$1-$ A $100m$ long pipe is used to fill a water tank at the far end of a land from the main water pipe in the front of the land. The pressure at the main water pipe is $250$kPa. If the pipe diameter is $D=5\mathrm{.}0cm$ and its inner roughness is $=0\mathrm{.}2mm$ find the flow rate into the tank when the water surface in the tank is $5m$ above the main water pipe. $(15$ points$)$

Ignore the minor losses. Assume density of water is $=1000k\frac{g}{m^3}$ and dynamic viscosity of water is $={10}^{-3}N.\frac{s}{m^2}.$