Q$2.$ The figure below represents a schematic of pipe network. A rate of $QL{s}^{-1},$ is pumped to feed two lines. The length and diameter of each pipe segment are listed in the table. The total head loss at $1$ is $27$ m above atmospheric pressure. Assume the pressures at $6$ and $10$ are atmospheric:

$($i$)$ Calculate the water flow rates at $6$ and $10,($ii$)$ the power of the pump required.

The viscosity and density of the water are respectively: $0\mathrm{.}0015$ Pa$.$s; $985k\frac{g}{m^3}.$

The loss coefficients for the fittings: $k_{2-3}=k_{2-7}=1\mathrm{.}1$;$k_{\text{e}\text{l}\text{b}\text{o}\text{w}}=1\mathrm{.}23$

Use the following expression to evaluate the friction factor with roughness ratio $(\frac{}{D}=0\mathrm{.}025)$:

$\frac{1}{\sqrt[\phantom{2}]{f}}$~$=-1\mathrm{.}8log[\frac{6\mathrm{.}9}{Re}+(\frac{\frac{8}{D}}{3\mathrm{.}7}{)}^{1\mathrm{.}11}]$

$\backslash$table$[[$Pipe section,Length $($m$),$Diameter $($cm$)],[1-2,30,40],[3-4-5-6,15,34],[7-8-9-10,25,28]]$