what would be the power requirements to maintain the same flow rate?