Problem $1(100$ points$)$

The cylindrical tank with dimension diameter $D_1=3m$ and $H$ is providing water via a cylindrical tube with dimensions $D_2=0\mathrm{.}06m$ and $L=0\mathrm{.}25m.$ Known that the gravity acceleration $g=9\mathrm{.}8\frac{m}{s^2}$ the density is $=1000k\frac{g}{m^3}$ the dynamic viscositv is $8\mathrm{.}9{10}^{-4}Pa*s.$

$(1)$ Known that the Darcy's friction coefficient is $f=0\mathrm{.}025,$ the roughness factor $lon=0\mathrm{.}00015.$ Get the Reynolds number of the water in the tube from the experimental Colebrook equation

$f=\frac{64}{Re}$ Laminar

$\frac{1}{\sqrt[\phantom{2}]{f}}=-2log[\frac{2\mathrm{.}51}{Re\sqrt[\phantom{2}]{f}}+\frac{lo\frac{n}{D}}{3\mathrm{.}72}]$ Turbulent

$(2)$ Get the major energy loss head of the tube.

$(3)$ Get the height $H$ via ignoring the major loss of the tank and all minor losses.